ARMY MEDICAL LIBRARY FOUNDED 1836 WASHINGTON. D.C. fd ELEMENTS OF PHYSICS JTATURAL PHILOSOPHY, GENERAL AND MEDICAL: WRITTEN FOR UNIVERSAL USE, PLAIN OR NON-TECHNICAL LANGUAGE; AND CONTAINING NEW DISQUISITIONS AND PRACTICAL SUGGESTIONS. COMPRISED IN FIVE PARTS, h SOMATOLOGY, STATICS j 3. PNEUMATICS, HYDUAU- AND DYNAMICS. i LICS AND ACOUSTICS. 2. MECHANICS. I 4. HEAT AND LIGHT. 5. ANIMAL AND MEDICAL PHYSICS. COMPLETE IN ONE VOLUME. BY NEILL AENOTT, M.D., OF THE ROYAL fcoftjEOE OF PHYSICIANS. A NEW EDITION, REVISED AND CORRECTED FROM THE LAST ENGLISH EDITION. WITH ADDITIONS, BY ISAAC HAYS, M. D. /^T^TVV PHILADELPHIA: LEA AND BLANC HARD 1848. F t; hi 1,1.e. #■" \ ele Entered according to the Act of Congress, in the year 1841, by LEA AND BLANCHARD, in the Clerk's Office of the District C ourt of the United States, in and for the Eastern District of Pennsylvania. j ADVERTISEMENT OF TI1F AMERICAN PUBLISHERS. The very valuable and popular work of Dr. Arnott has passed through several editions in this country, in the form.in which it was originally published by the author, in separate parts. A new edition being now called for, the work has been carefully revised and cor- rected, and the whole condensed into one volume. In this form it cannot fail to be more acceptable to the public, and rendered more convenient and useful for the purposes of instruction in the various Colleges and Seminaries of Learning that have adopted it as a Class Book for their pupils. This volume embraces all that has been pre- pared or published by the author. INTRODUCTION. To appreciate the importance of Physics or Natural Philosophy, as an object of study not only to all persons engaged in scientific pursuit, but, in the present day, to all who pretend to a moderately good education, we must take a rapid glance at the nature of human knowledge generally, and at its bearings on the existing condition of mankind. While the inferior races of animals on earth seem to have changed as little in any respect since the beginning of human records, as the trees and herbs of the thickets which give many of them shelter, the condition of man himself has fluctuated, but, on the whole, progressed in a very remarkable manner. The inferior animals were formed by their Creator such,that within one life or generation they should attain all the perfection of which their na- ture was susceptible. Their wants were either immediately provided for— as instanced in the clothing of feathers to birds, and of furs to quadrupeds ; or were so few and simple, that the supply was easy to very limited powers —except in a few cases where considerable art'was required, as by the bee in making its honey-cell, or by the bird in constructing its beautiful nest, and there, a peculiar aptitude or instinct was bestowed. Thus, a crocodile which issues from its egg in the warm sand, and never sees its parent, becomes as perfect and knowing as any crocodile that has lived before or that will appear after it.—But how different is the story when we turn to man! He comes into the world the most helpless of living beings, long to continue so ; and if deserted by parents at an early age, so that he can learn only what the expe- rience of one life may teach him,—as to a few individuals has happened who yet have attained maturity in woods and deserts,—he grows up in some respects inferior to the nobler brutes. Now as regards many regions of the earth, history exhibits the early human inhabitants in states of ignorance and barbarism, not far removed from this lowest possible grade, which civilized men may shudder to contemplate. But these countries, occupied formerly by straggling hordes of miserable savages, who could scarcely defend them- selves against the wild beasts that shared the woods with them, and the inclemencies of the weather, and the consequences of want and fatigue, and who to each other were often more dangerous than any wild beasts, unceas- ingly warring among themselves, and destroying each other with every spe- cies of savage, and even cannibal cruelty—countries so occupied formerly, are now become the abodes of peaceful, civilized and friendly men, where the desert and the impenetrable forest are changed into cultivated fields, rich gardens and magnificent cities. It is the strong intellect of man, operating with the faculty of language as a means, which has gradually worked this wonderful change. By language, fathers communicate their gathered experience and reflections to their chil- dren, and these to succeeding children, with new accumulation : and when. after many generations, the precious store had grown until simple memory could retain no more, the arts of writing, and then of printing, arose, making •> 6 INTRODUCTION. language visible and permanent, and enlarging illimitably the repositories of knowledge. Language thus at the present moment of the world's existence, may be said to bind the whole human race of uncounted millions into one gigantic rational being, whose memory reaches to the beginnings of written records, and retains imperishably the important events that have occurred; whose judgment analyzing the treasures of memory, has discovered many of the sublime and unchanging laws of nature, and has built on them all the arts of life, and through them, piercing far into futurity, sees clearly many of the events that are to come ; and whose eyes and ears, and observant mind at this moment, in every corner of the earth, are watching and recording new pheno- mena, for the purpose of still better comprehending the magnificence and beautiful order of creation, and of more worthily adoring its beneficent Author. It might be very interesting to show here, in minute detail, how the arts and civilization have progressed in accordance with the gradual increase of man's knowledge of the universe; but to do so would lead too far from the main subject. We deem it right, however, to make evident to the student the arousing truths, that the progress is not yet at an end ; that it has been vastly more rapid in recent times than ever; and that it seems still to pro- ceed with increasing celerity :—and we know not where the Creator has fixed the limits of the change! Although there are thousands of years on the records of the world, our Bacon, who first taught the true way to investigate nature, lived but the other day. Newton followed him, and illustrated his precepts by the most sublime discoveries which one man has ever made. Harvey detected the circulation of the blood only two hundred years ago. Adam Smith, Dr. Black and James Watt were friends, and the last, whose steam-engines are now changing rapidly the condition of empires, may be said to be scarcely cold in his grave. John Hunter died not long ago ; Herschel's accounts of newly-discovered planets, and of the sublime struc- ture of the heavens, and Davy's account of chemical discoveries not less im- portant to man, are in the late numbers of our scientific journals ;—illustrious Britons these, and who have left worthy successors treading in their steps. On the continent of Europe, during the same period, a corresponding constel- lation of genius has shone ; and Laplace was lately the bright star shining between the future and the past. But there is a change going on in the world, connected closely with the progress of science, yet distinct from it, and more important than a great part of the scientific discoveries ;—it is the diffusion of existing knowledge among the mass of mankind. Formerly, knowledge Avas shut up in convents and universities, and in books written in the dead languages—or in books which, if in the living languages, were so abstruse and artificial, that only a few per- sons had access to their meaning; and thus, the human race being considered as one great intellectual creature, a small fraction only of its intellect was allowed to come into contact with science, and therefore into activity. The progress of science in those times was correspondingly slow, and the evils of general ignorance prevailed. Now, however, the strong barriers which con- fined the stores of wisdom have been thrown down, and a flood is overspread- ing the earth ; old establishments are adapting themselves to the spirit of the age ; new establishments are arising; the inferior schools are introducing improved systems of instruction ; and good books are rendering every man's fireside a school. From all these causes there is growing up an enlightened public opinion, which quickens and directs the progress of every art and science, and through the medium of a free press, although overlooked by many, is now rapidly becoming the governing influence in all the affairs of INTRODUCTION. 7 man. In Great Britain, partly perhaps as a consequence of its insular situa- tion, which lessened among its inhabitants the dread of hostile invasion, and sooner formed them into a united and compact people, the progress of enlight- ened public opinion had been more decided than in any other state. The early consequences were more free political institutions ; and these gradually led to greater and greater improvement, until Britain became an object of admiration among the nations. A colony of her children, imbued with her spirit, now occupies a magnificent|territory in the new world of Columbus; and although it has been independent as yet for only half a century, it already counts more people than Spain, and will soon be second to no nation on earth. The example of the Anglo-Americans has aided in rendering their western hemisphere the cradle of many other gigantic states, all free, and following, although at a distance, the like steps. In the still more recently discovered continent of Australasia, which is nearly as large as Europe, and is empty of men, colonization is spreading with a rapidity never before wit- nessed; and that beautiful and rich portion of the earth will soon be covered with the descendants of free-born and enlightened Englishmen. Thence, still onward, they or their institutions will naturally spread over the vast archipelago of the Pacific Ocean, a track studded with islands of paradise. Such, then, is the extraordinary moment of revolution, or transit, in which the world at present exists! And where, we may ask again, has the Creator predestined that the progress shall cease? Thus far at least we know, that he has made our hearts rejoice to see the world filling with happy human beings, and to observe that the increase of the sciences can make the same spot maintain thousands in comfort and godlike elevation of mind, where with ignorance even hundreds had found but a scanty and degrading supply. The progress of knowledge, which has thus led from former barbarism to present civilization, has gone on by certain remarkable steps, which it is easy to point out; and which it is very useful to consider, because we thereby discover the nature of human knowledge, with the relations and importance of its different branches ; and we obtain great facilities for studying science, and for quickening its farther progress. The human mind, when originally directed to the almost infinity of objects in the universe around it, must soon have discovered that there were resem- blances among them ; in other words, that the infinity was only a repetition of a certain number of kinds. Among animals, for instance, it would distin- guish the sheep, the dog, the horse; among vegetables, the oak, the beech, the pine; among minerals, lime, flint, the metals, and so forth. And becom- ing aware that by studying an exemplar of each kind, its limited power of memory might acquire a tolerably correct knowledge of the whole, while this knowledge would enable the possessors more easily to obtain what was useful to them, and to avoid what was hurtful, the desire for such knowledge must have arisen with the first exercise of reason. Accordingly, the pursuit of it has been unremitting, and the labour of ages has at last nearly completed an arrangement of the constituent materials of the universe, under three great classes of Minerals, Vegetables, and Animals; commonly called the three kingdoms of Nature, and of which the minute description is termed Natural History: and museums of natural history have been formed which contain a specimen of almost every object included in these classes, so that now, a student, within the limits of an ordinary garden, may be said to be able to examine the whole of the material universe. While men were examining the forms and other qualities of the bodies around them, they could not avoid noticing also the motions or changes going 8 INTRODUCTION. on amon-r bodies; and here, too, they would soon make the grand discovery that there were resemblances in the multitude. Self-interest, as in the case of the bodies themselves, having prompted to careful classification, in the present day, as the result of countless observations and experiments made through the series of ages, we are enabled to say, that all the motions, or changes, or phenomena (words synonymous here) of the universe, are merely a repetition and mixture of a few simple manners or kinds of motion or chancre, which are as constant and regular in every case as where they pro- duce the returns of day and night, and of the seasons. All these phenomena are referable to four distinct classes, which we call Physical, Chemical, Vital and Mental. The simple expressions which describe them are denominated General Truths or Laws of Nature, and as a body of knowledge, they con- stitute what is called Science or Philosophy, in contradistinction to Natu- ral History, already described. Now as man cannot, independently of a supernatural revelation, learn any thing but what respects, 1st, the moment- ary state, past or present, of himself and the objects around him; and 2d, the manner in which the states have changed : Natural History and Science, in the sense now explained, make up the whole sum of his knowledge of nature. To exemplify the process by which a general truth or law of nature is dis- covered, we shall take the physical law of gravity or attraction. 1st. It was observed that bodies, in general, if raised from the earth, and left unsup- ported, fell towards it; while flame, smoke, vapours, &c, if left free, ascended away from the earth. It was held, therefore, to be a very general law, that things had weight; but that there were exceptions in such matters, as now mentioned, which were in their nature light or ascending. 2d. It was dis- covered that our globe of earth is surrounded by an ocean of air, having nearly fifty miles of altitude or depth, and of which a cubic foot, taken near the sur- face of the earth, weighs about an ounce. It was then perceived that flame, smoke, vapour, &c, rise in the air only as oil rises in water, viz., because not so heavy as the fluid by which they are surrounded; it followed, therefore, that nothing was known on earth naturally light, in the ancient sense of the word. 3d. It was found that bodies floating in water, near to each other, approached and feebly cohered; that any contiguous hanging bodies were drawn towards each other, so as not to hang quite perpendicularly; and that a plummet suspended near a hill was drawn towards the hill with force only so much less than that with which it was drawn towards the earth, viz., the weight of the plummet, as the hill was smaller than the earth. It was then proved that weight itself is only an instance of a more general mutual attrac- tion, operating between ail the constituent elements of this globe; and which explains, moreover, the fact of the rotundity of the globe, all the parts being drawn towards a common centre, as also the form of dew-drops, rain-drops, globules of mercury,and of many other things ; which, still farther, is the rea- son why the distinct particles of which any solid mass, as a stone or piece of metal, is composed, cling together as a mass, but which, when overcome by the repulsion of heat, allows the same particles to assume the form of a liquid or air. 4th. It was farther observed, that all the heavenly bodies are round, and must, therefore, consist of material obeying the same law. 5th. And lastly, that these bodies, however distant, attract each other; for that the tides of our ocean rise in obedience to the attraction of the moon, and become high or spring-tides, when the moon and sun operate in the same direction. Thus the sublime truth was at last made evident, and by the genius of the immor- tal Newton, that there is a power of attraction connecting together the bodies INTRODUCTION. 9 of this solar system at least, and probably limited only by the bounds of the universe. Acquaintance with the laws of nature has been very slowly obtained,owing to that complexity of ordinary phenomena, which is produced by several laws operating together, and under gre.it variety of circumstance. With re- spect to many laws of Chemistry and Life, men seem to be yet little farther advanced than they were with respect to the physical law of attraction, when they knew only that heavy things fell to the earth. But we have learned enough to perceive that the great universe is as simple and harmonious as it is immense ; and that the Creator, instead of interposing separately, or mira- culously, in the common sense of the word, to produce every distinct pheno- menon, has willed that all should proceed according to a few general laws. There is nothing in nature so truly miraculous and adorable as that the end- less and beneficent variety of results which we see, should spring from such simple elements. In times of ignorance, men naturally regarded every occur- rence which they did not understand, that is to say, which they could not refer to a general law, as arising from a direct interference of supreme power ; and thus, for many ages, and among some nations still, eclipses and earth- quakes, and many diseases, particularly those of the mind, and the winds and weather, were or are accounted miraculous. Hence arose, among heathens, many ceremonies, and sometimes even barbarous sacrifices, for propitiating or appeasing their offended deities ; but founded on expectations no more reasonable than if we should now pray to have the day or the year made shorter, or to have a coming eclipse averted. They had not yet risen to the sublime conception of the one God, who said, " Let there be light," and the light was ; and who gave to the whole of nature permanent laws, which he allows men to discover for the direction of their conduct in life—laws so unchanging, that by them we can calculate eclipses backward or forward for thousands of years, almost without erring, by the time of one beat of a pen- dulum : and as our knowledge of nature advances, we can anticipate and explain other events with equal precision. Even the wind and the rain, which, in common speech, are the types of uncertainty and change, obey laws as fixed as those of the sun and moon i; and already, as regards many parts of the earth, man can foretell them without fear of being deceived. He plans his voyages to suit the coming monsoons, and he prepares against the floods of the rainy seasons. The general laws of nature, divisible, as stated above, into the four classes of, 1st. Physics, often called Natural Philosophy; 2d. of Chemistry; 3d. of Life, commonly called Physiology; and 4th. of Mind, may be said to form the pyramid of Science, of which Physics is the base, while the others con- stitute succeeding layers in the order now mentioned ; the whole having cer- tain mutual relations and dependencies well figured by the parts of a pyramid. We must describe them more particularly, to show these relations. Physics.—The laws of Physics govern every phenomenon of nature in which there is any sensible change of place, being concerned alone in the greater part of these phenomena, and regulating the remainder which origi- nate from chemical action, and from the action of life.—The great physical truths, as comprehended in the present day by man, are reduced to four, and are referred to by the words atom, attraction, repulsion, and inertia. It gives an astonishing, but true idea of the nature and importance of methodical Science, to be told that a man, who understands these words, viz., how the atoms of matter by mutual attraction approach and cling together to form masses, which are solid, liquid, or aeriform, according to the quantity or 10 INTRODUCTION. repulsion of heat among them, and which, owing to their inertia or stub- bornness, gain and lose motion, in exact proportion to the force of attraction or repulsion acting on them,—understands the greater part of the phenomena of nature ; but such is the fact! Solid bodies existing in conformity with these truths, exhibit all the phenomena of Mechanics ; Liquids exhibit those of Hydrostatics and Hydraulics; Airs, those of Pneumatics; and so forth, as seen in the table of' heads given below, at page 12. And the whole of this work is merely a list of the most interesting physical phenomena, arranged in classes under these heads. Chemistry.—Had there been only one kind of substance or matter in the universe, the laws of Physics would have explained all the phenomena ; but there are iron, and sulphur, and charcoal, and about fifty others, which, to the present state of science, appear essentially distinct. Now these, when taken singly, obey the laws of Physics ; but when two or more of them are placed in contact under certain circumstances, they exhibit a new order of phenomena. Iron and sulphur, for instance, brought together and heated, disappear as individuals, and unite into a yellow metallic mass, which, in most of its properties, is unlike to either :—under other new circumstances, the two substances will again separate,and assume their original forms. Such changes are called chemical, (from an Arabic word signifying to burn, because so many of them are effected by means of heat,) but during the changes, the substances are not withdrawn from the influence of the physical laws,—their weight or inertia, for instance, is not altered ; and indeed the phenomenon is merely a modification of general attraction and repulsion. Many chemical changes, besides, are only the beginnings of purely mechanical changes, as when the new chemical arrangement produced by heat among the intimate atoms of gunpowder, causes the mechanical or physical motion of the sudden expansion or explosion. And all the manipulations of Chemistry, as the transferring of gases from vessel to vessel, the weighing of bodies, pounding, grinding, &c, are directed to Physics alone. Chemistry, then, is truly, as figured above, a superstructure on Physics, and cannot be understood or prac- tised by a person who is ignorant of Physics.—The chief departments of study involving the consideration of Chemical in conjunction with Physical laws, are enumerated in the table below, under the head of Chemistry. Life.—The most complicated state in which matter exists, is where, under the influence of life, it forms bodies with a curious internal structure of tubes and cavities, in which fluids are moving and producing incessant internal change. These are called Organized Bodies, because of the various distinct parts or organs which they contain ; and they form two remarkable classes, the individuals of one of which are fixed to the soil, and are called Vegetables; and of the other, are endowed Avith power of locomotion, and are called Ani- mals. Ttie phenomena of growth, decay, death, sensation, self-motion and many others, belong to life, but from occurring in material structures which subsist in obedience to the laws of physics and chemistry, the life is truly a superstructure on the other two, and cannot be studied independently of them. Indeed, the greater part of the phenomena of organic life are merely chemical and physical phenomena, modified by an additional principle.—The science of Life is divided into animal and vegetable Physiology, {see the table below.) Mind.—The most important part of all science is the knowledge which man has obtained of the laws governing the operations of his own mind. This department stands eminently distinct from the others, on several ac- counts. Unlike that of organic life, which could not be understood until physics and chemistry had been previously investigated, this had made extra- INTRODUCTION. 11 ordinary advances in a very early age, when the others, as methodical sciences, had scarcely begun to exist. In proof of this assertion we need only refer to the writings of the Greek philosophers. The most brilliant discoveries and applications, however, were reserved for the moderns, as will occur to many readers, on perusing, in the table below, the several divisions of the subject, and recollecting the honoured names which are now associated with each. It is truly admirable to see the modern analysis, deducing from a few simple laws of mind all the subordinate departments, just as it deduces mechanics, hydrostatics, pneumatics, &c, from the laws of physics : and let us hope that sound opinions on this subject, ensuring human happiness, and therefore beyond comparison more important than any other knowledge, will soon be widely spread.—The crowning science of Mind, although in certain respects independent of the science of Matter, is still closely allied to them in the fol- lowing ways. The faculties of the mind are originally awakened or called into activity solely by the impressions of matter or external nature : all the language used in speaking of mind and its operations, is borrowed from mat- ter ; and many mental emotions are entirely dependent on bodily conditions. The science of Mind, therefore, cannot be studied until after knowledge acquired of an external nature ; and cannot be studied extensively until that knowledge be extensive. Quantity.—To express most of the facts and laws of physics, chemistry and life, terms of quantity are required, as when we speak of the magnitude of a body, or say, that the force of attraction between two bodies diminishes, in a certain proportion, as their distance increases. Hence arises the neces- sity of having a set of fixed measures or standards, with which to compare all other quantities. Such measures have been adopted ; and they are, for numbers, the fingers, or fives and tens ; for length, the human foot cubit, pace, &c; and lately the seconds' pendulum and the French metre, (taken from the magnitude of our globe;) for surfaces, the simplest forms of circle, square, triangle, &c, compared among themselves by the lengths of their diameters or other suitable lines ; and for solid bulk, the corresponding sim- ple solids, of globe, cube, pyramid, cone,&c, similarly compared by the lengths of diameters or of other lines of dimension. The rules for applying these standards to all possible cases, and for comparing all kinds of quantities with each other, constitute a body of science, called the Science of Quantity, the Mathematics. It may be considered as a subsidiary department of human science, created by the mind itself, to facilitate the study of the others. Supposing description of particulars, or Natural History, to be studied along with the different parts of the System of Science sketched in the table, there will be included in the scheme the whole knowledge of the universe which man can acquire by the exercise of his own powers : that is to say, what he can acquire independently of a supernatural Revelation. And on this knowledge all his arts are founded,—some of them on the single part of Physics, as that of the machinist, architect, mariner, carpenter, &c; some on Chemistry, (which includes Physics,) as that of the miner, glass-maker, dyer, brewer, &c; and some on Physiology, (which includes much of Physics and Chemistry,) as that of the scientific gardener or botanist, agriculturist, zoologist, &c. The business of teachers of all kinds, and of governors, advo- cates, linguists, &c &c, respects chiefly the science of Mind. The art of medicine requires in its professor a comprehensive knowledge of all the departments. 12 INTRODUCTION. TABLE OF SCIENCE AND ART. 1. Physics. 2. Chemistry. Mechanics, Hydrostatics, Hydraulics, Pneumatics, Acoustics, Heat, Optics, Electricity, Astronomy, &c. Simple substances, Mineralogy, Geology, Pharmacy, Brewing, Dyeing, Tanning, &c. 3. Life. 4. Mind. Vegetable Physiology, Botany, Horticulture, Agriculture, &c. Animal Physiology, Zoology, Anatomy, Pathology, Medicine, &c. Intellect. Logic, Mathematics, &c. Motives to action. Emotions and Passions, Morals, Government, Political Economy, Theology, Education. In the first stages of education, viz., during the years of childhood and youth, the learning acquired is necessarily of the most mixed kind, and much of it is determined by what is called accident; but from the mutual depend- ence of the different departments of science, as explained in the preceding paragraphs, it follows that with a view to complete erudition, the order exhi- bited in " The Table," is that in which they should afterwards be studied, so as to prevent repetitions and anticipations, and to diminish, as much as pos- sible, the labour of acquirement. Every man may be said to begin his education, or acquisition of knowledge, on the day of his birth. Certain objects, repeatedly presented to the infant, are, after a time, recognized and distinguished. The number of objects thus known gradually increases, and from the constitution of the mind, they are soon associated in the recollection, according to their resemblances, or obvi- ous relations. Thus, sweetmeats, toys, articles of dress, &c, soon form distinct classes in the memory and conceptions. At a later age, but still very early, the child distinguishes readily between a mineral mass, a vegetable, and an animal; and thus his mind has already noted the three great classes of natural bodies, and has acquired a certain degree of acquaintance with Na- tural History. He also soon understands the phrases "a falling body," •' the force of a moving body," and has therefore a perception of the great physical laws of gravity and inertia. Then having seen sugar dissolved in water, and wax melted round the wick of a burning candle, he has learned INTRODUCTION. 13 some phenomena of Chemistry. And having observed the conduct of the domestic animals, and of the persons about him, he has begun his acquaint- ance with Physiology and the science of Mind. Lastly, when he has learned to count his fingers and his sugar-plums, and to judge of the fairness of the division of a cake between himself and brothers, he has advanced into Arithmetic and Geometry. Thus, within a year or two, a child of common sense has made a degree of progress in all the great departments of human science; and in addition has learned to name objects, and to express feelings, by the arbitrary sounds of language. Such, then, are the beginnings or foun- dations of knowledge, on which future years of experience, or methodical education, must rear the superstructure of the more considerable attainments which befit the various conditions of men in a civilized community. In the course of the preceding disquisition, we have seen that Physics or Natural Philosophy, the subject of the present volume, is fundamental to the other parts, and is therefore that of which a knowledge is indispensable. Bacon truly calls it "the root of the sciences and arts." That its import- ance has not been marked by the place which it has held in common sys- tems of education, is owing chiefly, 1st, to the misconception that a know- ledge of technical mathematics was a necessary preliminary; and, 2d, to an opinion, also erroneous, that the degree of acquaintance with Physics which all persons acquire by common experience, is sufficient for common pur- poses : now it is true, that the toys of childhood, as the windmill, ball, syphon, tube, and a hundred others, furnish so many exemplifications of the laws of Physics, and may well be called a philosophical apparatus; but they give information which is exceedingly vague, and not at all such as is absolutely requisite in the practice of many of the arts. If, then, the study of Physics be so easy as now appears, and so important as we shall try still farther to show, there can be no excuse for neglecting it. The greatest sum of knowledge acquired with the least trouble is, perhaps, that which comes with the study of the few simple truths of Physics. To the man who understands these, very many phenomena, which, to the unin- formed, appear prodigies, are only beautiful illustrations of his fundamental knowledge, and this he carries about with him, not as an oppressive weight, * but as a charm supporting the weight of other knowledge, and enabling him to add to his valuable store every new fact of importance which may offer itself. With such a principle of arrangement, his information, instead of resembling loose stones or rubbish thrown together in confusion, becomes as a noble edifice, of correct proportions and firm contexture, and is acquiring greater strength and consistency with the experience of every day. It has been a common prejudice, that persons thus instructed in general laws had their attention too much divided, and could know nothing perfectly. But the very reverse is true ; for general knowledge renders all particular knowledge more clear and precise. The ignorant man maybe said to have charged his hun- dred books of knowledge, to use a rude simile, with single objects, while the informed man makes each support a long chain, to which thousands of kin- dred and useful things are attached. The laws of Philosophy may be com- pared to keys which give admission to the most delightful gardens that fancy can picture; or to a magic power, which unveils the face of the universe, and discloses endless charms of which ignorance never dreams. The informed man, in the world, may be said to be always surrounded by what is known and friendly t© him, while the ignorant mans is as one in a land of strangers and enemies. A man reading a thousand volumes of ordinary books as agree- able pastime, will receive only vague impressions * but he who studies the 14 INTRODUCTION. methodized Book of Nature, converts the great universe into a simple and sublime history, which tells of God, and may worthily occupy his attention to the end of his days. We have said already, that the laws of Physics govern the great natural phenomena of Astronomy, the tides, winds, currents, &c. We will now mention some of the artificial purposes to which man's ingenuity has made the same laws subservient. Nearly all that the civil engineer accomplishes, ranges under the head of Physics. Let us take, for instance, the admirable specimens scattered over the British Isles:—the numerous canals for inland traffic; the docks to receive the riches of the world, pouring towards us from every quarter; the many harbours offering safe retreat to the storm-driven mariner; the magnificent bridges which everywhere facilitate intercourse; hills bored through to open ways for commerce by canals, common roads and rail-roads, the canals in some places being supported, like the roads, on arches across valleys or above rivers, so that here and there the singular phenomenon is seen of one vessel sailing directly over another; vast tracts of swamp or fen-land drained, and now serving for agricultural; the noble light-house, rearing its head amidst the storm, while the dweller within trims his lamp in safety, and guides his endangered fellow-creature through the perils of the night, &c. &c. In Holland, great part of the country has been won and is now preserved from the sea, by the same almost creating power; and now rich cities and an extended garden smile, where, as related by Caesar, were formerly only bogs and a dreary waste. As a general picture, it is interesting to consider, that in many situations on earth where formerly the rude savages beheld the cataract falling among the rocks, and the wind bending the trees of the forest, and sweeping the clouds along the mountain's brow, or whitening the face of the ocean, and regarding these phenomena with awe and terror, as marking the agency of some great but hidden power, which might destroy him; in the same situa- tions now, his informed son, who works with the laws of nature, can lead the waters of the cataract, by sloping channels, to convenient spots, where they are made to turn his mill-wheel, and to do his multifarious work; the rushing winds, also, he makes his servant, by rearing in their course the • broad-vaned wind-mill, which then performs a thousand offices for its mas- ter, man; and the breezes which whiten the ocean are caught in his expanded sails, and are made to waft their lord and his treasures across the deep, for his pleasure or his profit. In Architecture, also, Physics is supreme, and has directed the construc- tion of the temples, pyramids, domes and palaces, which adorn the earth. In respect to machinery, generally, Physics is the guiding light. There are, for instance, the mighty steam-engine; machines for spinning and weav- ing, and for moulding other bodies into various shapes, yea, even iron itself, as if it were plastic clay ; wind-mills and water-mills, and wheel carriages; the plough, and implements of husbandry ; artillery and the furniture of war: the balloon, in which man rides triumphantly above the clouds, and the diving-bell,in which he penetrates the secret caverns of the deep; the imple- ments of the intellectual arts, of printing, drawing, painting, sculpture, &c; musical instruments ; optical and mathematical instruments, and a thousand others. But Physics is also an important foundation of the healing art. The medi- cal man, indeed, is the engineer pre-eminently; for it is in the animal bodv that true perfection and the greatest variety of mechanism are found. Where INTRODUCTION. 15 to illustrate Mechanics, is to be found a system of levers and hinges, and moving parts, like the limbs of an animal body ; where such an hydraulic apparatus, as in the heart and blood-vessels ; such a pneumatic apparatus, as in the breathing chest; such acoustic instruments, as in the ear and larynx ; such an optical instrument, as in the eye ; in a word, such variety and* per- fection, as in the whole of the visible anatomy ? All these structures, then, the medical man should understand, as a watchmaker knows the parts of a time-piece about which he is employed. The watchmaker, unless he can discover where a pin is loose, or a wheel injured, or a particle of dust adher- ing, or oil wanting, &c, would ill succeed in repairing an injury ; and so also of the ignorant medical man in respect to the human body. Yet will it be believed, that there are many medical men who neither understand me- chanics, nor hydraulics, nor pneumatics, nor optics, nor acoustics, beyond the merest routine ; and that systems of medical education are put forth at this day which do not even mention the department of Physics 1 That such is the case, furnishes an illustration of what is stated in the beginning of this essay ; viz., that the sciences and arts are progressive, and that perfect methods of education must arise gradually, like all other things of human contrivance. It is within the recollection of persons now living, that political economy was discovered to be a grand foundation of the art of government, indicating means of security against many national misfortunes common in former times, yea, even against famine and war. And the day is not distant, when the members of the medical profession generally will understand how much the correct knowledge of animal structure and function, and of many remedies, must depend on precise acquaintance with Physics.—Besides the more strictly professional matters contained in the medical sections of the present work, there are many others scattered through it which greatly interest the medical man; such are the subjects of meteorology, climate, ventilation and warming of dwellings, specific gravities, &c. &c. The laws of Physics having an influence so extensive as appears from these paragraphs, it need not excite surprise that all classes of society are at last discovering the deep interest they have to understand them. The lawyer finds that in many of the causes tried in his courts, an appeal must be made to Physics,—as in cases of disputed inventions ; accidents in navigation, or among carriages, steam-engines, and machines generally ; questions arising out of the agency of winds, rains, water-currents, &c: the statesman is con- stantly listening to discussions respecting bridges, roads, canals, docks, and the mechanical industry of the nation: the clergyman finds ranged among the beauties of nature, the most intelligible and striking proofs of God's wis- dom and goodness : the sailor in his ship has to deal with one of the most admirable machines in existence : soldiers, in using their projectiles, in marching where rivers are to be crossed, woods to be cut down, roads to be made, towns to be besieged, &c, are dependent chiefly on their knowledge of Physics : the land-owner, in making improvements on his estates, building, draining, irrigating, road-making, &c; the farmer equally in these particu- lars, and in all the machinery of agriculture ; the manufacturer, of course ; the merchant who selects and distributes over the world the products of manu- facturing industry—all these are interested in Physics ; then also the man of letters, that he may not, in drawing his illustrations from the material world, repeat the scientific heresies and absurdities which have heretofore prevailed, and which, by shocking the now better-informed public, exceed- ingly lower the estimation in which such specimens of the Belles Lettres are held, and lessen their general utility: and, lastly, parents of either sex, 16 INTRODUCTION. whose conversation and example have such powerful effects on the character of their children, who, when grown up, are to fill all the stations in society ; all should study Physics, as one important part of their education. And it is for such reasons that Natural Philosophy is becoming daily more and more a part of common education. In our cities now, and even in an ordinary dwelling-house, men are surrounded by prodigies of mechanic art, and cannot submit to use these, regardless of how they are produced, as a horse is regardless of how the corn falls into his manger. A general diffu- sion of knowledge, owing greatly to the increased commercial intercourse of nations, and therefore to the improvements in the physical departments of astronomy, navigation, &c, is changing everywhere the condition of man, and elevating the human character in all ranks of society. In remote times the inhabitants of the earth were generally divided into small states or socie- ties, which had few relations of amity among themselves, and whose thoughts and interests were confined very much within their own little terri- tories and rude habits. In succeeding ages, men found themselves belonging to larger communities, as when the English heptarchy was united ; but still distant kingdoms and quarters of the world were of no interest to them, and were often totally unknown. Now, however, every one feels that he is a member of one vast civilized society, which covers the face of the earth ; and no part of the earth is indifferent to him. In England, for instance, a man of small fortune may cast his looks around him, and say with truth and exultation, " I am lodged in a house which affords me conveniences and comforts which, some centuries ago, even a king could not command. Ships are crossing the seas in every direction, to bring me what is useful to me from all parts of the earth. In China, men are gathering the tea-leaf for me ; in America, they are planting cotton for me ; in the West Indies, they are preparing my sugar and my coffee ; in Italy, they are feeding silk-worms for me ; in Saxony, they are shearing the sheep to make me clothing ; at home, powerful steam-engines are spinning and weaving for me, and making cutlery for me, and pumping the mines that minerals useful to me may be procured. Although my patrimony was small, I have post-eoaches running day and night, on all the roads, to carry my correspondence ; I have roads, and canals, and bridges, to bear the coal for my winter fire; nay, I have protecting fleets and armies around my happy country, to secure my enjoy- ments and repose. Then I have editors and printers, who daily send me an account of what is going on throughout the world, among all these people who serve me. And in a corner of my house I have Books ! the miracle of all my possessions, more wonderful than the wishing-cap of the Arabian Tales ; for they transport me instantly, not only to all places, but to all times. By my books I can conjure up before me, into vivid existence, all the great and good men of antiquity; and for my individual satisfaction I can make them act over again the most renowned of their exploits ; the orators declaim for me ; the historians recite ; the poets sing ; and from the equator to the pole, or from the beginning of time until now, by my books, I can be where I please." This picture is not overcharged, and might be much ex- tended, such being God's goodness and providence, that each individual of the civilized millions dwelling on the earth, may have nearly the same enjoy- ments as if he were the single lord of all. Reverting to the importance of Natural Philosophy as a general study, it may be remarked that there is no occupation which so much strengthens and quickens the judgment. This praise has usually been bestowed on the Ma- thematics, although a knowledge of abstract Mathematics existed with all the INTRODUCTION. 17 absurdities of the dark ages; but a familiarity with Natural Philosophy, which comprehends Mathematics, and gives tangible and pleasing illustra- tions of the abstract truths, seems incompatible with the admission of any gross absurdity. A man whose mental faculties have been sharpened by ac- quaintance with these exact sciences in their combination, and who has been engaged, therefore, in contemplating real relations, is more likely to disco- ver truth in other questions, and can better defend himself against sophistry of every kind. We cannot have clearer evidence of this than in the history of the sciences, since the Baconian method of reasoning by induction took place of the visionary hypotheses of preceding times. Until then, even powerful minds did not recoil from the most absurd theories on all subjects. Astronomy was mixed with Astrology ; Chemistry with Alchemy ; Physi- ology with the singular hypotheses which preceded the discovery of the cir- culation of the blood ; Politics with the errors of monopolies, prohibitions, balance of trade, &c. Even Religion itself, in various ages and countries, has felt the influence of the state of the public mind as to solid attainments. Tn a man with the knowledge of nature which we now possess, the fables and licentious abominations of the Greek and Roman theologies are shocking indeed; as are the religions of the God of Fire in China, of Vishnoo in India, of Mahomet's imposture and pretended miracles, &c. But the enlight- ened Christian minister earnestly recommends the study of nature; first, because from contemplating the beauty of creation, with the wisdom and benevolent design manifest in all its parts, there spring up in every unde- praved mind those feelings of admiration and gratitude, which constitute the adoration of natural religion, and which form, as shown by many estimable writers on Natural Theology, a fit foundation for the sublime doctrine of immortality, and secondly, because a Revelation being probable only by the miracles occurring at its establishment; to enable men to distinguish between miracles and the usual course of nature, a perfect knowledge of that course, or of Natural Philosophy, is essential: all the false religions of antiquity were founded on, and upheld by pretended miracles. As regards the ques- tion of immortality, even independently of Revelation, no man who con- templates the order and beauty of the material world, and then thinks on the hideous deformities of the moral world—where vice so often triumphs, and modest virtue pines and dies—can for a moment believe that they are the work of the same author, unless there be a hereafter of retribution ; and feeling thus that eternal justice requires another state for man, he embraces with delight the cheering promises of immortality. There have been, how- ever, at various times, even among Christians, sincere, but weak-minded or ill-informed men, who decried the study of the natural sciences, as inimical to true religion ; as if God's ever-visible and magnificent revelation of his attributes in the structure of the universe could be at variance with any other revelation. But such prejudices are now quickly passing away. Wherever considerable'knowledge- of nature exists, debasing and gloomy superstition must cease. It is not the abject terror of a slave which is in- spired by contemplating the majesty and power of our God, displayed in his works, but a sentiment akin to the tender regard which leads a favoured child to approach with confidence a wise and indulgent parent. It remains for the author now only to say a few words with respect to the present work. He was originally led to the undertaking with the view of supplying the desideratum in medical literature, of a treatise on Medical Physics; but soon perceiving that the preliminary investigation of General Physics, necessary to adapt the work to medical readers, would require to 18 INTRODUCTION. be nearly as extensive as it would for general readers, and reflecting that every person of liberal education must now possess such a book, not to be read once and then thrown aside as a novel is, but to be frequently consulted as a manual, he determined to make his book as complete and as extensively useful as possible. He has been encouraged, during his labour, by the belief that the growing light of science, which now exhibits more clearly the natu- ral relations of the different departments of study, as attempted to be por- trayed in the preceding pages, might enable him to avoid some of the defects of former elementary treatises, and to add features of novelty and improve- ment to his own. The sections on Animal Physics were, of course, written for medical men ; and a great service will be rendered by the work, if it only awakens them to a just sense of the importance of Physics as one of the foundations of their art. But even for general readers there are few parts of these sections which the author would exclude. There is nothing more admirable in nature than the structure and functions of the human body, and there are many reasons why no liberal mind should be careless of the study. The details here given are not more anatomical than the illustrations from the animal economy contained in the common treatises on Natural Theology. From the attempt in this work to compress into the smallest possible space the greatest possible sum of scientific information, few his- torical details have been admitted, whether relating to the distinguished men who have benefited the world as authors or inventors, or to the history of the progress of science :—such details form an interesting, but distinct branch of study. The author must not conclude without observing, that no treatise on Natu- ral Philosophy can save, to a person desiring full information on the sub- ject, the necessity of attendance on experimental lectures or demonstrations. Things that are seen, and felt, and heard, that is, which operate on the exter- nal senses, leave on the memory much stronger and more correct impres- sions than where the conceptions are produced merely by verbal description, however vivid. And no man has ever been remarkable for his knowledge of Physics, Chemistry, or Physiology, who has not had practical familiarity with the objects. With reference to this familiarity, persons who take a philanthropic interest in the affairs of the world, must observe, with much pleasure, the now daily increasing facilities of acquiring useful knowledge, afforded by the scientific institutions formed and forming, not only throuo-h this kingdom, but through most civilized nations. Bedford Square, 1st March, 1827. ELEMENTS OF NATURAL PHILOSOPHY. SYNOPSIS, OR GENERAL REVIEW. If it excite our admiration that a varied edifice, or even a magnificent city can be constructed of stone from one quarry, what must our feeling be to learn how few and simple the elements are out of which the sublime fabric of the universe, with all its orders of phenomena, has arisen, and is now sustained! These elements are general facts and laws which human saga- city is able to detect, and then to apply to endless purposes of human advan- tage. Now the four words, atom, attraction, repulsion, inertia, point to four general truths, which explain the greater part of the phenomena of nature. Being so general, they are called physical truths, from the Greek word signi- fying nature, as also "truths of Natural Philosophy," with the same mean- ing, and sometimes "mechanical truths," from their close relation to ordinary machinery. These appellations distinguish them from the remaining general truths, namely, the chemical truths, which regard particular substances, and the vital and mental truths, which have relation only to living beings. And even in the cases where a chemical or vital influence operates, it modifies, but does not destroy, the physical influence. By fixing the attention, then, on these four fundamental truths, the student obtains, as it were, so many keys to unlock, and lights to illuminate the secrets and treasures of nature. 1st. Atom. Every material mass in nature is divisible into very minute indestructible and unchangeable particles,—as when a piece of any metal is bruised, broken, cut, dissolved, or otherwise transformed, a thousand times, but can always be exhibited again as perfect as at first. This truth is con- veniently recalled by giving to the particles the name atom, which isaGreek term, signifying that which cannot be farther cut or divided, or an exceeding minute resisting particle. 2d. Attraction. It is found that the atoms above referred to, whether separate or already joined into masses, tend towards all other atoms or masses, —as when the atoms of which any mass is composed are, by an invisible influence, held together with a certain degree of force; or when a block of stone is similarly held down to the earth on which it lies; or when the tides on the earth rise towards the moon. These facts are conveniently recalled by connecting with them the word Attraction (a drawing together) or gra- vitation. 3d. Repulsion. Atoms under certain circumstances, as of heat diffused among them, have their mutual attraction countervailed or resisted, and they 20 SYNOPSIS. tend to separate;—as when ice heated melts into water, or when water heated bursts into steam, or when gunpowder ignited explodes. Such facts are conveniently recalled by the term Repulsion, (a thrusting asunder.) 4th. Inertia. As a fly-wheel made to revolve, at first offers resistance to the force moving it, but gradually acquires speed proportioned to that force, and then resists, being again stopped, in proportion to its speed, so all bodies or atoms in the universe have about them, in regard to motion, what may be figuratively called a stubbornness, tending to keep them in their existing state, whatever it may be—in other words, they neither acquire motion, nor lose motion, nor bend their course in motion, but in exact proportion to some force applied. Many of the motions now going on in the universe with such regularity—as that turning of the earth which produces the phenomena of day and night—are motions which began thousands of years ago, and continue unvarying in this way. Such facts are conveniently recalled by the term in- ertia applied to them. A person comprehending fully the import of these four words, that is to say, having present to his mind numerous good types or exemplars of the facts referred to them, may predict or anticipate correctly, and may control very many of the facts and phenomena which the extended experience of a life can display to him; and such a person is commonly said to know the causes or reasons of things and events. Now it is important here to observe, that when a person gives a reason or explanation of any fact, other than that it is a fact, or than that the Creator has willed it, he is merely, although he may not be aware of this, showing its resemblance to many other facts, no one of which he understands better than itself—and what he calls a general truth, or law, or principle, is merely an expression for the observed but un- accountable resemblance of the facts. Thus, when a man says that a stone falls because of attraction or gravitation, he only uses a word which recalls thousands of instances which he has witnessed of one body approaching another: but any cause of the approach, other than that God has willed it, is to him utterly unknown. Should men, in the progress of their re- searches, discover that the phenomena now classed by them under the heads of attraction and repulsion, although apparently opposite, are really as closely allied as they already know the rising of a balloon and the falling of a stone to be, (the balloon rises like a cork in water, being pushed up by the fluid air around it, heavier than it, and seeking to descend,) they will not have disco- vered a new cause, but a new resemblance, (new to them) among phenomena, and will only have advanced one step farther in perceiving the simplicity of creation. In accordance with these views, it will be found that this volume is chiefly an extensive display of the most important phenomena of nature and art, classified so as to be explained by the four physical truths, and mu- tually to illustrate one another. They will be distributed under the follow- ing heads or divisions: PART I. constitution of masses, motions and forces. The four fundamental truths extensively examined, and used to explain generally, in Section 1. The nature or constitution of the material masses which compose the universe ; (a department technically called Somatology, from Greek words signifying a discourse on body.) SYNOPSIS. 21 2. The motions or phenomena going on among the masses ;—a department including the common divisions of Statics (things stationary or at rest,) and Dynamics (what relates to force or power.) PART II. phenomena of solids. The four truths explaining the peculiarities of state and motion among solid bodies :—a department called, in a restricted sense, Mechanics, (from the Greek word signifying a machine.) PART III. phenomena of fluids. The truths explaining the peculiarities of state and motion among fluid bodies :—a department called Hydrodynamics (from Greek words signifying water and force.) Section 1. Hydrostatics (water at rest or in equilibrium.) 2. Pneumatics (air phenomena.) 3. Hydraulics (water or fluid in motion.) 4. Acoustics (phenomena of sound and hearing.) PART IV. phenomena of imponderable substances. The truths aiding to explain the more recondite phenomena of Imponde- rable Substances, under the heads of Section 1. Heat or Caloric. 2. Light or Optics. PART V. animal and medical physics. In this part will be ranged the most interesting illustrations afforded by the animal economy, constituting—Animal and Medical physics. As no man can well understand a subject of which he does not carry a dis- tinct outline in his mind, it is recommended to the reader of this work to study the general synopsis, and the analysis placed at the heads of the chap- ters and sections, until the memory be well impressed with them. 3 22 CONSTITUTION OF MASSES. PART I. THE FOUR FUNDAMENTAL TRUTHS MINUTELY EXAMINED, AND USED TO EXPLAIN GENERALLY, FIRST, THE NATURE OR CONSTITUTION OF THE MATERIAL MASSES WHICH COMPOSE THE UNIVERSE, AND SECONDLY, THE MOTIONS OR PHENO- MENA GOING ON AMONG THEM. SECTION I.—THE CONSTITUTION OF MASSES. ANALYSIS OF THE SECTION. The visible universe is built up of very minute indestructible atoms called matter, which, by mutual attraction, cohere or cling together in masses of various form and magnitude. The atoms are more or less approxi- mated, according to the quantity or repulsion of heat among them, and hence arise the three remarkable forms in the masses, of solid, liquid and air, which mutually change into each other with change in the quantity of heat. Certain modifications of attraction and repulsion produce the subordinate peculiarities of state called crystal, dense, hard, elastic, brittle, malleable, ductile and tenacious. " Minute Indestructible Atoms."* That the smallest portion of any substance which the human eye can per- ceive, is still a mass of many ultimate atoms or particles, which may be separated from each other, or newly arranged, but which cannot individu- ally be hurt or destroyed, is deduced from such facts as the following: A particle of powdered marble, hardly visible to the naked eye, still ap- pears to the microscope a block susceptible of indefinite division ; and, when it is broken by fit instruments, until the microscope can hardly discover the separate particles of the fine powder, these may be yet farther divided, by solution in an acid ; the whole becoming then absolutely invisible, as part of a transparent liquid. A small mass of gold may be hammered into thin leaf, or drawn into fine wire, or cut into almost invisible parts, or liquefied in a crucible, of dissolved in an acid, or dissipated by intense heat into vapour ; yet, after any and all these changes, the atoms can be collected again to form the original mass of gold, without the slightest diminution or change. And all the substances or * The different heads or titles, which appear thus, throughout the work, between inverted commas, are the successive portions of the Jlnulysis, detached for separate consideration. The reader is particularly requested to re-peruse the analysis at the several interruptions, that he may have constantly befe>re him that clear view of the general relations among the different parts of the subject, which is essential to a perfect understanding of it. CONSTITUTION OF MASSES. 23 elements of which our globe is composed, may thus be cut, torn, bruised, ground, &c, a thousand and a thousand times, but are always recoverable as perfect as at first. And, with respect to delicate combinations of these elements, such as exist in animal and vegetable bodies, although it be beyond human art, originally to produce, or even closely to imitate many of them—for we cannot build up a feather or a rose—still, in their decomposition and apparent destruction, the accomplished chemist of the present day does not lose a single atom. The coal which burns in his apparatus, until only a little ash remains behind, or the wax-taper which seems to vanish altogether in flame, or the portion of animal flesh which putrefies, and gradually dries up and disappears—present to us phenomena which are now proved to be only changes of connection and arrangement among the indestructible ultimate atoms ; and the chemist can offer all the elements again, mixed or separate, as desired, for any of the useful purposes to which they are severally applicable. When the funeral piles of the ancients, with their charge of human remains, appeared to be wholly consumed, and left the idea with survivors that no base use could be made, in after time, of what had been the material dwelling of a noble or beloved spi- rit, the flames had only, as it were, scattered the enduring blocks of which a former edifice had been constructed, but which were soon to serve again in new combinations. Facts, to be stated under the heads of "chemical composition" and "crys- tal," will prove, that the ultimate particles of any substance must be, among themselves, perfectly similar. "Minute.'''' (Read the Analysis, page 22.) The following are interesting particulars in the arts or in nature, helping the mind to conceive how minute the ultimate atoms of matter must be. Goldbeaters, by hammering, reduce gold to leaves so thin, that 360,000 must be laid upon one another to produce the thickness of an inch. They are so thin, that if formed into a book, 1,800 would occupy only the space of a single leaf of common paper ; and an octavo volume an inch thick would have as many pages as the books of a well-stocked ordinary library contain- ing 1,800 volumes of 400 pages each; yet those leaves are perfect, or free from holes, so that one of them laid upon any surface, as in gilding, gives the appearance of solid gold. Still thinner than this is the coating of gold, upon the silver wire of what is called gold lace ; and we know not that such coating is of only one atom thick. If we place a piece of [this wire in nitric acid, so as to dissolve the silver within, the gold coating remains as a metallic tube of exquisite tenuity. Platinum can be drawn into wire much finer than human hair. A grain of blue vitriol or carmine, will tinge a gallon of water, so that in every drop the colour may be perceived. A grain of musk will scent a room for twenty years, and will have lost but little of its weight. The carrion crow seems to smell its food at a distance of many miles. The thread of the silk-worm is so small, that many folds have to be twisted together to form our finest sewing thread; but that of the spider is smaller still, for two drachms of it by weight would reach from London to Edinburgh, or 400 miles. In the milt of a cod-fish, or in water in which certain vegetables have been infused, the microscope discovers animalcules, of which many thou- 24 CONSTITUTION OF MASSES. sands together do not equal in bulk a grain of sand; yet these have their blood and other subordinate parts like larger animals ; and, indeed, nature, with a singular prodigality, has supplied many of them with organs as com- plex as those of the whale or elephant. Now the body of an animalcule consists of the same elementary substances, or ultimate atoms, as the body of man himself. In a single pound of matter, it thus appears, that there may be more living creatures than of human beings on the face of this globe. What scenes has the microscope laid open to the admiration of the philoso- phic inquirer ! Water, mercury, sulphur, or, in general, any substance, when sufficiently heated, rises as invisible vapour or gas ; in other words, is made to assume the aeriform state. Great heat, therefore, would cause the whole of the ma- terial universe to disappear, the previously most solid bodies becoming as invisible and impalpable as the air we breathe. Utter annihilation would seem but one stage beyond this. " Matter" The inconceivable minuteness of ultimate atoms, as shown above, has led some inquirers to doubt whether there really be matter; that is to say, whether what we call substance or matter have existence or not. In answer to this, it has been usual to adduce, besides the weights of the substances, and the proofs of indestructibility already mentioned, which seem conclusive, the fact that every kind or portion of matter obstinately occupies some space to the exclusion of all other matter from that particular space. This occu- pancy of space is the simplest and most complete idea which we have of ma- terial existence. The awkward word impenetrability has been used to ex- press it, with reference of course to the individual atoms. The following are elucidations : We cannot push one billiard-ball into the substance of another, and then a second and then a third, and so on ; or the material of the universe might be absorbed in a point. A mass of iron on a support will resist the weight of thousands of pounds laid upon it and pressing to descend into its place ; and although a very great weight might crush or break it into pieces, still one particle would not be annihilated. In a forcing-pump, or in Braham's water-press, millions oi pounds cannot push the piston down, unless the water below it be allowed to escape. A weight laid upon bladders full of air, or on the piston handle of a closed air-pump, is supported in the same manner. A quantity of air escaping from a vessel under water ascends through the water as a bubble, displacing its bulk of water in its way. A glass tube, left open at bottom, while the thumb closes the top, if pressed from air into water, is not filled with water, because the air con- tained in it resists; but if the air be allowed to escape by removing the thumb from the top, the tube becomes filled immediately to the level of the water around it. In a goblet or basin pushed into water, with the mouth downwards, the entrance of water is resisted for the like reason ; and if the goblet be inverted over a floating lighted taper, this will continue to float under it, and to burn in the contained air, however deep in the water it may be carried—exhibiting the curious phenomenon of light below water, and being an emblem of the living inmate of a diving bell, which is merely a larger goblet holding a man instead of a candle. GENERAL ATTRACTION. 25 " Mutual Attraction." (See the Analysis, page 22.) Any visible mass of matter, then, as of metal, salt, sulphur, &c, we know to be really a collection of dust, or minute atoms, by some cause made to cohere or cling together; yet there are no hooks connecting them, nor nails, nor glue; and the connection may be broken a thousand times, by processes of nature or art, but is always ready to take place again; the cause being no more destroyed in any case by interruption, than the weight of a thing is 'destroyed by frequent lifting from the ground. Now the cause we know not, but we call it attraction. The phenomena of attraction and its contrary, repulsion, particularly when occurring between bodies at consider- able distances from each other, are as inexplicable as any subjects which the human mind has to contemplate; but the manner or laws of the pheno- mena are now well understood. The general nature and extensive influence of attraction may be judged of from the following facts: Logs of wood floating in a pond, or ships in calm water, approach each other, and afterwards remain in contact. When the floating bodies are very small, or can approach very near to each other at the water's edge—as glass bulbs in a teacup—an additional force is called into play, as will be ex- plained under the head of "capillary attraction." The wreck of a ship, in a smooth sea after a storm, is often seen gathered into heaps. Two bullets or plummets suspended by strings near to each other, are found by the delicate test of the torsion balance (which will be described afterwards) to attract each other, and therefore not to hang quite perpendicu- larly. A plummet suspended near the side of a mountain inclines towards it, in a degree proportioned to its magnitude; as was ascertained by the well- known trials of Dr. Maskeleyne near the mountain Schehallion, in Scotland. And the reason why the plummet in such a case tends much more strongly towards the earth than towards the hill, is only that the earth is larger than the hill. At New South Wales, which is situated on our globe nearly opposite to England, plummets hang and fall towards the centre of the globe, as they do here; so that in respect to England, they are hanging and falling upwards, and the people there, like flies on the opposite side of a pane of glass, are standing with their feet towards us,—hence called our antipodes. Weight, therefore, is merely general attraction acting everywhere. But it is owing to this general attraction that our earth itself is a globe:— all its parts being drawn towards each other, that is, towards a common centre, the mass assumes the spherical or rounded form. And the moon also is round, and all the planets; nay,the glorious sun, too, so much larger than these, is round;—suggesting the inference that all must at one time have been to a certain degree fluid, and that all are subject to the same law. Descending again to the earth and observing minuter masses, we have many interesting instances of roundness from the same cause; as—the parti- cles of a mist or fog floating in air—these, mutually attracting and coalescing into larger drops, and so forming rain—dew-drops—water trickling on a duck's wing—the tear dropping from the cheek—drops of laudanum—glo- bules of mercury, like pure silver beads, coalescing when near, and forming larger ones—melted lead allowed to rain down from an elevated sieve, and 26 CONSTITUTION OF MASSES. by cooling as it descends so as to retain the form of its liquid drops, becom- ing- the spherical shot-lead of the sportsman, &c The cause of this extraordinary phenomenon which we call attraction, acts at all distances.—The moon, though 240,000 miles from the earth, by her attraction, raises the water of our ocean under her, and forms what we call the tide.—The sun, still farther off, has a similar influence; and when the sun and moon act in the same direction, we have the spring tides.—1 he planets, so distant that they appear to us little wandering points in the heaven, yet, by their attraction, affect the motion of our earth in her orbit, quickening it when she is approaching them, retarding it when she is receding. The attraction is greater the nearer the bodies are to each other; as the light of a taper is more intense near to the taper than at a distance. A board of a foot square, represented in fig. 1 by A B, at a certain distance from a light, supposed at C, just shadows a board of two feet square, as E D, at double distance; but a board with a side of two feet has four times as much surface as a board with a side of one foot, for it is not only twice as high or long, which would make it double, but twice as broad also, which Fig. l. CS^?-U= makes it quadruple—as a globe of two feet in diameter requires just four times as much paper to cover it as a globe of one foot,—and the corner, or fourth part, E F, of the larger square here shown is just equal to the whole of the smaller square A B. Light, therefore, at double distance from its source, being spread oVer four times the space, has only one-fourth of the intensity; and for a similar reason, at thrice the distance it has only a ninth part, at four times a sixteenth part, and so on. Now light, heat, attraction, sound, and, indeed, every influence from a central point, are found to decrease in the proportion here illustrated, viz., as the surface of squares which shadow one another increases. The technical expression is, " the intensity is in- versely as the square of the distance;" (the distances being estimated from the centres of attraction or radiation) or one-fourth part as strong at double distance, four times as strong at half distance, and in a corresponding manner for all other distances. Accordingly, what weighs 1,000 lbs. at the sea-shore, weighs five lbs. less at the top of a mountain of a certain height, or when raised in a balloon—as is proved experimentally by a spring balance, or other means;—and at the distance of the moon, the weight, or force towards the earth, of 1,000 lbs., is diminished to five ounces, as is proved by astronomical tests. Attraction has received different names as it is found acting under different circumstances. The chief distinctions are Gravitation, Cohesion, Capil- lary and Chemical attractions. Gravitation is the name given to it when acting at sensible distances, as in the cases of the moon lifting the tides—the sun and earth attracting each COHESIVE ATTRACTION. 27 other—a stone falling, &c. Most of the facts enumerated at page 25, belong to this head. Cohesion is the name given, when it is acting at very short distances, as in keeping the atoms of a mass together. It might appear at first sight that it cannot be the same cause which draws a piece of iron to the earth with the moderate force called its weight, and which maintains the constituent atoms of the iron in such strong cohesion ; but when we recollect that attraction is stronger as the substances are nearer to each other, the difficulty is met. Atoms very nearly in contact may be a million times nearer to each other than when only a quarter of an inch apart, and therefore when the heat among the atoms of any mass allows them to approach very near, they should attract mutually with great force. If, then, the surfaces of the bodies were not in general so very rough and irregular, that, when applied to each other, they can touch only in a few points of the million, perhaps, which each surface contains, bodies would be invariably sticking together or cohering by any accidental contact. The effect of artificially smoothing the touching surfaces is seen in the following examples :—we may remark, however, that besides irregularity of surface, there is another reason, explained a little farther on, which prevents the cohesion. Similar portions being cut off with a clean knife from two leaden bullets, and the fresh surfaces being brought into contact with a slight turning pres- sure, the bullets cohere, almost as if they had been originally cast in one piece. Fresh-cut surfaces of India-rubber or caoutchouc cohere in a similar way. We may hence make elastic air-tight tubes, by cutting off the edges of a strip of India-rubber and bringing the cut surfaces into contact by winding the strip spirally round any small rod or cylinder, and fixing it there for a time with tape or cord. Two pieces of perfectly smooth plate glass or marble, laid upon each other, adhere with great force : and so indeed do most well-polished flat surfaces. Cohesion between a solid and liquid, and between the particles of a liquid among themselves, is seen in the following instances. A flat piece of glass, balanced at the end of a weighing beam, and then allowed to come into contact with water, adheres to the water, and with much more force than the weight of water remaining upon it when again forcibly raised! If there were not cohesion or attraction of the water par- ticles among themselves, as well as to the glass, the latter could only be held down by the weight of the water which directly adhered to it. In pouring water from a mug or bottle-lip, the water does not at once fall per- pendicular, but runs down along the inclined outside of the vessel; chiefly in consequence of the attraction between this and the water; hence the dif- ficulty of pouring from a vessel which has not a projecting lip. The particles of water cohere among themselves in a degree which causes small needles gently laid on the surface to float:—the weight of the needles is not sufficient to overcome the cohesion of the water surface. For the same reason many light insects can walk upon the surface of wa- ter without being wetted. It is chiefly the different force of the attraction of cohesion in different 28 CONSTITUTION OF MASSES. liquids that causes their drops or gutts from the lip of a phial to be of different magnitude. Sixty drops of water fill the same measure as 100 drops of laudanum from a lip of the same size. In a larger mass of liquid, the attraction which, if acting alone, would draw the particles into the form of a distinct globe, yields to that which draws them towards the centre of the earth, and therefore the liquid assumes, more or less completely, what is called the level surface, that is to say, a surface corresponding with the general surface of the globe of the earth. Attraction is called capillary when it acts between a liquid and the interior of a solid, which is tubular or porous. When an open glass tube is partially immersed in water, the water within it stands above the level of that on the outside ; and the difference of level is greater as the tube is less, because in small tubes, the glass all round being nearer to the raised water, attracts it more powerfully. Between two plates of glass standing near to each other, with their lower edges in water, a similar rising of water will occur; and if they are closer at one perpendicular edge than at the other, the surface of the suspended water will be higher there. The two plates of glass in such a case are found to be drawn towards each other by the interposed waters with a certain force, as happens also to glass beads, or other small bodies, floating in water with their surfaces so near to each other at the water's edge, that the water may rise between them,—and the nearer they approach, the higher the wa- ter rises, and the more strongly it attracts. Water, ink, or oil, coming in contact with the edge of a book, is rapidly absorbed far inwards among the leaves. A piece of sponge or a lump of sugar touching water by its lowest corner, soon becomes moistened throughout. The wick of a lamp lifts the oil to supply the flame, from two to three inches below it. A mass of cotton thread hanging over the edge of a glass from the water within it will empty it as a syphon would. A towel will empty a basin of water in the same way. Dry wedges of wood driven into a groove formed round a pillar of stone, on being moistened, will swell so as to rive off the portion from the block. In some quarries of Germany, mill-stones are thus cut from the rock. An immense weight or mass suspended by a dry rope may be raised a little way, by merely wetting the rope ;—the moisture imbibed by capillary attraction into the substance of the rope causes it to swell laterally, and to become shorter. At one time, the small vessels of vegetables were supposed to raise the sap from the roots, by capillary attraction ; but this is known now to be chiefly an action of vegetable life. Attraction has received the name of chemical attraction, or affinity, when it unites the atoms of two or more distinct substances into one perfect compound. * There are about fifty substances in nature which appear, in the present state of science, distinct from each other, and are therefore called kinds of matter: such as the various metals, sulphur, phosphorus, &c. ; but whether these are in truth, originally and essentially different or are only one simple CAPILLARY ATTRACTION. 29 primordial matter, modified by circumstances as yet unknown to us, we cannot at present positively determine. Diamond and pure black carbon are the same substance only with "different arrangement of atoms; and steel, which in the soft state the graver cuts as it would copper or silver, is exactly the same substance as when, after being tempered by heating and sudden cooling, it has become as hard nearly as diamond itself. Yet these differences are more striking than appear between some substances, which we now ac- count essentially distinct. It is found, however, that the atoms of what we call different substances will not cohere and unite indifferently, to form masses, as atoms of the same kind do,—there being singular preferences and dislikes among them, if it may be so expressed, or affinities as the chemists term it: and when atoms of two kinds do combine, the resulting compound generally loses all resem- blance to either of the elements.—Thus : Sulphuric acid will unite with copper and form a beautiful translucent blue salt; with iron it will form a green salt; and if a piece of iron be thrown into a solution of the copper salt, the acid will immediately let fall the cop- per, and take up or dissolve the iron.—Sulphuric acid will not unite with or dissolve gold at all.—Quicksilver and sulphur unite in certain proportions and form the paint called vermilion; in other proportions they form the black mass called Ethiops Mineral.—Lead with oxygen absorbed from the atmosphere or other source, forms what is called red lead, used by painters.—Sea-sand or flint, and the substance called soda, when heated together, unite and form that most useful substance called glass.—Certain proportions of sulphur and of iron combine and produce those beautiful cubes of pyrites or gold-like metal which are seen in slate. Chemical attraction operating thus, does not, in the slightest degree, interfere with general attraction or gravity, for every chemical compound weighs just as much as its elements taken separately. The history and classification of such facts connected with the combina- tions and analysis of different substances, constitute the science of chemistry, so attractive and so useful. It explains how the fifty kinds of matter above alluded to, by variously combining, form the endless diversity of bodies which constitute, as far as it has yet been explored, the mass of our globe. The reasons of these various modifications of attraction are yet much hidden from us. It is a remarkable truth, that when different substances combine in the way now described, the proportions of the ingredients are always uniform, and such as to lead to the conclusion, that for every atom present, of one substance, there is exactly one, or two, or three, &c. of the other; so that, if there be ten atoms of one substance, there are exactly ten, or twenty, &c. of the other, but never an intermediate number, as 13 or 23 to 10, for then a particle of the compound would consist of one atom of the first, and of one and three- tenths, or two and three-tenths, &c. of the second substance, an absurdity if the atom be indivisible. For instance, a certain number of atoms of quick- silver, which weigh twenty-five grains, combine with a certain number of atoms of sulphur, weighing two grains, and form a black compound called Ethiops Mineral, or black sulphuret of mercury ; and if a little more of either ingre- dient be added, it lies as a foreign mixture in the sulphuret of mercury ; but if just as much more sulphur be added as at first, so that there may be two atoms of it, instead of one, in every particle of the compound, a perfect combination of the whole will take place, and a new substance will appear which we call vermilion. Many elementary substances will only unite with each other in one proportion, so that any two such substances form only one compound ; 30 CONSTITUTION OF MASSES. but others unite in several proportions, so that several distinct compounds arise out of the same two elements. It thus appears, that although we do not know the exact number of atoms in a given quantity of any substance,—whether, for instance, a grain of sul- phuret of mercury has more or less than a million of them ; still, as we know that in that grain there are just as many atoms of sulphur as of mercury, and that the weight of the whole sulphur to that of the whole mercury is as two to twenty-five, we know that the single atoms must have the same relation, or that the atom of mercury is 12| times as heavy as that of sulphur. Tables have been formed exhibiting the relative weights of the atoms of different substances ; and the number standing opposite to each substance is called its chemical equivalent,—that is to say, the weight of its atom in rela- tion to the weight of the atom of some other substance chosen as a standard. The equivalent of a compound substance depends of course both on the equi- valents of the ingredients, and on the number of atoms existing in one inte- grant particle of the compound. There is no such thing as an atom of vermilion, or of any other com- pound, for the ultimate molecule or particle must contain at least one atom of the respective ingredients. The facts of the peculiarities and constancy of chemical unions are among the strongest arguments for the existence of similar ultimate atoms. Besides the simple cases of attraction now explained, there are two curious modifications, called electrical and magnetical attractions, which, from their peculiarities, are reserved for consideration in a future division of this work. " Atoms are more or less close, according to the quantity or Repulsion oj heat among them; hence the forms of solid, fluid, air, SfC." (Read the Analysis, p. 22.) Were there in the universe only atoms and attraction, as hitherto ex- plained, the whole material of creation would rush into close contact, forming one huge solid mass of stillness and death. But there is also heat or caloric, which counteracts attraction, and singularly modifies the results. It has been described by some as a most subtile fluid, pervading all things, somewhat as water pervades a sponge : others have accounted it merely a vibration among the atoms. The truth is, that we know little more of heat as a cause of repulsion than of gravity as a cause of attraction: but we can study and clas- sify most accurately the phenomena of both. When a continued addition of heat is made to any body, it gradually in- creases the mutual distance of the constituent atoms, or dilates the body A solid thus is first enlarged and softened ; then melted or fused, that is to say, reduced to the state of liquid, as the cohesive attraction is overcome ; and lastly, the atoms are repelled to still greater distances, so that the substance is converted into elastic fluid or air. Abstraction of heat from such air causes return 01 states in the reverse order. Thus ice when heated becomes water, and the water when farther heated becomes steam; the steam when cooled again becomes water as before, and he water when cooled becomes ice. Ice, water and steam, therefore, are three forms or states of the same substance-one of the most common in nature, being the material of the ocean. Other substances are similarly affected by heat, but as all have different relations to it, some requiring much for liquefaction, and some very little, we LIQUID AND AIR. 31 have that beautiful variety of solids, liquids and air, which constitutes our external nature. Dilatation.—A rod of iron, which, when cold, will pass through a certain opening, and will lie lengthwise between two fixed points, when heated, be- comes too thick and too long to do either.—For accurate mensuration, there- fore, rods or chains used as the measure, must either be at a given tempera- ture, or due allowance must be made for the difference. The walls of a building, under the pressure of a heavy roof, had begun to bulge out so as to threaten its stability. No force tried was sufficient to re- store them to perpendicularity, until the idea occurred of using the contracting force of cooling iron. The opposite walls were then connected by a number of iron bars, passing through both, and having nuts to screw close to the wall, upon their projecting ends, of which bars one-half were heated at a time, viz., every second or alternate bar, by lamps placed under them, and while lengthened in consequence, and projecting farther beyond the wall, their nuts were again screwed close up ; so that, on cooling and contracting, they pulled trie wall in a degree back to its place. The nuts of the second set of bars being then screwed home, the others were again heated, and advanced the object as much as the first; and so on, until the object was accomplished. The iron rim of a coach wheel, when heated, goes on loosely and easily, but when afterwards cooled, it binds the wheel most tightly, giving remark- able firmness and strength. Iron hoops on masts and casks are made to bind in a similar manner. The common thermometer for measuring degrees of heat, is a glass bulb, filled with mercury or other fluid, and having a narrow tube rising from it, into which the fluid, on being expanded by heat, ascends, and so marks the degree. A bladder not quite full of cold air, on being heated, becomes tense, and if weak, may even be burst. Liquid and Air.—A piece of gold, lead, pitch, ice, sulphur, or of other thing, if sufficiently heated, melts or becomes liquid; each substance, how- ever, requiring a different degree of heat—gold requires 5,000 degrees, lead 600, ice 32, and so forth ; and if the heating be afterwards continued, most things at certain higher temperatures suddenly expand again to many times the liquid volume, and become aeriform fluids. The conversion of water into steam is familiarly known to all. One pint of water driven off as steam from the boiler of a low-pressure steam-engine, fills a space of nearly 2,000 pints, and raises the piston through this, with a force of many thousands of pounds : it immediately afterwards appears again in the cold condenser as a pint of water. Six times as much heat is required to convert a pint of water into steam, as to raise it from an ordinary temperature to that of boiling; but the steam, by occupying nearly 2,000 times the space of the water, proves that heat merely produces a repulsion among the particles, and by no means fills up the interstices. The steam rising from boiling water does not appear to the thermometer hotter than the water itself; and hence it was that Dr. Black, whose genius shed so much light on this part of knowledge, gave the excess of heat the name of latent heat. The latent heat of common air is made sensible ift the match syringe. In this, which is close at the bottom, the piston is driven down quickly and strongly, so as to compress very much the air which is underneath it, and the heat Then condensed with the air is sufficiently intense to light a small piece of tinder attached to the bottom of the piston. 32 CONSTITUTION OF MASSES. Not only are spirits, aethers, oils,&c, convertible, as water is into aeriform fluid but also sulphur, phosphorus, mercury, and, indeed, all the metals and elementary substances;—some of them, however, requiring heats of great The varieties of form, then, in the bodies on the face of this earth, may be considered accidental, as dependent on the temperature of the earth, and do not mark the permanent nature of the substances. In the planet Mercury, which is near the sun, resin, tallow, wax, and many vegetable substances deemed by us naturally solid, would all be liquid, as oil is with us; and a certain mixture of tin, zinc and lead, which with us is solid at common temperatures, but melts in boiling water, would there be always liquid like our quicksilver. Our water, oils, and spirits, would there be in a state of steam or air, and could not be known as liquids, except by cooling processes and compression, such as we have lately learned to use for reduc- ing our different airs to the form of liquids. Again, in the cold planet Herschel, which is nineteen times farther from the sun than our earth is, water, if it exist, can be known only as rock crys- tal, which fire would have to melt as it does glass with us : our oils would be as butters or resins, and quicksilver might be hammered, as lead or silver is with us. On our own earth, near the equator, common sealing-wax will not retain impressions; butter is oil in the day, and a soft solid at night; and tallow candles cannot be used. And near our pole, in winter, the quicksilver from a broken thermometer is solid metal; water must be melted by fire for use; oils are solid, &c. To judge, then, of the constitution of nature aright, we must always take extended surveys, and not allow prejudice to mislead us, as it did that Eastern potentate, who put a traveller to death for saying he had visited remote northern countries, where water was sometimes to be seen solid like crystal, and sometimes white and fleecy, like feathers.—The ancients believed that there were just four elements concerned in forming our globe, with all upon it, viz., earth, water, air and^re. What a contrast between former and pre- sent knowledge! R.epulsion without sensible Heat. As we stated in a former paragraph that, besides general attraction, under the names gravitation, cohesion, capillary and chemical attraction, there are modifications which have the names of electrical and magnetical attractions; so we have now to remark, that, besides the general repulsion of heat just described, there are peculiarities which we call electrical and magnetical re- pulsions. Whether these depend altogether on different causes, or are only modifications of effect from the same cause, we cannot yet positively decide. And it is a curious fact connected with the subject, that there seems to be a Mm of repulsion, so to express it, covering the general surfaces of all bodies, and preventing their meeting in absolute contact, even when thev appear to the human eye so to meet. Were it not for this, things would be constantly approaching so closely to each other, that they would stick or cohere, in a way to disturb the common operations of nature. The following facts illus- trate this superficial repulsion, and the means which art uses to overcome it tor particular purposes. Newton found that a ball of glass, or a watch-glass, laid upon a flat surface REPULSION OF SURFACES. 33 of glass, does not really touch it and cannot be made to touch it by a force of even 1,000 pounds to the inch. In like manner, when glass, stone, porcelain, or indeed almost any body is broken, we cannot make the parts cohere again by simply pushing them together in their former position. Where a union, therefore, between separate masses is desired, we are compelled to have recourse to various artifices. A few cases in which cohesion is easily affected, were enumerated at page 27: the following are other instances of a different kind. Gold leaf laid upon clean steel, and then forcibly struck by a hammer, coheres to the steel, and gilds it permanently. But iron can be made to cohere to iron, only by rendering both pieces red hot before hammering :—the process is called welding. Iron and platinum are the only metals that can be welded. Tin and lead, in sheets, pressed together between the strong rollers of a flatting-mill, cohere. The other metals require to be melted before the superficial repulsion gives way so as to allow separate quantities to cohere or run into one mass. It is thus, for instance, that gold, silver, lead, &c, are treated. In many cases the substances are not such as can be melted, (wood or mar- ble, for instance,) and then it is necessary to use some soft glue or cement. Cements must have strong attraction for both substances, and, when dry or cool, must be tenacious in themselves ; solder, paste, common glue, mortar, &c, are the principal substances of this kind. " Certain modifications of attraction produce the subordinate states, called crystal, porous, dense, 8fc." (Read the Analysis, page 22.) It is a remarkable circumstance, that attraction, in causing the atoms to cohere so as to form solid masses, seems not to act equally all around each atom, but between certain sides or parts of one, and corresponding parts of the adjoining one ; so that when atoms are allowed to cohere according to their natural tendencies, they always assume a certain regular arrangement and form, which we call crystaline. Because in this circumstance they seem to resemble magnets, which attract each other only by their poles, the fact has been called the polarity of atoms. It is the cause of several of the pecu- liarities above enumerated, as elasticity, &c. " Crystalization" is exemplified in the following particulars : Water beginning to freeze, shoots delicate needles across the surface; these thicken and interweave until the whole mass has become solid, but the crystaline arrangement always remains. In most substances, this arrange- ment is remarkably proved, by the forms of the surfaces left, when the mass is broken. Moisture, freezing on the window-pane in winter, exhibits a beautiful vari- ety of arborescence. A flake of snow viewed in the microscope, is seen to be as symmetrically formed as a fern-leaf or a swan's feather. If a piece of copper be thrown into a solution of silver in nitric acid, it is preferred by the acid to the silver, and is dissolved accordingly : the silver in the mean time, during its precipitation or separation, assumes the form of a singularly beautiful shrub or tree, resting on the remaining copper as its root. This appearance is called the arbor Dianse. Any metal which has been melted, when allowed to cool again, slowly and 34 CONSTITUTION OF MASSES. at rest, becomes solid first on the outside of the mass. If, before the cooling be completed, the remaining liquid be poured from within, a curious internal crystaline structure, like grotto work, is seen. What is called the grain of a metal is the result of this crystalization. Saltpetre, glauber salt, copperas (to use popular names,) or any other of the many neutral salts, being dissolved in water, and the water being then allowed slowly to evaporate, reappears in beautiful regular crystals, each salt having its peculiar forms, bounded by perfectly plane and polished surfaces. If any such crystal be broken in any part, the broken surface appears to the microscope as if regular layers of particles had been disturbed, (as we see on a larger scale in a broken stack of bricks, or broken pile of shot in a battery yard,) and the defect of the crystal will be exactly filled up by replacing it in the evaporating solution—proving that the ultimate particles are all of the same size. All the precious stones are crystals, and can be well cut only parallel to their natural surfaces. The basaltic pillars of the Giant's Causeway in Ireland, and of the Isle of Staffa, which appears like a garden supported on magnificent columns in the midst of the ocean, are natural crystaline arrangements of particles, equaling in regularity and beauty any human work, and in grandeur so far surpassing even the Egyptian pyramids, that superstitious conjecture naturally supposed them the work of giant architects. It would be endless to go on enumerating crystaline masses, for nature's forms generally, in the inanimate creation, as well as in organized bodies, are regular and symmetrical; and what we see on earth of broken continents, and islands, and rocks, and wild Alpine scenery, are the effects of subsequent convulsions, which have deranged a primitive and natural order. Much ingenuity has been employed to account for the specific forms which different crystaline bodies assume ; but the subject is not yet reduced to a state fitting it to be a part of this elementary study. A familiarity with the various figures which the exact science of measures treats of, is required in the person who expects to pursue it with pleasure or advantage. The facts are extremely curious, and the scientific investigation of them may ultimately give important information respecting the. intimate constitution of material nature. "Porous."—The crossing of the constituent crystaline needles or plates in bodies, causes them to be porous or full of small vacant spaces. In some cases these are visible to the eye, in many more cases, they are visible to the microscope, and in all, they are to be proved in some way. Owing to the porosity arising from the new arrangement of atoms of solidi- fying, water and a very few other substances become more bulky in the change from the liquid to the solid state. Water then dilates with such force as to burst the strongest vessels which art can provide, and in winter to split even rocks, where it has been retained in their crevices ;—freezing water thus curiously producing effects which surpass those of exploding gunpowder. lhis agency oT water contributes to the gradual breaking down of our Alpine summits, and the falling of their destructive fragments into the valleys. 1 he stone called hydrophane (agate) is opaque, until dipped into water, when it absorbs into its pores one-sixth of its weight of the water, and after- wards gives passage to light. Into crystalized sugar, and various stones, much water will enter without increasing the bulk. former1. °f Sandst0ne' suitably shaPed> fo™s an excellent filter or strainer DENSITY. 35 Pressure will force water through the pores of the most solid gold :—as was seen in the famous Florentine experiment, where a hollow, thick, golden ball, being filled with water and squeezed, to try the compressibility of water, was found to perspire all over. . The examples of porosity in animal and vegetable bodies, are, however, the most remarkable. Bone is a tissue of cells and partitions, as little solid as a heap of empty packing-boxes. Wood is a congeries of parallel tubes, like bundles of organ pipes.—It has lately been proposed to prepare wood for certain purposes, as for making the great wooden pins or nails used in ship-building, by squeezing it to,half its lateral bulk between very strong rollers, and thus making its density approach to that of metal. A piece of wood sunk to a great depth in the ocean, and exposed to the pressure there, has its pores soon filled with water, and becomes nearly as heavy as stone. Thus it was with the boat of a whale-fishing ship, which had been dragged far under water by a whale, and which, on being afterwards drawn up, was supposed by the crew to be bringing a piece of rock with it. A piece of cork in a strong close glass vessel nearly full of water, may be seen floating at the top ; but if more water be then forcibly pumped into the vessel, the cork will be squeezed and reduced in size, until at last it becomes heavier than water and sinks. On water being afterwards allowed to escape, the cork will resume its bulk and will rise. A cork sunk 200 feet under water, will never rise again of itself. A bottle of fresh water, corked and let down thirty or forty feet into the sea, often comes up again with the water saltish, although the cork be still in its place: the explanation being, that the cork, when far down, is so squeezed as to allow the water to pass in or out by its sides, but on rising, resumes its former size. " Density," or the quantity of atoms which exist in a given space, is very different in different substances. A cubic inch of lead is forty times heavier than the same bulk of cork. Mercury is nearly fourteen times heavier than an equal bulk of water. The density must depend on, first, the size or weight of the individual atoms ; secondly, the degree of porosity just now explained ; and thirdly, the proximity of the atoms in the more solid parts which stand between the pores. From many circumstances it appears, that the atoms even of the most solid bodies are nowhere in actual contact, but are retained in their places by a balance between attraction and repulsion—thus, A body dilates or contracts, according as heat is added or taken away from it. A weight placed on any upright rod or pillar, shortens it and lessens its bulk, and if suspended from the bottom, lengthens it and increases its bulk,— the rod in both cases returning to its former dimensions when the weight is removed. When a plank or rod is bent, the atoms on the concave side are, for the time, approximated, and those on the convex side are drawn more apart. It is remarkable in solid bodies, not only how precisely the balance between attraction and repulsion determines the relative position of the particles, but also how strongly ; for any farther separation of the particles is resisted by 36 CONSTITUTION OF MASSES. all the force which we call the tenacity or cohesion of the substance, and any approach by all the force which we call the hardness or incompressi- nearer Tm and copper, when melted together, to form bronze, occupy less space bv one-fifteenth than when separate : proving that the atoms of the one are nartiallv received into what were vacant spaces in the other. A similar con- densation is observed in many other mixtures. A pound of water and a pound of salt, when mixed, form two pounds of brine, but which has much less bulk than the ingredients apart. So also of a pound of sugar dissolved in a pound of water. . . . Water and liquids generally resist compression very powerfully, but yield enough to show that the particles are not in contact. It is found that at 1,000 fathoms down in the sea the water is compressed by the superincum- bent water so as to have bulk about a hundredth part less than it would have ■fit the suriEicc In aeriform masses the atoms are very distant, and hence the masses are more easily compressed. A pint of water, on assuming the aeriform state, in which it is called steam, under ordinary pressure, acquires nearly 2,000 times its former bulk. A hundred pints of common air may be compressed into a pint vessel, as in the chamber of an air-gun; and if the pressure be much farther increased, the atoms will at last collapse and form a liquid. The heat which was contained in such air, and gave it its form, is squeezed out in this operation, and becomes sensible all around. From these proofs of the non-contact of the atoms, even in the most solid parts of bodies ; from the very great space obviously occupied by pores—the mass often having no more solidity than a heap of empty boxes, of which the apparently solid parts may still be as porous in a second degree, and so on ; and from the great readiness with which light passes in all directions through dense bodies like glass, rock crystal, diamond, &c, it has been argued that there is so exceedingly little of really solid matter, even in the densest mass, that the whole world, if the atoms could be brought into abso- lute contact, might be received into a nut-shell. We have as yet no means of determining exactly what relation this idea has to truth. The comparative weights of equal bulks of different bodies are called their specific gravities. In thus comparing bodies, it was necessary to choose a standard; and water, as being the substance most easily procurable at all times and in all places, has been generally adopted. The metal called platinum, the heaviest of known substances, is about twenty-two times as heavy as an equal bulk of water, and is therefore said to have specific gravity of 22—gold is nineteen times as heavy—mercury thirteen and a half—lead eleven—iron eight and a half—copper eight—com- mon stones about two and a half—woods from half to one and a half—cork one quarter, &c. " Hardness," is not proportioned, as might be expected, to the density of the different bodies, but to the polarity of the atoms in them, that is, to the force with which the atoms hold their places in some particular arrangement. Hardness is measured generally by the circumstance of one body being capable of scratching another.—It is here worthy of notice, however, that DENSITY. 37 the powder or dust of a softer body will often, through an effect of motion to be described below, aid in wearing down or polishing one that is harder. Gold, though soft, is four times heavier than the hard diamond; and mercury, which is fluid, is nearly twice as dense as the hardest steel. Diamond is the hardest of known substances. It cuts or scratches every other body, and is generally polished by means of its own dust. Glass-cutters use a point of diamond as a glass-knife for dividing and shaping their panes. Common flint also cuts glass, as is proved by the frequent scribblings on windows. It is remarkable, that the preparation of iron, called steel, may either be soft like pure iron, or from being heated and suddenly cooled, in the process called tempering, may become nearly as hard as diamond. The discovery of this fact is, perhaps, second in importance to few discoveries which man has made ; for it has given him all the edge tools and cutting instruments by which he now moulds every other substance to his wishes. A savage will work for twelve months, with fire and sharp stones, to fell a great tree, and to give it the shape of a canoe ; where a modern carpenter, with his tools, could accomplish the object in a day or two. The project has lately been realized of engraving on plates of soft steel instead of copper, and afterwards tempering the steel to such hardness, that it may be used as a type or die to make its impression, not on paper, but on other plates of soft steel or of copper; each of which is then equal in value to an original and distinct engraving. By this means the beautiful produc- tions of art, instead of being limited to a comparatively small number of copies and of persons, may be multiplied almost to infinity, becoming the cheap delight of all. "Elasticity" is present in a mass when the atoms, cohering in a particular arrangement only, yield, however, to a certain extent, when force is applied, but move back or regain their natural positions on the force being with- drawn. Elastic bodies vary much as to the extent to which they yield without breaking, and as to the degree of perfection with which, after the bending, or displacement of atoms, they regain their former state. India rubber is extensively elastic, for it yields far ; but it is not perfectly elastic, for when stretched much or often, it becomes perfectly elongated. Glass, again, is perfectly elastic, for it will retain no permanent bend ; but, unless in very thin plates indeed, or in fine threads, it will not bend far without breaking. All hard bodies are elastic, as steel, glass, ivory, &c, and many soft ones, as caoutchouc, silk, a harp string, &c The aeriform bodies are all per- fectly elastic, as is rudely seen in a bladder filled with air, when squeezed, and allowed to expand again ; and they will change volume to a very great extent. Liquids also are perfectly elastic, but to a small extent. A good steel sword may be bent until its ends meet, and yet when allowed will return to perfect straightness. A rod of bad steel, or of other metal, will be broken in bending, or will retain a bend. An ivory ball, let fall on a marble slab, rebounds, owing to the great elas- ticity of both bodies, nearly to the height from which it fell, and no mark is left cm either. If the slab be wet, it is seen that the ivory or marble, or both, had yielded considerably at the point of contact, for a circular surface of 4 38 CONSTITUTION OF MASSES. some extent on the slab is found dried by the blow. The sudden expulsion of air from between the meeting surfaces might contribute to the effect, but the result is very nearly the same when the experiment is made m a vacuum. Billiard-balls scarcely "lose even their polish by long wear, although the touching parts yield at every stroke. j-r.ii" A marble chimney-piece long supported by its ends, is found at last to be bent downwards in the middle; and the bend is permanent. A steel watch-spring, although so much and so constantly bent, resumes its original form when freed at the end of a century ; but occasionally with- out evident cause, while in action,,it will suddenly give way. Elasticity is a property of bodies of'great utility to man, as in his time- pieces, carriage-springs, gunlocks, &c. &c. " Brittleness" designates that constitution of a body where, with-hardness, and elasticity perfect as far as it goes, the cohesion among the atoms exists within such narrow limits that a very slight change of position or increase of distance among them is sufficient to produce a rupture. A compara- tively slight force, therefore, if sudden, breaks them. It belongs to most very hard bodies. Glass scratches an iron hammer, proving that it is harder than iron—yet glass is the very type of fragility ; yielding to the stroke of soft wood, or, indeed, of almost any thing which can give a blow. Steel, when tempered so as to be very hard, becomes brittle also. The steel chisels and tools with which artificers now shape the stones and metals as they formerly did wood, require of course, to be exceedingly hard; but they thereby lose in regard to the extent of their elasticity, and hence are frequently broken. Cast iron, which is much harder than malleable or wrought iron, is very brittle, while soft iron and steel are the toughest things in nature. " Malleable," or reducible into thin plates or leaves by hammering. This property, in opposition to elasticity and brittleness, belongs to bodies whose atoms cohere equally in whatever relative situations they happen to be, and -therefore yield to force, and shift about among each other, with- out fracture or change of property, almost like the atoms of a fluid. Gold is remarkably malleable, for it may be reduced to leaves of the thin- ness of 360,000 to the inch, or of 1,800 to a sheet of common paper. For gold-beaters the metal is first formed into rods, these are afterwards rolled or flattened into ribbons ; the ribbon is cut into portions, which are extended by hammering to great breadth and thinness, and which, being again divided into portions, are hammered and extended to the thinness described. Silver, copper and tin may also be hammered until very thin. Most other metals crack or are torn before the operation is carried far; and some, on being struck, are broken at once, almost like glass. " Duct}k" or susceptible of being drawn into wire. One might expect mal- leability and ductility to belong to the same substances and in the same degrees—but they do not. In ductile substances, as in malleable, the atoms seem to have no more fixed relation of position than in a liquid, but yet they cohere very strongly. One end of a rod of iron, or other ductile metal, being reduced in size so as to pass through an opening in a plate of steel, is seized by strong nippers DENSITY. 39 on the other side of the plate, and the whole rod is drawn through. It is thus reduced, of course, to the size of the opening, and is lengthened in a like proportion. By repeating the operation through smaller holes successively, a wire may at last be obtained of the size of a hair. Dr. Wollaston's ingenuity produced platinum wire finer than spider's thread. He filled a space in the axis of a silver wire with small platinum wire. He then drew or reduced the compound piece to the smallest wire possible, and on dissolving the silver from the outside, he exposed to view the delicate filament of platinum. The order in which metals may be ranged according to their ductility is, platinum, silver, iron, copper, gold, &c. Melted glass has great ductility. The workers draw or spin it into threads by merely attaching a point, pulled out from the mass, to the circumference of a turning-wheel. A uniform thread then continues to be drawn out and wound upon the wheel, at a rate of 1,000 yards or more per hour. This glass thread, when lying together in quantities, resembles beautiful white hair, and when cut in bunches, it serves as an ornament to the female head, wav- ing in the air like the delicate plume of a bird of paradise " Pliant." In bodies distinguished by this title, the cohesion is not destroyed by considerable change of direction among the particles, but there is little elasticity, and unlike what happens in a ductile mass, the same atoms always remain together. Of all pliant things, the chief are animal and vegetable fibres and membranes —as silk, bladder, lint, hemp, &c. &c. " Tenacity" means the force of cohesion among the atoms of any mass. It belongs more or less to all solids, and even to liquids. This property varies much in different substances. Iron and its modifica- tion called steel possess it in the most remarkable degree. The following table shows the comparative tenacity, or strength to resist pulling, of certain metals and woods. Supposing similar wires or rods of each to be used, and of such a size that the surface of a broken end or cross-section would be the one-thousandth of a square inch, the weights supported would be nearly as follows : METALS. Cast Steel . 134 lbs. Best wrought iron 70 Cast iron 19 Copper 19 Platinum 16 Silver . 11 Gold . 9 Tin . 5 Lead . 2 WOODS. Teak .... 13 Oak . - . . . 12 Beech. . . . 12| Ash .... 14 Deal .... 11 40 CONSTITUTION OF MASSES. Iron, compared in this way, is five or six times stronger than oak. Steel wire will support about 39,000 feet, that is, 7 1-2 miles of its own length. . i n ,i Certain animal substances have great tenacity; as—the silk-worm s thread, which is our strongest connecting or sewing material, and has such flexibility united with its strength—the ligaments and tendons of the animal body, pos- sessing at once such admirable strength, elasticity and pliancy: these, when dried, and otherwise prepared, constituted the tough bow-strings of our re- mote forefathers—the hair or wool of animals, twisted into threads, and worked into strong and beautiful textures of the loom—strips of animal intes- tine prepared and twisted, forming the cords of harp and violin, and in strength and uniformity rivaling the steel wires of keyed instruments. The gradual discovery of substances possessed of strong tenacity and which man could yet easily mould to his purposes, has been of great importance to his progress in the arts of life. The place of the hempen cordage of European navies is still held in China by twisted canes and strips of bamboo; and even the hempen cable of Europe, so great an improvement on former usage, is now rapidly giving way to the more complete and commodious security of the iron chain—of which the material to our remote ancestors "existed only as a useless stone or earth. And what a magnificent spectacle is it, at the present day, to behold chains of tough iron stretched high across a channel of the ocean, as at the Menai Strait, between Anglesea and England, and supporting there an admirable bridge-road of safety along which crowded processions may pour, regardless of the deep below, or of the storm; while under it, ships with full sails spread pursue their course, unmolesting and unmolested! APPENDIX TO PART I. —SECTION I. BY THE AMERICAN EDITOR. If the reader has studied the preceding section with attention he is prepared to understand the following propositions. Prop. 1.—Matter is endowed with properties. Prop.- 2.—The properties of matter are distinguishable into two classes, first, those which are general or belong to all kinds of matter, and second, those which are peculiar or belong only to particular kinds of matter. Prop. 3.—The general properties of matter are, indestructibility (p. 22;) extension or the property of occupying a portion of space (p. 24;) divisibility (p. 23;) impenetrability (p. 24;) and inertia, (p. 42.) Prop. 4.—Every particle of matter, and also all masses, have a mutual at- traction for one another, or endeavour to get near each other; and this attrac- tion is inversely as the squares of the distances. Attractions may be primarily distributed into two classes: one consisting of those which exist between the molecules or constituent parts of bodies, and the other between the bodies themselves. The former are called mole- cular or atomic attractions, the latter gravitation (p. 26:) of the former there are several varieties, 1st, cohesion (p. 27;) when this variety of molecular attraction is exhibited by liquids pervading the interstices of porous bodies, ascending in crevices or in the pores of small tubes, it is called capillary at- traction (p. 28.) The other varieties of molecular attractions are affinity or chemical attraction (p. 28,) and electric and magnetic attraction, (p. 30.) Prop. 5.—Attraction of gravitation, or that force by which all the masses of matter tend towards each other, is exerted at all distances. Prop. 6.—Attraction of cohesion acts only within certain limits, and where its sphere of attraction ends, a repulsive force begins. Prop. 7.—Repulsion, except when dependent on electricity or magnetism, is owing to the presence of heat, which latter pervades all matter. Prop. 8.—The particles of matter are more or less close, according to the quantity of heat among them ; but they are never in actual contact (p. 30- 31,) and hence porosity is usually considered as one of the properties of matter. Prop. 9.—The peculiar properties of matter are density (p. 35,) hardness (p. 36,) elasticity (p. 37,) brittleness (p. 38,) malleability (p. 38,) ductility (p. 38,) pliability (p. 39,) tenacity, (p. 39,) &c. 42 MOTIONS AND FORCES. SECTION II —THE MOTION OR PHENOMENA OF THE UNIVERSE.* ANALYSIS OF THE SECTION. The bodies or masses composing the universe may be at rest or in motion, and to change any present state, force proportioned to the quantity of the body and to the degree of change, is equally required, whether to give motion, to take it away, or to bend it:—a truth expressed by saying that matter has inertia, or figuratively, a stubbornness. Uniform^ straight motion, then, is as naturally permanent as rest. And the motion in any body,.measured by its velocity, quantity of matter and direction, is the measure of the amount and direction of any single force or of any com- bination of forces, which has produced it, as also of the force or momen- tum which the body can exhibit again when opposed or made to act itself as a cause of some new motion. The great forces of nature, referred to by the two words attraction and repulsion, acting upon inert matter, produce the equable, accelerated, retarded and bent motions which constitute the great phenomena of the universe.—Tides, currents, winds, falling bodies, fyc, exemplify attrac- tion.—Explosion, steam collision, fyc, exemplify repulsion. And as in every case of attraction or repulsion two masses at least must be con- cerned, there is no motion or action in the universe, without an equal and opposite motion or re-action. "Motion" Is the term applied to the phenomenon of the changing of place among bodies. Were there no motion in the universe it would be dead. It would be without the rising or setting sun, or river-flow, or moving winds, or sound, or light, or animal existence. To understand the nature and laws of the motions or changes which are going on around him, is to man of the greatest importance, as it enables him to adapt his actions to what is coming in futurity, and often to interfere so as to control futurity for his special purposes. Motion, in any particular case, is described by referring to certain objects to mark place, and to some other motion chosen as the standard of velocity. —A man sitting on the deck of a sailing ship, has common motion with the ship: if walking on the deck, he has relative motion to the ship; but if he be walking towards the stern, just as fast as the ship advances, he is at rest relatively to the bottom or shore. A ship sailing against the tide, just as fast as the tide runs, is as much at rest relatively both to the earth and water as if she were at anchor. Absolute motion is that which is rela- tive to the whole universe, or rather to the space in which the universe ex- ists. We have no means of ascertaining such: for although we know how fast our globe whirls upon its axis and wheels round the sun, we have no measure of the motion of the sun himself—revolving possibly round some * The reader should here re-peruse the title and Analysis at page 22. MOTION. 43 more distant centre, but almost certainly having a progress in space, and carrying all the planets along with him. Motion is called rapid, as that of lightning—slow, as that of the sun-dial shadow ; both terms having reference to the ordinary intermediate velocities observed upon earth. It is called straight or rectilineal, inthe apparent path of a falling body—bent, or curvilinear, in the track of a body thrown ob- liquely—accelerated, in a stone falling to the earth—retarded, in the stone thrown upwards while rising to the point where it stops before again de- scending. " Owing to the inertia of bodies, force is equally required to impart motion and to take it away. (Read again the last Analysis.) If a man put his hand to the crank of a heavy fly-wheel or grindstone, to turn it, he experiences a certain resistance, which, however, gradually yields to his effort, and he leaves the wheel whirling with velocity proportioned to the effort. If he then puts out his hand again to stop the wheel, he experi- ences an opposite but similar resistance, which, however, as before, gradually yields, and he brings the wheel to rest. In the second case the effort re- quired of him is less than in the first, by reason of the friction of the turning axle, and the resistance of the air in which the wheel moves,—obstructions which, when he was giving motion, opposed him, but when taking it away assisted him. That these obstructions caused the whole difference in such a case, and that they are the great reasons why all ordinary motions on earth seem to tend of themselves to cease, will be shown in subsequent pages. It is the resistance overcome in moving the wheel or in stopping it, and occa- sioning an expenditure of force proportioned to the mass and to the degree of change of state, which is called the inertia of the mass, or the vis iner- tise, and sometimes, to help the conception of the student, the stubbornness, sluggishness, or inactivity ; but no one of these words can originally sug- gest to the mind all that is intended to be conveyed. An exact measure of the amount of inertia is contained in the familiar fact that a body Jet fall near the surface of the earth, falls rather more than 16 feet in the first second of time,—the well-known weight of the body, or force of terrestrial attraction acting upon it for one second, being just suffi- cient to overcome its inertia to the extent stated. Were the inertia of matter only half of what it is, a body near the earth would fall 32 feet in the second, instead of 16, as it equally would, if, with present inertia, the attraction of the earth were doubled. And were there no inertia, it would fall or pass through any height, however great, in one instant. As the amount of iner- tia thus determines the amount of other force required to give motion to a mass, so does it determine the amount of force required to destroy motion in a mass. A heavy cannon-ball, if wanting inertia, might be dispatched with the speed of lightning by the slightest force, but then the stiffness'of a stalk of corn would suffice to arrest it; and while the ball, with the inertia now existing, takes the force of pounds of gunpowder to give it its usual motion, it may not be stopped, even by the cohesion of a block of granite, which according!}'' it shivers to pieces. The numerous examples now to follow will prove the immense importance of inertia in the general opera- tions of nature. When the sails of a ship are first spread to receive the force or impulse of the wind, the vessel does 'not acquire her full speed at once, but slowly, as the continuing force gradually overcomes the inertia of her mass. When the 44 MOTIONS AND FORCES. sails are afterwards taken in, she does not lose her motion at once, but slowly again, as the continued resisting force of the water destroys it. Horses must make a greater effort at first to put a carriage in motion than to maintain the motion afterwards. And a strong effort is required to stop a moving carriage. When a carriage, of which the body hangs from springs, is first moved, the body appears to fall back, and a person within seems to be suddenly forced against the back cushion. When the carriage is stopped again, the body swings forward, and if the stoppage be very sudden, a care- less passenger may unwittingly pop his head through a front glass. These particulars prove the inertia, first of rest, and secondly of motion. A man standing carelessly at the stern of a boat, when the boat begins to move, falls into the water behind; because his feet are pulled forward while the inertia of his body keeps it where it was, and therefore behind its sup- port. The stopping of a boat, again, illustrates the opposite inertia of motion, by the man's falling forward. An awkward rider on horseback may be left behind, when his horse starts forward suddenly ; or may be thrown off on one side by the horse starting to the other. A horse at speed, stopping suddenly, often sends his cavalier over his ears—as was mortifyingly experienced by a coxcomb, who, on an old cavalry horse, chose to canter along a foot-path, to the annoyance of the com- pany, and whose horse, on hearing the word halt loudly addressed to it by a waggish officer of the regiment, who happened to be there and to recognize it, suddenly stood, and got rid of its load. The mind or will of the beau had sinned against the law of propriety, but his body very perfectly obeyed the laws of inertia and gravity, by shooting forward in a parabolic curve to the earth. A young man not yet accustomed to the whip, drove his phaeton against a heavy coach on the road, and then to his father foolishly excused his awk- wardness, in a way which led to a prosecution of the coachman for furious driving. At the trial, the youth and the servant both deposed that the shock of the coach was such as to throw them over their horses' heads, and thus lost the cause, by unconsciously proving, that the faulty velocity was their own. A man jumping from a carriage at speed is in great danger of falling for- ward, when his feet reach the ground; for his body has as much forward velocity as if he had been running with the speed of the carriage ; and unless he advance his feet like a running man, to support his advancing body, he must as certainly be dashed to the ground, as a runner whose feet are sud- denly arrested. A man racing who receives a signal to stop, and a man jumping from a flying vehicle, must check their motion nearly in the same way. J A person wishing to leap over a ditch or chasm, first makes a run, that the motion thereby acquired may help him over. A standing leap falls much short of a running one. An African traveller saw himself pursued by a tiger, from which he could not escape by running ; but perceiving that the animal was watching an op- portunity to seize him by its usual spring or leap, he artfully led it to where he plain terminated ,n a precipice hidden by brush-wood, and he had just ime to transfer his hat and cloak to a bush, and to retreat a few paces when the tiger sprung upon the bush, and by the motal inertia of its body, was carried over the precipice and destroyed. snihTwtf1.!8 °1 **********ly Pushed forward on a table, the water is spilt or left behind ; but if the glass be already in motion, as when carried by I MOTION. 45 a person walking, and if it then be suddenly stopped by coming against an impediment, the water is thrown or spilt forward. A servant carrying a tray of glasses or china in the dark, and coming sud- denly against an obstacle, hears all his freight slipping forward and crashing at his feet: and a too hurried departure with such a load causes equal destruc- tion, on the opposite side. The actions of beating a coat or a carpet with a cane, to expel the dust; of shaking the snow from one's shoes, by kicking against a door-post; of clean- ing a dusty book by knocking it against a table, or shutting it violently—all illustrate the same principle. If a guinea be laid on a card which is already balanced on the point of the finger, a small fillip or blow to the edge of the card will cause it to dart off, but the guinea, owing to its inertia, will remain resting on the finger,—its inertia being greater than the friction on it of the card passing from under- neath it. When we desire a person, with suspected disease of the brain, to shake his head, and tell whether and where he feels pain, we are doing nearly as if we touched the naked brain with the finger to find the tender part; for the inertia of the brain, when the skull is moved, causes a momentary pressure between it and the skull, almost equivalent, for the purpose desired, to such a touch. This kind of pressure is sufficient to break and destroy tender wares—as glass or eggs—in packages which are too suddenly moved or stopped. A weight suspended by a spring on ship-board is seen vibrating up and down as the ship pitches with the waves. It seems to fall as the ship rises, and to rise as the ship falls : but the motion is really in the ship, and the comparative rest is in the weight. A heavy weight so supported, and con- nected with a pump-rod, would work the pump. Like the-weight last mentioned, the mercury of a common barometer on ship-board is seen rising and falling in the tube; and until the important improvement was lately made, of narrowing one part of the tube to prevent this, the mercurial barometer was useless at sea. The explanation is, that the tube rises and falls with the ship, from being connected with it; but the mercury, which plays freely in the tube, and is supported by the atmospheric pressure, tends, by its inertia, to remain at rest, and thus makes the motion of the ship apparent. What happens to the mercury in the barometer-tube on ship-board, indi- cates what happens to the blood in the vessels of animals under similar cir- cumstances. In any long vein below the heart, when the body falls, the blood, by its inertia and the supporting action of the vessels, does not fall so fast, and therefore really rises in the vein : and as there are valves in the veins preventing return, the circulation is thus quickened without any muscular exhaustion on the part of the individual. This helps to explain the effect of the movement of carriages, of vessels at sea, of swings, &c, and of passive exercise generally, on the circulation, and leaves it less a mystery why these means are often so useful in certain states of weak health. If a cannon-ball were to break to pieces in its flight, its parts would still advance with the previous velocity. And thus, in the deadly contrivance of the Shrapnell-shell, which is in a case containing hundreds of musket bullets, when these are scattered at the desired distance from the devoted body of men, they retain the forward velocity of the shell, and spread death around like the near discharge of a whole battalion of musketry. On the awful occasion of a ship in rapid motion being suddenly arrested 46 MOTIONS AND FORCES. bv a sunken rock, all things oft board, men, guns, and furniture, start from their places and dash forwards ; while the onward inertia or motal obstinacy of the hinder parts of the ship, suffices to crush her bow against the rock. "Motion as naturally permanent as rest." From the instances now given, it is seen that a body at rest would never move if force were not applied, and that a body put in motion retains motion, at least for a time, after the force has ceased ; but there is a feeling from com- mon experience, that motion is an unnatural or forced state of bodies, and that all moving things, if left to themselves, would gradually come to rest. It is recollected that a stone projected comes to rest, or a wheel left moving, or a bowl rolled on the green, or the waves heaving after a storm—and, in a word, that there is no perpetual motion on earth. On more attentive consideration, however, it may be perceived that there are prodigious differences in the duration of motions, and that the differences are always exactly proportioned to evident causes of retardation, and chiefly to friction and the resistance of the air. Friction is the resistance which bodies experience when rubbing or sliding upon each other; and however much it may be diminished by art, it can in no case be annihilated. Air-resistance, again, to motions going on in air, is of the same nature as water-resistance to motions going on in water, only less in degree : and as advancing science has shown the true nature of our atmo- sphere, the amount of this resistance is perfectly .ascertained. A smooth ball rolled on the grass soon stops—if rolled on a green cloth over a smooth plank it goes longer—on the bare plank, longer still—on a smooth and level sheet of ice, it hardly suffers retardation from friction, and, if the air be moving with it, will reach a distant shore. Two little windmill-wheels set in motion together with equal volocity, but of which one has the flat sides of the vanes turned to their course, and the other the edges, if moving in the air, will stop at very different times, but if tried in a vessel from which the air has been removed, they will both go much longer, and will then stop exactly together. As it is to facilitate the motion of fishes in the water, that they are of sharp form before and behind ; so it is to facilitate the motion of birds in the air that they have somewhat of a similar form. A large spinning-top, with a fine hard point, set in motion in a vacuum, and on a hard, smooth surface, will continue turning for hours. A pendulum moving in a vacuum has only to overcome slight friction at its point of suspension, and, therefore, if once put in motion, will vibrate for a day or more. But it is in the celestial spaces that we see motions completely freed from the obstacles of air and friction—and there they seem eternal. Had the human eye, unassisted, been able to descry the four beautiful moons of Jupiter, wheeling around him for these thousands of years, with such unabated regularity, and which now form, to the telescope of the astro- nomer, a perfect and magnificent time-piece in the sky, or had science long proved that the velocity imparted to our globe, when first launched into its present orbit, still wheels it along as swiftly as in the days of the first man, this error or prejudice, that motion is always tending to rest, would never have arisen. J ° Indeed, had these and other such truths, been long familiar to the common MOTION UNIFORM. 47 mind, the opposite prejudice might as well have obtained, that motion is the natural state, and rest a forced or unknown state. We know of nothing which is absolutely at rest. The earth is whirling round its axis and round the sun; the sun is moving round its axis and round the centre of gravity of the solar system, and, possibly, round some more remote centre in the great universe, carrying all his planets and comets about his path. If there were any natural tendency in moving bodies to stop, a thing float- ing in a trough of water, on board a sailing ship, should always be found at the end of the trough nearest the stern; and in all the seas and lakes of the earth, the floating things should be accumulated on the western shores, because the surface of the earth is always turning to the east. We know that neither of these suppositions is truth. A man on board a moving ship can throw any body just as far towards the bow as towards the stern; although in the two cases the volocity, as regards the earth, is so different. Ignorance of the law of motal inertia led a story-telling sailor to assert, as a proof of the speed of his favourite ship, that when a man one day fell from the mast-head, the ship had passed from under him before he reached the deck: the fact, in such a case, being, that he must have fallen on the same part of the deck, whether the ship were in motion or at rest, because his body had just the motion or rest which belonged to the ship. Another equally sapient man, reflecting that the earth turned round once in twenty-four hours, proposed rising in a balloon, and waiting aloft, until the country which he desired to reach should be passing under him. "Motion naturally uniform." (See the Analysis.) It is only repeating that a body can neither acquire motion nor lose motion without a cause, to say that free motion must be uniform. The perfect uniformity of undisturbed motion is proved by every fact observed in the universe. If any continued motion, as of a planet, for in- stance, be found at one time to have certain relative velocity to some other continued motion, the same relation is found always to hold: or deviations from perfect uniformity are exactly proportioned to the disturbing causes. Thus we can foretell the exact time of an eclipse, a thousand years before its occurrence. Had motion not been in its nature uniform, man could have formed no rational conjecture or anticipation as to future events; for it is by assuming, for instance, that the earth will continue to turn uniformly on its axis, that he speaks of to-morrow and of next week, &c, and that he makes all his arrangements for future emergencies: and were the coming day, or season, or year, to arrive sooner or later than such anticipation, it would throw such confusion into all his affairs, that the world would soon be desolate. To calculate futurities, then, or to speak of past events, is merely to take some great uniform motion as a standard with which to compare all others; and then to say of the remote event, that it coincided or will coincide with some described state of the standard motion. The most obvious and best standards are the whirling of the earth about its axis, and its great revolution round the sun. The first is rendered very sensible to man by his alternately seeing and not seeing the sun, and it is called a day; the second is marked by the succession of the seasons, and it is called a year. The earth turns upon its axis nearly 365 times while it is performing one circuit round the sun, and thus divides the year into so many smaller parts, and the day is divided into smaller parts, by the progress of the earth's whirling being so distinctly narked, 48 MOTIONS AND FORCES. in the constantly varying direction of the sun, as viewed from any given spot on the face of the earth.—When advancing civilization made it of importance for men to be able to ascertain with precision the very instant of the earth's revolution, connected with any event, various contrivances were introduced for the purpose; as,—sun-dials, where the shadow travels progressively round the divided circle ;—the uniform flux of water through a prepared opening;—the flux of sand in the common hour-glass, &c. But the great triumphs of modern ingenuity are those astronomical clocks and watches, in which the counted equal vibrations of a pendulum, or balance-wheel, have detected periodical inequalities even in the motion of the earth itself, and have directed attention to unsuspected disturbing causes, important to be known. It is the natural uniformity of undisturbed motion which causes any num- ber of bodies moving together, as the furniture of a sailing ship, to appear among themselves as if at rest,—no one tending to pass before, or to fall behind, or to move to one side of another. For the same reason a person who is moving with such bodies is absolutely insensible of his uniform pro- gression, and knows it only by reasoning from such facts as the changing appearances of other objects around which do not share the motion, the rush- ing of the waves or wind, &c. When a ship is becalmed at sea, she may, as numberless sad accidents have proved, be carried by rapid currents in any direction, without one of the crew suspecting that she has motion at all; and if the suspicion do arise, the truth can be come at only by such means as the sounding line, where the bottom can be reached, or careful observation of the heavenly bodies where it cannot. A man in the hold of a ship in a river or tides-way cannot say whether the rushing of water, which he hears from without, be a rapid tide passing the ship at anchor, or the effect of the ship's advance in the river. A man in a balloon going 80 miles an hour, knows not in what direction he is moving, nor, indeed, that he is moving at all, but by observing the objects below. This explains why men are not sensible of the motion of the earth itself, which they know, however, to be turning round its axis once in twenty-four hours, and therefore to have its surface near the equator moving with a speed of more than 1,000 feet per second; and as in the case of a ship or balloon, there would be no difference of sensation whether the speed were of one mile per hour or of 10 or 100, so in the case of the earth, there would be none whether it turned as now, once in twenty-four hours; or, like the planet Jupiter, once in ten. A hunter among the hills, who, during the heat of noon, rests and contemplates around him a sublime scene of solitude and silence, may little think that if, amidst that apparent repose of nature, he were for a moment lifted up from the earth and held at rest above its surface, he would see its face of hill and dale sweeping past beneath him at the prodi- gious rate of 1,000 miles an hour, on account solely of the whirling of the earth. The fact that a cannon-ball can be shot just as far upon the surface of the earth, eastward, in the direction of the earth's motion, as westward, against it, illustrates the truth, that whatever common motion objects may have, it does not interfere with the effect of a force producing any new relative mo- tion among them. All the motions seen on earth are really only slight differ- ences among the common motions : as in a fleet of sailing ships, the apparent changes of place among them are in reality only slight alterations of speed or direction, in their individual courses. A man continuing to throw upwards a ball or orange, or several of them at once, and to catch and return them alternately, uses no difference of art as MOTION STRAIGHT. 49 regards them, whether he be standing on the earth and whirling with it, or on a sailing ship's deck, or in a moving carriage, or on a galloping horse's back. He and the oranges have always the same forward common motion. And when a man, standing on a galloping horse, leaps through a hoop held across his course, he does not leap forward—for this would throw him over the horse's ears—but merely jumps up, and allows his motal inertia to carry him through. The reason that a lofty spire or obelisk stands more securely on the earth, than even a short pillar stands on the bottom of a moving wagon, is, not that the earth is more at rest than the wagon, but that its motion is uniform.— Were the present rotation of our globe to be arrested but for a moment, imperial London, with its thousand spires and turrets, would, by the motal inertia, be swept from its valley towards the eastern ocean, just as loose snow is swept away by a gust of wind. " Force is required to bend motion" If a body moving freely cannot vary its velocity without a cause, neither can it vary its course without a cause ; and free motion, therefore, is straight as well as uniform. A ball shot directly up or down gives men their simplest idea of straight motion. A bullet or arrow, projected horizontally, is gradually drawn downwards by the attraction of the earth, but it deviates neither to the right hand nor to the left. William Tell, trusting to the natural straightness of motion, obeyed the tyrant's order, and shot an apple placed on his child's head. And the right eye of Philip of Macedon is said to have been destroyed by an arrow which brought a label on it, telling its destination. Riflemen shooting at a target, hit the very spot they choose to aim at. A stone in a sling, the moment it is set at liberty, darts off as straightly as an arrow from the bow-string or a bullet from a gun-barrel, and it is only because the point of its circle, from which it should depart, cannot in prac- tice be accurately determined, that the same sure aim cannot be taken with it. A body moving in a circle, then, or curve, is constrained to do what is contrary to its inertia. A person, on first approaching this subject, might suppose that a body, which for a time has been constrained to move in a circle, should naturally continue to do so when set at liberty. But on reflecting that a circle is as if made up of an infinite number of little straight lines, and that the body moving in it has its motion bent at every step of the progress, the reason is seen why constant force becomes necessary to keep it there, and force just equal to the inertia with which the body tends, at every point of the circle, rather to Fig. 2. pursue the straight line, called a tangent, of which that point, as seen in fig. 2, is the commencement, than the circle itself. The force required to keep the body in the bent course, is called centripetal or centre-seeking force ; while the inertia of the body tending outwards, that is, to move in a straight line rather than in a curve, is called the centrifugal or centre-flying force ; and the term cen- tral, forces is applied to both. A slintr-cord is always tight while the stone is whirling: and its tension is of course the measure both of the centripetal and centrifugal force. A means, D 50 MOTIONS AND FORCES. then of measuring the tension of a sling-cord would experimentally demon- strate the amount of centrifugal force ; and such a means we possess in the contrivance called the " whirling table," upon which a leading sling, or any mass with a string attached to it, may be placed to revolve, at any desired distance from the centre, and with any desired velocity, while the string passing over a pulley at the centre, is made to lift weights proportioned to the outward dragging of the revolving mass. By this apparatus it is found, as would be expected, that centrifugal force—in other words, the force with which the inertia of moving matter resists the bending of its course from straight to circular, is proportioned, first, to the quantity of matter moved— every separate particle having its own inertia; second, to the size of the circle or orbit described in the same time—a body moving in a circle of double diameter for instance, having to be forced inwards from the tangent, at every departure, twice as far in a given time ; third, that with a double revolution in the same time, the centrifugal force is not double but quadruple (a corresponding proportion existing for other velocities,) because, not only are there twice as many bendings or angular departures from the tangent for the two circles as for one, requiring, as may be said, twice as many tugs or impulses of the centripetal force, but every impulse must be made with double energy, for it has to drive the mass inwards through the required dis- tance in half the time ; and twice as many impulses, every one being twice as strong, make a quadruple amount of force on the whole; fourthly and lastly, it is found, agreeing with the relation between inertia and terrestrial gravity described at page 43, that a body revolving, for instance, in a circle of four feet diameter, that it may have centrifugal force just equal to its weight, requires to complete its revolution in one second and a half of time. This and similar facts will be more particularly considered when we come to treat of the motions of the planets round the sun. This analysis of central forces will suffice to excite in the student a due interest touching the kindred phenomena now to be described. Bodies laid on a whirling horizontal wheel, are readily thrown off. In a corn-mill, the grain, after being admitted between the stones through an opening in the centre of the upper stone, is then kept turning round between them, and is, by its centrifugal force, always tending and travelling outwards until it escapes as flour from the circumference. A man, if he lie down on a turning millstone with his head near the edge, falls asleep, or dies of apoplexy, from the new pressure of blood on the brain. A wet mop, or bottle-brush, made to turn quickly on its handle as an axis, throws the water off in all directions, and soon dries itself. Sheep, in wet weather, thus discharge the water from their fleeces, by a semi-rotatory shake of the skin. Water-dogs, on coming to land, dry them- selves by the same action. A tumbler of water placed in a sling, may be made to vibrate like a pen- dulum with gradually increasing oscillation, and at last to describe the whole circle, and continue revolving about the hand, without spilling a drop:—the water, by its inertia of straightness, or centrifugal force, tending more away from the centre of motion towards the bottom of the tumbler, even when that is uppermost, than towards the earth by gravity. As solid bodies laid on a whirling table are thrown off, so water in a vessel caused to spin round in any way, as on the centre of a horizontal wheel, instead of lying at the bottom, is raised up all around, against the sides of CENTRIFUGAL FORCE. 51 Water, poured obliquely into a funnel, runs round the interior of it, and often leaves an open passage of air all the way down through it, as if there were merely a lining of water to the funnel. The centrifugal force of the turning water is a chief reason of this phenomenon:—another reason will be considered farther on, under the head of atmospheric pressure. Great whirlpools at sea, and smaller ones, or eddies in rivers, occur when- ever a current is obliged suddenly to bend, as in rounding a point of land or a rock, or in meeting and mingling with a contrary current. The water, by tending to continue its straight motion, falls in behind the obstruction, reluct- antly as it were, and leaves there a pit surrounded by a liquid revolving ridge. Charybdis, in the Mediterranean, and the great whirlpool off the Norwegian coast, are noted examples. It is owing to the centrifugal force in any bending part of a stream of water, that is to say, the tendency away from the centre of the curvature, that when a bend has once commenced, it increases, and is soon followed by others, until that complete serpentine winding is produced, which charac- terizes most rivers in their course across extended plains. The water being thrown by any cause to the left side, for instance, wears that into a curve or elbow, and, by its centrifugal force, acts constantly on the outside of the bend, until rock or higher land resists the gradual progress; from this limit being thrown back again, it wears a similar bend to the right hand, and after that, another to the left, and so on. Carriages are often overturned in quickly rounding corners. The inertia carries the body of the vehicle in the former direction, while the wheels are suddenly pulled round by the horses into a new one. A loaded stage-coach running south, and turning suddenly to the east or west, strews its passen- gers on the south side of the road. Where a sharp turning in a carriage-road is unavoidable, the road towards the outside of the bend should always be made higher than at the inside, to prevent such accidents. A man or a horse turning a corner at speed, leans much inwards, or towards the corner, to counteract the centrifugal force, that would throw him away from it. In skating with great velocity, this leaning inwards at the turnings be- comes very remarkable, and gives occasion to the fine variety of attitudes displayed by the expert; and if a skater, in running, finds his body inclined to one side and in danger of falling, he merely makes his skate describe a slight curve towards that side, when the tendency of his body to move straightly, or its centrifugal force, refusing to follow in the curve, allows the foot to push itself again under the body, and to restore the perpendicularity. Skating becomes to the intelligent man an intellectual as well as a sensitive or bodily treat, from its exemplifying so pleasingly the laws of motion. The last example explains, also, why a hoop rolled along the ground goes so long without falling: if it incline to one side, threatening to fall, by that very circumstance, the part touching the ground is made to bend its course to that side, and as in the case of the skater who turns his foot, the sup- porting base is again forced directly under the mass of the body. A coin dropped on the table or floor often exhibits the same phenomenon. It is said to run and hide itself-in the corner. Just before falling, if not ob- structed, it describes several turns of a decreasing spiral, the minute exami- nation of which is a pleasing mathematical exercise. The reason also why a spinning top stands, will be understood here. While the top is quite upright, the extremity of its peg, being directly under its centre, supports it steadily, and although turning so rapidly, and with much 52 MOTIONS AND FORCES. friction, has no tendency to move from the place : but if the top incline at all, the edge or side of the peg, instead of its very point, is in contact with the floor, °and the peg then becoming as a turning little roller, advances quickly, and describes a curve somewhat as a skater's foot does, until it come directly under the body of the top as before. It thus appears that the very fact of the top inclining, causes the point to shift its place, and to con- tinue moving until it comes again directly under the centre of the top. It is remarkable that even in philosophical treatises of authority the standing of a top is still vaguely attributed to centrifugal force. And some persons be- lieve that a top spinning in a weighing scale, would be found lighter than when at rest; and others most erroneously hold that the centrifugal force of 'the whirling, which of course acts directly away from the axis, and quite equally in all directions, yet becomes, when the top inclines, greater upwards than downwards, so as to counteract the gravity of the top. The way in which centrifugal force really helps to maintain the spinning of a top is, that when the body inclines or begins to fall in one direction, its motion in that direction continues until the point describing its curve, like the foot of a skater, has forced itself under the body again. By reason of centrifugal force also, it is easier to do feats of horsemanship in a small ring as at our theatres, than if the animal were running on a straight road. We see the man and the horse always inclining inwards, to counter- act centrifugal force, and if the rider tend to fall inwards, he has merely to quicken the pace ; if to fall outwards, he has to slacken it, and all is right again. If a pair of common fire-tongs, suspended by a cord from the top, be made to turn by the twisting or untwisting of the cord, the legs will separate from each other with force dependent on the speed of rotation, and will again collapse when the turning ceases. Mr. Watt adapted this fact most ingeniously to the regulation of the speed of his' steam-engine. His steam- governor may in truth be described as a pair of tongs with heavy balls at the ends, to make their opening more energetic, attached to some turning part of the machine. If the engine move with more than the assigned speed the balls open or fly asunder beyond their middle station, and by a simple contrivance are then made to act on a valve which contracts the steam tube; on the contrary, with too slow a motion, they collapse and open the valve. A half-formed vessel of soft clay, placed in the centre of the potter's table,—which is made to whirl and is called his wheel,—opens out or widens merely by the force of its sides and thus assists the worker in giving its form. B b A ball of soft clay, with a spindle fixed through its centre, if made to turn quickly, soon ceases to be a perfect ball. It bulges out in the middle, where the centrifugal force is great, and becomes flattened towards the ends, or where the spindle issues. This change of form is exactly what has happened to the ball of our earth. It has bulged out seventeen miles at the equator, in consequence of its daily rotation, and is flattened at the poles in a corresponding degree.- A mass of lead that weighs one thousand pounds at our pole, weighs about five pounds less at the equator, by reason of the centrifugal force. in the planets Jupiter and Saturn, of which the rotation is much quicker than of our earth, the middle or equator bulges out still more-even so as to offend an eye which expects a perfect sphere. hnJL n,TOta!.1(m °f £Ur earth were seve«teen times faster than it is, the bodies or matter at the equator would have centrifugal force equal to their QUANTITY OF MOTION. 53 gravity, and a little more velocity would,cause them to fly off altogether, or to rise and form a ring round the earth like that which surrounds Saturn. Saturn's double ring seems to have been formed in this way, and is now supported chiefly by the centrifugal force of the parts. Were it to crumble to pieces, the pieces might still revolve, as so many little satellites. His true satellites are only more distant masses sustained in the same manner. And our earth and the other primary planets have the same relation to the sun that these satellites have to Saturn—all being sustained by an admirable balance between centrifugal force and gravity. " The quantity of motion in a body measured by the velocity and quantity of matter." If a single atom of matter were moving at the rate of one foot per second, it would have a definite quantity of motion expressed by these words; and if it were moving ten feet per second it would have ten times the quantity. Again, in a mass consisting of many atoms, the quantity of motion would be still as much greater as there were more atoms in it than one. By experiment it is found, that if a ball of soft clay of one pound, sus- pended by a cord as a pendulum, be allowed to fall, with a velocity of ten feet per second, against a ball of nine pounds suspended in the same way, but at rest, the two, after contact, will start together at the rate of one foot per second, the original quantity of motion being then diffused through ten times the quantity of matter, and therefore exhibiting only one-tenth of the velocity. A cannon-ball of a thousand ounces, moving one foot per second, has thus the same quantity of motion in it as a musket-ball of one ounce, leaving the gun-barrel with a velocity of a thousand feet in the second. " The quantity of motion in a body is the measure of the force zuhich pro- duced it." The experiment of the balls of clay mentioned above furnishes one instance of this truth. Again, a body falling for ten seconds, acquires ten times as much velocity as by falling for one second; its motion thus measuring the force of gravity which has been exerted upon it. ^V hen a large body or mass of many atoms falls, it of course has as much more motion than a smaller body, as there are more atoms in it than in the smaller: but as gravity acts equally on every atom, the force causing either body to fall is still exactly indicated by the quantity of motion in it. A large body or mass of many atoms falls, where there is no impediment, with the same velocity as a smaller body or a single atom; for gravity pulls equally at each atom, and must overcome its inertia equally, whether it be alone or with others. This remark contradicts the popular opinion, that a large and heavy body should fall to the earth much faster than a small and light one ; an opinion which has arisen from our constantly seeing such contrasts, as the rapid fall of a gold coin, and the slow descent of a. feather. The true cause of the contrast is, that the atoms of the feather are much spread out, so as to be more resisted by the air than those of the gold* If the two be let fall toge- ther in a vessel from which the air has been extracted—as in the common air-pump experiment, they arrive at the bottom in exactly the same time: and even in the air, if the coin be hammered out into gold leaf, it will fall still more slowly than the feather. One brick dropped from a height, be- cause its motion is not much affected by the air, reaches the earth very nearlv 5 54 MOTIONS AND FORCES. as soon as ten bricks let fall near it, whether they be connected or separate —as a single horse may reach the goal as soon as ten horses galloping abreast. A man's force will move a small skiff quickly, a loaded batge very slowly, and a laro-e ship in a degree scarcely to be perceived. In each case, however, the quantity of motion may be the same, and a true measure of the force which produced it. . A ball of one pound weight, impelled by a given force, moves twice as fast as a ball of two pound' impelled with the same; yet, although the velocities are different, the quantities of motion, as ascertained by the rule already given, are equal, and indicate an equality of producing force. " The quantity of motion in a body is the measure also of the force or mo- mentum which it can exhibit again." (See the Analysis, p. 42.) Bodies, owing to their inertia, may be regarded as passive reservoirs of force or motion, always ready to return as much as they have received. Mo- mentum is the name given to the motion in a body, with reference to the production by it of new motions or the overcoming of resistances, and is but another term for the quantity of motion. A cannon-ball, according to the quantity of motion in it, may have only the force or momentum that will bruise a plank, or it may have enough to penetrate a tree, or even to shoot its rapid way through a block of the hardest stone. A block of wood, floating against a man's leg with moderate velocity, would be little felt; but a loaded barge, coming at the same rate, and pressing it against the quay, might break the bones ; a large ship, again, although mov- ing no faster, would crush his body against any fixed obstacle ; and an island of ice, opposed in its approach to another, even by a first-rate man-of-war, would destroy it, as meeting barges destroy a floating egg-shell. A hail-stone falling, strikes rudely; a stone rolled from a height, as of old, by the besieged against besiegers, may carry death with it to many; an avalanche, breaking from its hold on a mountain steep, may sweep away a village. To meeting bodies, the shock is the same, whether the motion be shared between them or be all in one. If a running man come against a man who is standing, both receive a cer- tain shock. If both be running at the same rate in opposite directions, the shock is doubled. In some such cases, as where swift skaters have met, the shock has proved fatal. The meeting fists of boxers not unfrequently dislocate or break bones. A man's skull is fractured as certainly by its being dashed against a tree or beam, while he is on a galloping horse, as by the blow of a similar beam com- ing upon him with the velocity of the horse. When two ships in opposite courses meet at sea, although each may be sailing at a moderate rate, the destruction is often as complete to both as if with a double velocity they had struck on a rock. Many melancholy in- stances of this kind are on record. In the darkness of night a large ship has met one smaller and weaker, and in the lapse of a few seconds, have followed the shock of the encounter, the scream of the surprised victims, and the hor- rible silence when the waves had again closed over them and their vessel for ever.—In November, 1S25, on the coast of Scotland, the Comet steamboat was thus destroyed, and carried to the bottom with her about seventy passen- DIRECTION OF FORCES. 55 Fig. 3. gers, into whose ears the drowning water rushed before the sounds of ar- rested music and joy had died away. " Direction of the force or forces producing motion." When only one force acts on a body, the body obeys in the exact direction of the force. A ball floating in water, or lying on smooth ice, is driven exactly south by a wind blowing to the south. A bullet issues from the mouth of a cannon, in the direction of the axis of a cannon—which is, as the force impels it. When two or more forces, not in the same direction, act upon a body at the same time, as it cannot move two ways at once, it holds a middle course between-the directions. This course is called the resulting direction, viz., resulting from the composition of the forces. A ball or ship moving south by a direct wind, may, at the same time, be carried east, just as fast, by a tide or current moving east; every instant, therefore, it will go a little south and a little east, and really will describe a middle line pointing south-east. These particulars may be well represented on paper, as by fig. 3: where b is the original place of the ball or ship, e the east, s the south, and b a the middle line pointing to the south-east, and showing the true course of the vessel. This figure is called the parallelogram of forces, and is an important help to the understanding of many facts in natural philosophy. The minute investigation of the subject belongs to the sci- ence of measures, or technical mathematics ; but the gene- ral truths are quite intelligible to common sense, or the mathematics of common experience. When two forces act upon a body, like the wind and tide in the last example, the result is the same, whether they act together or one after the other. For instance, if the wind drive a vessel one mile south, as" from b to s, fig. 3, and immediately afterwards the tide drive it one mile east, as * to a, the vessel will be in the same place at last, viz., at a, as if she had been driven at once south-east, in the line b a, by the simultaneous action of the two. Therefore by drawing the lines b s and b e to represent the force and direction of the two causes of motion, and by then adding one of them, or an equivalent, to the end of the other, as s a to b s, or e a to b e, the square or parallelogram is sketched, of which the middle line or diagonal, as it is called, shows the resultant of the forces, and the true course of the body obeying them. What is thus true of the effect of continued forces like wind and tide is true also of momentary impulses, like the blows of clubs simultaneously strik- ing a ball, or of two billiard-balls striking a third. When the forces exactly cross each other, and are equal, as in the case of Fig. 4. Fig. 5. '^^ 56 MOTIONS AND FORCES. the ship above supposed, the figure becomes a square, as at fig. 3 ; but if one of the forces be greater than the other, the figure becomes oblong, as at fig. 4; if the forces cross obliquely, the figure becomes as at fig. 5 ; and if they cross in an opposing direction, it will be as at fig. 6. In all the cases, however, the diagonal still shows the result. It is evident that the same line may be the diagonal of many figures, as seen in b a at fig. 7; and therefore, that very different degrees and directions of combined forces may produce the same result. Forces crossing each other so obliquely as to be represented by lines drawn in almost opposite directions, would form a parallelogram having scarcely any breadth, that is to say, the diagonal would approach to nothing ; showing thus, that opposing forces neutralize or destroy each other. In fig. 6, by reason of this crossing, the resultant is less than either of the constituents. And for the same reason, when forces cross so acutely as to advance nearly parallel to each other, the resultant is longer than either, as seen in fig. 5. Forces directly opposed, or entirely agreeing in direction, give as their result- ant their difference or their sum , Forces crossing each other directly, or at right angles, as is true of the exactly eastward force b e, and the exactly southward force b s, in figures 3 and 4,—do not in the slightest degree neutralize or alter each other, for the body, when arrived at a, is just as far east as it would be at e, and as far south as it would be at s. This explains why the progressive motion of the planets in their orbits is not at all affected by the directly crossing centripetal force of gravity which keeps them at their due distances from the sun. In all cases where the two crossing forces are equal, with whatever obli- quity they cross, the resulting direction must be midway between them.— Thus a boat impelled by oars, goes straight, although the direction in which the oars act is constantly changing; because the changing obliquity of the force is always the same on both sides.—This explains also why a bird fly- ing, or a man swimming, holds a perfectly straight course, although in both cases the direction of the impelling forces is constantly varying.—And it explains why a body suspended, as a plummet, or falling to the earth as an apple does from a tree, is always in a line towards the centre of the earth: for, while the part of the earth immediately under the body is pulling it straight down to the centre, the action of parts on any one side of the perpendicular is exactly counterbalanced by the action of corresponding parts on the opposite side ; and the perpendicular is still the diagonal or middle line of every pair of attracting parts. In fig. 8, b a represents the common dia- gonal. In speaking of the attraction of our earth, therefore, which really is the united attraction of all the individual atoms, we may always consider it as a single force acting towards the centre of the earth. When a body is carried below the surface of the earth, its weight becomes less, because the matter then above it is drawing it up, instead of down, as before. A dfescent of a few hundred feet makes a sensible difference, and at the centre of the earth, if man could reach it, he would find things to have no weight at all; and there would be neither up nor down, because bodies would be attracted equally in all directions. When more than two forces act on a body, the resulting direction may be found, first of two, and then of the last resultant with each of the others successively ;—or the forces may be represented on paper by lines tacked together, of which one denotes the strength and direction of each: the ex- DIRECTION OF FORCES. \ 57 tremity of the last line will mark the place of the body after being acted upon by the combined forces. A sailor, to know the true place of his ship and the course which she has steered, considers, first, the forward progress as found by the log, then the leeway or sideward motion produced by a cross wind, and then the effect of any tide or current in which he may be sailing-. Fi-. 9. Resolution of Forces is a phrase pointing to another important use of such parallelograms or figures as have just been described, viz., the enabling us, when force or motion is given, to find the forces or motions in any other directions of which it may be the resultant, and those into which it may itself be resolved. Thus, if a line b a (in any of the preceding figures 4, 5, 6, &c.) repre- sent a force or motion,4and the line b s represent one of two elements com- posing it, we have but to complete the parallelogram b s a e to obtain the other line, b e representing the only other force or motion which, combined with the first element, can produce the given resultant.—If a ship pass from b to a (fig. 5) while sailing through the water eastward, a distance expressed by b e, she must at the same time have been carried by a tide current to the dis- tance and in the direction marked by the line b s. Again, if a line be given representing a single force, or motion, as b a, and if it be desired to know how much there is in this capable of acting in another direction, as b d; it is only necessary to draw a line in the direction b d, from the commencement of b a, and to cut such line by another drawn directly upon it—or at right angles to it, as the term is, from the other end of b a: the length of b d, so cut off, viz., b s, shows the proportion required. It is thus that a sailor who knows how far he has sailed in any oblique direction, finds out how much he has gone north and east or south and west; in other words, finds out the difference in latitude and longitude between his present place and a former one. In the above figure, b a may represent the course and distance sailed, b s the difference of latitude, and b e the differ- ence of longitude. Thus again, if a ball b strike a table a c, with velocity and direction, both represented by the line be; and if the ball be supposed afterwards with the same velocity to approach the table in the oblique direction e c, it will then strike with as much less force than before, as the line e a is shorter than e c. For e a is found, according to the rule for decomposing a force, given above ; and, to common sense, it is obvious, that if the whole velocity of the ball be represented by e c, the rate of approxi- mation towards the table, or merely downward velocity, and therefore the downward force is marked by the line e a. The body only falls through the distance e a while moving all the way from e to c. Figure 10, explains the important cases of the force of wind upon ships' sails, windmill vanes, &c; and the force of water upon float-boards, wa- ter-wheels, &c; showing that the moving mass exerts force upon a sur- Fig, 10. 58 MOTIONS AND FORCES. face not in proportion to the speed with which it may be passing along or near the surface, but to the rate of perpendicular approximation. It explains also, why the slanting blow of a club or ball is so slight, compared with the direct blow. " The two great forces of Nature are Attraction and Repulsion." (Read the Analysis.) A person, on first approaching this subject, is far from supposing that the beautiful and almost endless variety of phenomena exhibited m the universe around, are all referrible to the two principles, attraction and repulsion, exa- mined in the first section:—but such is the truth.—It will first be shown here, how the great classes of accelerated, retarded, and bent motions arise from them. Attraction.—Until Newton said, that what we call weight of bodies is merely an instance of that universal attraction of matter which diminishes with increasing distance, it was never suspected that weight was less, high up in the air than on the ground ; or on a lofty mountain than on the sea- shore. But this we now know to be the case. However, in studying what goes on in obedience to gravity near the surface of the earth, except in few very nice cases, gravity may be considered as a uniform power ; for man has neither approached the centre of the earth in mines, nor receded from it in balloons, by more than about a thousandth part of his distance from it; and weight has relation to the distance from the centre, not to the distance from the surface. "Accelerated Motion from Gravity." Owing to the inertia of matter, any force continuing to act on a mass which is free to obey it, produces in the mass a quickening or accelerated motion: for as the motion given in the first instant, continues afterwards without any farther force, merely on account of the inertia, it follows, that as much more motion is added during the second instant, and as much again during the third, and so on. A falling body, therefore, under the influence of attraction, is, as it were, a reservoir, receiving every instant fresh velocity and momentum. It is said that Newton's sublime genius read the nature of attraction in the simple incident of an apple falling before him from a lofty branch in his gar- den.—The eye which perceives an apple beginning to fall, can follow it for a time and mark the gradual acceleration of its descent, but soon sees its path only as a shadowy line. A boy letting a ball drop from his hand, can catch it again in the first in- stant, but after a little delay his hand pursues it in vain. A fragment of rock, detached from the brow of a hill by the lightning stroke, begins its motion slowly; but once fairly launched, it gathers fresh speed and momentum with every instant, and bounds from steep to steep driving every obstacle before it. Any liquid falling from a reservoir, forms a descending mass or stream, of which the bulk diminishes from above downwards, in the same proportion as the velocity of the particles increases. This truth is well exemplified in the pouring out of molasses or thick syrup : if the height of the fall be consi- derable, the bulky sluggish mass, which first escapes, is reduced, before it reaches the bottom, to a small thread : but the thread is moving proportion- ately faster, and fills the receiving vessel with surprising rapidity. The same truth is exhibited on a vast scale in the Falls of Niagara; where the broad MEASURE OF ATTRACTION. 59 river is seen first bending over the precipice a deep slow moving mass, then becoming a thinner and a thinner sheet as it descends,until at last, surrounded by its foam or mist, it flashes into the deep below, apparently with the velo- city of lightning. When velocity becomes considerable in any case of falling, it cannot be measured accurately by the eye, but its effects ascertain it. A man leaps from a chair with impunity, from a table with a shock, from a high window with fracture of his bones, and in falling from a balloon his body is literally dashed to pieces. The force of gravity or general attraction is such at the surface of this earth, that, in the first second of time, it gives to a body allowed to fall a velocity of 32 feet nearly per second, that is, a velocity which, remaining uniform from the end of the second, would carry it, without farther action of gravity, through 32 feet in the next second. Yet the body falls only 16 feet in the first second; and the reason is, that the velocity of 32 feet pos- sessed at the end of the second is gradually acquired, the body having only half of it at the half second, and as much less than half at any distance be- fore that time, as it has more than half at the same distance afterwards; and the average, therefore, is only half of the 32, or 16 feet in the whole second. In the next second, it falls of course through the whole 32 feet, with 16 additional, from tr-he new action of gravity, in all three times as much as in the first second; and in two seconds, therefore, it falls altogether four times as far as in one second. At the end of two seconds the velocity is doubled, or is 64 feet per second, so that in the third second the body falls 64, and other new 16, in all, five times as much as in the first second; and in three seconds, therefore, it has descended nine times as far as in one second, &c. Knowing this progress, the velocity acquired by a falling body, and the dis- tance through which it falls, in any given time, are easily calculated; and the height of a precipice, or the depth of a well, may be ascertained by marking the time required for a body to fall through the space. The doctrines of falling bodies are of such importance in the minute exami- nation of many of the phenomena of nature, that much attention has been bestowed upon them. Mr. Atwood's ingenious contrivance by which the motion of falling bodies may be retarded in any desired degree, without the character of the motion being otherwise altered, has enabled experimenters to render evident to the senses all that abstract calculation had anticipated. A pound weight, left quite free, falls towards the ground sixteen feet in the first second, proving that attraction of one pound is just sufficient to overcome the inertia of one pound at that rate. But if the inertia were doubled, or • tripled, or increased in any other degree, the fall of course would be just so much slower. Now Mr. Atwood's machine in effect increases it, by causing falling weights to overcome not only their own Fig. 11. inertia, but also that of other weights ; fig. 11. Thus, a and b, being weights of two pounds each, balancing each other over the very easily turned pulley c, are moved by a weight of one pound d, hooked to one of them; and gravity in pulling this down, with force of one pound, has to overcome, not the inertia of one pound, but of five, for the other two weights must move as fast as the one pound does; and thus, the velocity being re- duced to one-fifth of what is natural to a falling body, the descent can be minutely observed. The experiments with Atwood's machine may be varied exceedingly, and they are most inte- resting. 7J a* 60 MOTIONS AND FORCES: "Retarded Motion," from gravity. What has been said of the changing velocity of a falling body, from gra- vity, is exactly true, in a reversed way, respecting a rising body exposed to the same influence. , . . A bullet shot directly upwards, every instant loses a part of its velocity, until at last it comes to rest in the sky,—where a soaring eagle might see the messenger of death motionless and harmless for a moment by his side :—the ball then descends again, and so that, at corresponding points of the ascent and descent, but for the resistance of the air, the velocities would be equal; and, on reaching the ground, it would have acquired exactly the velocity with which it first departed. It is explained in a preceding paragraph, that a body falls four times as far in two seconds as in one, although the velocity at the end of two seconds is only doubled. For the same reason, a body shot upwards with double velo- city rises four times as far as if shot with a single velocity; if shot with triple velocity, it rises nine times as far, and so forth. In aiming for amusement at bodies thrown up into the air, it is easy to hit them near their point of turning, and more difficult always as they are nearer to the ground, whether rising or falling. An upward jet of water is small below, where it issues fwm the pipe with great velocity, but it becomes more bulky as the water loses velocity in ascending, and at the top, it often spreads a little like a palm tree, and any light round solid will continue supported and playing upon its summit. The rise of a pendulum from the bottom of its arc, is an exact copy, re- versed, of its previous descent to that point. " The Pendulum" exemplifies well both accelerated and retarded motion. The name is appli- cable to any body so suspended, that it may sAving freely backwards and forwards. When such a body is made of certain form and length, although so simple, it is one of the most admirable contrivances of man's ingenuity. Galileo having observed the hanging chandeliers of lofty ceilings to con- tinue vibrating long and with singular uniformity, after any accidental cause of disturbance, was led to investigate the laws of the phenomenon; and out of what, in some shape or other, had been before men's eyes, but uselessly, from the beginning of the world, his powerful genius extracted the most important results. Independently of the light which the theory of the pen- dulum has thrown on various branches of physics, the instrument itself, with a few wheels attached, to record its vibrations, has now become the perfect time-keeper, regulating many of the affairs of men. A common pendulum consists of a ball, fig. 12, as a suspended by a rod from a fixed point as b, and made to swing F,S- l2- backwards and forwards, or to vibrate un- , der this point. Being raised toe,and then set at liberty, it falls back to a with an ac- celerating motion like a ball rolling down a slope, and when arrived there, it has just acquired momentum enough to carry it to d, at an elevation on the other side; from this it falls back again, again to rise; and would so go on for ever, but for the impedi- £s ments of air and friction.—The pendulum is strictly an object of mathematical study; & f PENDULUM. 61 but we shall give a general idea of its important characteristics in common language. 1. The times of the vibrations of a pendulum are very nearly equal, whe- ther it be moving much or little, that is to say, whether the arc described by it be large or small. This remarkable property is what makes it a time- keeper. The reason that a large vibratian is performed in the same time as a small one, in other words, that the pendulum always moves faster in pro- portion as its journey is longer—is, that in proportion^as the arc described is more extended, the steeper are its beginning and ending, and the more rapidly, therefore, the pendulum falls down at first, sweeps along the intermediate space, and stops at last. It is evident, for instance, that the portion c e of the arc (fig. 12) is much more steep than the equal portion e a.—A pendulum made to vibrate in the curve called a cycloid, which, in the central part, very nearly coincides with a circular arc, but towards the extremity Mses a little more steeply, has its beats perfectly isochronous, or in equal times, whatever their extent. A common clock is merely a pendulum with wheel-work attached to it, to record the number of the vibrations, and with a weight or spring having force enough to counteract the retarding effects of friction and the resistance of the air. The wheels show how many swings or beats of the pendulum have taken place, because at every beat, a tooth of the last wheel is allowed to pass. Now if this wheel has sixty teeth, as is common, it will just turn round once for sixty beats of the pendulum, or seconds, and a hand fixed on its axis projecting through the dial-plate, will be the second hand of the clock. The other wheels are so connected with the first, and the numbers of teeth on them so proportioned, that one turns sixty times slower than the first, to fit its axis to carry a minute hand, and another by moving twelve times slower still, is fitted to carry an hour hand. 2. The length of a pendulum influences the time of its vibration.—Long pendulums vibrate more slowly than short ones, be- cause, in corresponding arcs or paths, the hob or ball Fig. 13. of the long pendulum has a greater journey to per- .-, form, without having a steeper line of descent. If a /j pendulum b a be twice as long as another reaching / ! from b to e, it has twice as much to fall in its descend- d^/ X? ing arc c a, as the other in its arc d e, while in cor- /-*■•-.".....v}': responding parts of the two paths, the slope or inch- / .......\e nation is always equal:—the ball of the long pendulum j/ may be considered as having rolled twice as far down (&j.....................?...... J? a given slope as the ball of the short pendulum. Now \... as a body falls four times as far, either directly or on *'"-•-.... ^—s. any uniform slope, in two seconds, as in one, a pendu- ~^ lum must be four times as long, to beat once in two seconds, as to beat every second. A pendulum of a little more than 39 inches beats seconds; one of four times the length is required to beat double seconds, and one of one-fourth the length to beat half seconds.—As a pendulum to answer its purpose must be of invariable length, one which beats seconds constitutes an easily found standard of measure. ' Because the smallest change in a length of a pendulum alters the rate of going of the clock, it is important to be able to counteract the dilatation or con- traction of pendulums caused by the changing heat of the seasons ; and for this purpose various ingenious means have been contrived. One of the best of these is the gridiron pendulum, as it is called, from consisting of various 62 MOTIONS AND FORCES. Fig. 14. met 1 j? Od i rods of metal. It renders the different dilatability by heat of two metals composing it, the cause of unchanged length in the whole. The adjoining sketch may show that if the central rod of brass represented by the strong line from b to c, dilate alone just as much as the two rods of steel, represented by the weaker lines on either side of the other* dilate together (the expansion of brass by heat is about double that of steel,) it will exactly counteract the lengthening of these, and will keep the ball d always at the same distance from the point of suspension a. Some astronomical clocks in the present day are so perfect that they do not err one beat of the pendulum in a year. Common clocks are regulated by a screw which lifts or lets down the ball of the pendulum, and so changes the effective length, that is, the distance between the • point of suspension and what is called the centre of oscillation, treated of in the next chapter. 3. The force of gravity, of course, is what determines how long the pen- dulum shall be in falling to the bottom of its arc, and how long in rising, for the ball of the pendulum, as already stated, may be considered as a body descending by its weight on a slope ; a change in the force of gravity, there- fore, would at once alter the rate of all the clocks on earth. At the equator of our earth, where the gravity of bodies is counteracted in a small degree by the centrifugal force arising from the earth's motion (as explained at page 53,) a pendulum vibrates more slowly than elsewhere, and must therefore be made shorter to answer the same purpose. Corresponding results take place when a pendulum is carried to a mountain top, and therefore farther away from the centre of the earth, which is the centre of attraction—or when car- ried to the bottom of a mine, where it is attracted by the matter above it, as well as by the matter beneath. The popular prejudice refuted at page 53, that a large or heavy body should fall to the earth, even in a vacuum, more quickly than a small or light body, attaches itself also to the case of a heavy and a light pendulum. Now there is no difference for pendulums of the same length, whatever their weight or material, but what depends on the resistance of the air. It is a very remarkable fact thus proved, that in all substances the gravity and inertia perfectly agree. There is a small pendulum called a metronome, used by musicians for marking time ; which, although very short, may still be made to beat whole seconds, or even longer intervals. The reason of its slow motion is, that its rod is prolonged beyond its axis of support, at a, up- wards, to b, and has a ball upon the top at b, as well as on the bottom at c; which upper ball prevents the under one from moving so fast as it otherwise would, just as a small weight attached to one end of a weighing-beam, prevents a greater weight attached to the other end from falling so fast as it would if there were no counterpoise. The rate of motion changes with any change in the dis- tance of the ball b from the centre of motion a; and to allow of such change, the ball b is made to slide. A pocket-watch differs from a clock in having a vibrating wheel instead of a vibrating pendulum ; and as, in a clock, gravity is always pulling the pendulum 'down to the bottom of its arc, which is its natural place of rest, but does not fix it there, because the momentum acquired during its fall 15. "a PENDULUM. 63 from one side is just sufficient to carry it up to an equal height on the other —so in a watch, a spring, generally spiral, surrounding the axis of the ba- lance-wheel is always forcing this towards a middle position of rest, but does not fix it there, because the momentum acquired during its approach from either side to the middle position, carries it just as far past on the other side, and the. spring has to begin its work again. The balance-wheel at each vibration allows one tooth of the adjoining wheel to pass, as the pendulum does in a clock, and the record of the beats is preserved by the wheels which follow, as already explained for the clock. A main-spring is used to keep up the motion of a watch, instead of the weight used in a clock ; and as a spring acts equally, whatever be its position, a watch keeps time although carried in the pocket or in a moving ship. As the rate of a clock is influenced by the length of its pendulum, so is the rate of a watch by the size or diameter of its balance-wheel; and heat, which retards the motion of a common clock by lengthening the pendulum, retards the motion of a common watch by dilating the balance-wheel. Inge- nuity, however, has found a remedy for the latter case as for the former, viz., the contrivance called the expansion balance-wheel. Of this the circum- ference, instead of being a continuous ring, is made up of two half-rings, each attached by one end only, to a cross-bar, and which half-rings being of brass on the outside and of steel within, bend or curl inwards by heat—as a sheet of damp paper bends when held to the fire—and thus diminish the size of the wheel at their loose extremities, so as just to counterbalance its increase by the expansion of the cross-bar. As the motion of a pendulum has relation to the force of gravity, so has the motion of a balance-wheel to the stiffness of the balance-spring; and the regulator of a watch is merely a pin which bears against the balance- spring, and by sliding backwards or forwards, so as to shorten or lengthen the part of the spring left free to act, changes the degree of its stiffness. A change produced by the variation of temperature is compensated for by the expansion-wheel described above. It would be exceeding the limit marked out for this general work, to speak more particularly here of those admirable watches which have been pro- duced within the last thirty years under the name of chronometers, for the purpose of ascertaining the longitude at sea; but. the author may perhaps be excused for mentioning a moment of surprise and delight which he expe- rienced, on first seeing their singular perfection actually proved. After months spent in a passage from South America to Asia, his pocket chrono- meter, with others on board, announced one morning that a certain point of land was then bearing east from the ship at a distance of fifty miles ; and in an hour afterwards, when a mist had cleared away, the looker-out on the mast gave the joyous call of "Land a-head !" verifying the report of the chronometers almost to a mile after a voyage of thousands. It is natural, at such a moment, with the dangers and uncertainties of ancient navigation be- fore the mind, to exult in contemplating what man has now achieved. Had the rate of the wonderful little instrument in all that time been changed even a little, its announcement would have been worse than useless,—but in the night and in the day, in storm and in calm, in heat and in cold, while the persons around it were experiencing every vicissitude of mental and bodily condition, its steady beat went on, keeping exact account of the rolling of the earth and of the stars ; and in the midst of the trackless waves it was always ready to tell its magic tale of the very spot of the globe over which it had arrived. The mode of using a chronometer for so valuable a purpose will be explained in the section on astronomy. 64 MOTIONS AND FORCES. Bent or curvilinear motion from attraction.—This takes place when- ever attraction is acting across the path of any existing free motion. The flying cannon-ball or stone, drawn down by gravity, is an example, for the projectile force ceases with the first impulse, but the bending force is acting, every instant, and by every instant producing a new effect, causes a curvili- near path. An oblique jet of water is to the eye a permanent exhibition of the curve described by a body thus projected. The particles of the liquid move in the line which they would describe if projected singly and the continued succession of them marks the line of situations through which each passes in its course to the earth. A cannon or musket-ball, shot quite horizontally over a level plain, will touch the ground or plain just as soon as another ball dropped at the same instant directly from the cannon's mouth; for the forward or projectile mo- tion does not, in such case, at all interfere with the action of gravity. This result, which most persons, before consideration, would be disposed to doubt, makes strikingly sensible the extraordinary speed of the cannon-ball; viz., that it has already moved, perhaps, six hundred feet forward, during the half second that a ball dropped from the hand of a standing person requires to reach the earth only four feet beneath. This fact also explains why, for a long range, the guns must be pointed more or less upwards. A dozen marbles swept horizontally from off a table by a stick, all reach the floor at the same instant, how different soever the distances to which they may respectively be driven. The particular study of the subject projectiles is very important to military engineers ; and we know how successfully they have pursued it, by the pre- cision with which they now direct their shot and shells to objects at very great distances. A cannon-ball shot horizontally from the top F'S- '6- of a lofty mountain, would go three or four miles. (The mountain is here represented on an enlarged scale, as standing on the globe b, c, d, at a.) If there were no atmosphere, to resist its motion, or if the mountain top were above the surface of the atmosphere, the same original velocity would carry it thirty or forty miles be- fore it fell, as to b : with more force still, it would reach to c, and with still more to d. And if it could be dispatched with about ten times the velocity of a common cannon-shot, it would not have approached nearer to the earth than at first, even when it had again reached round e or to a; and its velocity being undiminished, it would perform a second similar tour, and then a third, and so forth : it would, in fact, have become. a little satellite, or planetary body, revolving round the earth. In the suc- cessive ranges represented in the figure, it is seen that the centrifugal force of the ball, or its tendency to move in a straight line, becomes more and more nearly a counterbalance to gravity, and at last is exactly equal to it. If he force given to the ball were more than sufficient to bring it round again to the level of a, it would for a time fly off, or increase its distance from the earth, acquiring somewhat of the eccentric motion of a comet. There may really be such revolving masses above our atmosphere, although invisible to us, owing to their smaUness. It has been supposed by some, that the PROJECTILES. 65 meteoric stones, which fall to the earth every now and then, come from such bodies, or are the entire masses, having become entangled in our atmosphere, so as to lose their forward velocity. The four little planets discovered lately beyond the orbit of Mars, are not larger than a six-thousandth part of our earth. Repulsion,—produces accelerated, retarded, and bent motions, like attrac- tion, but it acts only at minute distances, while attraction draws from the sun, or from the very limits of the universe; repulsion acts, for instance, be- tween the adjoining atoms of an elastic fluid. Yet repulsion plays a part in the economy of nature, not at all inferior to its sister attraction. We have already seen, when considering the constitution of masses in section first, that repulsion prevents or modifies the contact of the atoms of all bodies; that with increase of temperature, it causes these atoms to separate, and of a solid forms a liquid, or even an air; that it operates around all masses as if it were a film or covering, preventing their mutual cohesion, &c. &c. Accelerated motion from repulsion is seen when the atoms of gunpowder explode and propel the bullet from the bottom of a piece to the muzzle with such rapidly increasing velocity. The strength of this repulsion of gun- powder is so much greater than the strength of gravity or common attraction, that its action on a bullet, during the passage along a barrel of five or six feet in length, may not be overcome by gravity, during an ascent of a mile or more. A visible retarded motion from repulsion is exemplified by a moving body coming against a spring or a bladder full of air, or against the piston-handle of an air-syringe, so as to compress the air beneath it. Any elastic body striking against another body and recoiling, exhibits in conjunction the phenomena of retardation, acceleration, and often also of bending, chiefly from repulsion ; for instance: An ivory ball driven forcibly against a marble slab, does not stop at the instant that apparent contact takes place, but still advances and compresses that part of the substance which is against the marble,—«as is proved by the facts mentioned at page 37. While this compression of the ivory is going on, the resistance made by the increasing repulsion of the particles gradually retards, and ultimately destroys the forward motion of the ball; and at the instant of its final arrest, the parts in contact, both of the ball and of the mar- ble, being in their greatest degree of compression, act on the ball, and repel it again with gradually accelerating motion, until it leaves the marble with the same velocity which it had on approaching. The retardation and acce- leration take place here within so small a space, and in so short a time, that they are not apparent to sense, but the mind perceives the nature of the phe- nomenon as distinctly as if the ball had rolled against the end of a long steel spring.—If the ball strike the marble obliquely, as from a to c, in a path form- ing the angle a cd with a perpendicular line, it does not rebound in the same line by which it approached, but just as obliquely to- wards the other side, viz. from c to b; and it then exhibits a.bent motion from repulsion. This case illustrates also the " resolution of motions,*' for the oblique descent a c being composed of a direct downward motion from a to the table, and a horizontal or forward motion from a to- wards the perpendicular, the table destroys the down- ward motion and converts it into an opposite directly upward motion, but it does not affect the forward mo- tion, which immediately combines again with the up- 66 MOTIONS AND FORCES. ward and carries the ball as far beyond the perpendicular at 6 as it was dis- tant from it at a. The important law in physics, of which this case is an example, is usually expressed—"The angles of incidence and of reflection are equal." It applies to all reflected bodies, as balls, waves, sound, light, IT the ivory ball and marble, in the above case, were supposed to be both perfectly hard, and without elasticity, still the repulsion which surrounds all bodies, as a thin covering, preventing their cohesion (see page 32,) would act exactly as the real elasticity of the ivory, and would cause a retarded motion until perfect rest came, and then an accelerated motion back again, until the ball recovered its primitive velocity. Collision between hard bodies always exhibits more or less of the truth now described: when it occurs between soft bodies, as lumps of lead or of moist clay, the approaching parts mutually displace each other, and there is no recoil. . . When a straight steel plate, of which the end is fixed in a block, is bent, as by a ball rolling against it, the particles on the side which becomes con- cave are made to approximate, and there is a resistance or repulsion gradu- ally increasing among them; the particles on the convex side, again, are drawn a little more from each other, and are therefore exertirig attraction to return: the recoil of the spring is thus owing to both forces trying to replace the particles in their former relative situations. " Tides, Winds, fyc, exemplify Attraction." (Read the Analysis, page 42.) Until we reflect attentively on this subject, we are far from perceiving that all the phenomena of nature are only instances of attraction and repulsion acting under a variety of circumstances. Attraction.—Tides are raised by the attraction of the moon and sun, and fall again by the general attraction of the earth; producing in many of the shallower parts of the ocean very rapid horizontal currents. They do a great deal of work for man. They carry his ships along the coasts, and up and down the rivers; they turn water-wheels for him; they fill his docks and canals at convenient times; they rise to receive his ships, launched from ele- vated building-yards, &c. What a busy scene, is a great sea-port river, dur- ing the rising and falling of the tide—with the thousands of people along its banks, borrowing assistance in their various occupations! Winds are produced chiefly by the fluid atmosphere seeking its level, in obedience to the attraction of the earth, after the action of disturbing causes, such as the heat of the sun, &c. They help man in the important business of navigation; they turn his windmills, &c. The currents of rivers are water constantly descending on slopes, that is, regaining its level, in obedience to the earth's attraction. Water-mills and inland navigation are among the advantages which they afford to man. , All falling and pressing bodies exhibit attraction in its simplest form. Repulsion—is instanced in explosion, steam, the action of springs, 8fC. Explosion of gunpoAvder is repulsion among the particles when assuming the form of air. Steam,by the repulsion among its particles,moves the piston of the steam- engine. In our days it performs half the labour of society. Accidental explosions of fire-damp, or hydrogen in mines, and the tre- / PRODUCTION OF GREAT VELOCITIES. 67 mendous evolutions of elastic fluid in volcanoes and earthquakes, are other instances of the same class. Elasticity, as seen in springs, collision, &c, belongs chiefly to repulsion; as seen in India-rubber, and other substances resuming their usual length after extension, it belongs chiefly to attraction. A spring is often, as it were, a reservoir of force, kept ready charged for a purpose ; as when a gunlock is cocked, a watch wound up, &c. It will be remarked, with respect to many of the phenomena now and here- after to be mentioned, that it is not the original Attraction or Repulsion which man uses as his servant, but the momentum gradually accumulated in masses by the exertion of such attraction or repulsion ; in other words, the inertia is used as a great working power or force. Electrical, galvanic, magnetical, and optical phenomena, are also in great part peculiar attractions and repulsions, as will be seen in the chapters devoted to the explanation of them. And even the actions of animals, so infinitely varied, are all results of a shortening of the fleshy threads called muscular fibres, which is produced by the mutual attraction of their component parti- cles ;—just as the varied motions of a telegraph, or of a ship's yards, are pro- duced by the shortening of certain ropes of connection. , However closely allied the last-mentioned particular attractions and repul- sions may be to the general attraction and repulsion formerly treated of, it is found convenient to consider them apart. In the remarkable phenomena of nature and art, all the motions being caused, as now shown, by Attraction and Repulsion, these forces do not operate by a single impulse, but through a repetition of impulses, or a continued action, of which the effect is gradually accumulated in the inertia of matter. Thus all great velocities and momenta are the terminations of an accele- rated motion. Meteoric stones, falling from great heights, bury themselves deep in the earth by the force of their gradually acquired velocity. When the w*bod-cutters among the Alps launch an enormous tree from high on the mountain side, along the smooth wooden trough or channel prepared for it, and in fewer minutes than it traverses miles, it is seen plunging into the lake below ; it acquires its frightful velocity, not at once, but through the action of gravity continued during the whole of its descent. The shock or blow of the ram of a pile-engine, is not the effect of momen- tary attraction between it and the earth, but of that attraction accumulating motal inertia or power, during the descent of the ram through a space of twenty or thirty feet. A common hammer, in its instantaneous shock, has the condensed effect of the arm and of gravity, as accumulated through its whole previous course; and when a powerful blow is intended, the hammer, or hatchet, or club, or fist in boxing, is lifted high, or carried far back, that there may be time and space for imparting greater power. The inferior animals, by many of their actions, illustrate the same truth, and prove their experimental or instinctive acquaintance with it. Sea-birds carry shell-fish up into the air, and drop them on smooth stones to break them, and to obtain the food. It is related in Grecian story, that a bird once mistook the venerable bald head of a sage meditating on the sea- \ gg MOTIONS AND FORCES. shore for a smooth stone, and by the same act killed an oyster and the philo- S°¥here are some long-necked birds,that fight and kill their prey by a blow of their beak. They draw back the head, bending the neck like a swan or serpent, and then dart it forward, with a continued effort, until the strong wedge-like beak reaches its destination, almost with the volocity of a pistol bullet. One snake in darting its fangs at another passing swiftly across its coil, has been known to miss its aim and inflict a mortal wound on its own flesh. Bulls, rams and goats, in fighting, alternately recede and run at each other, that the shock may be great when their foreheads meet. A horse in kicking* from the great length of his leg, and the consequent space through which he can be adding velocity to his foot, drives it at last against the object almost like a cannon-shot. A bow-string propelling an arrow, follows it through a considerable space, and so gives the great velocity at last produced. A sling gives to the hand the power of adding velocity to the stone through a long path ; for the hand moves in a small circle while the stone moves in a larger, and the hand being kept always somewhat in advance of the stone, pulls at it without intermission, until the moment of discharge. The battering-rams of the ancients allowed those about them to accumulate in them the efforts of many hands, and of a considerable duration of action, so as to give at last one great and sudden shock. Even the gentle action of the human breath, exerted for a time on a pea or small hard ball of clay while passing through a long smooth tube, gives a velo- city which will inflict a sharp and painful stroke on a distant animal. In Bor- neo and others of the Eastern Islands, poisoned arrows are thrown in this way with great force and precision. The action of gunpowder on bullets, although appearing so sudden, is still not an instantaneous, but a gradual, and therefore accelerating action ; and ac- cordingly we find the effect to depend much on the length of the piece along which the force pursues the ball. A small fast sailing vessel with a single long gun, has often i compelled a very superior vessel, whcse guns were shorter, to yield. For the same reason that all great velocities require continued action or re- peated impulse to produce them, so do they also to destroy them; the inertia of motion and of rest being exactly equal. A vast mass of rock suspended like a pendulum, and allowed to sweep down its curve from a considerable elevation, would arrive at the bottom like a battering-ram, with force sufficient to shake a thick wall or rampart to its foundation. The continued action of gravity would have given this force, and if, instead of the solid resistance supposed, and which would scarcely be sufficient to take the whole momentum away, the mass were merely allowed to continue its course as a pendulum, and to ascend on the other side, the continued action of gravity then opposing its motion, would bring it to pow- erless rest again, by the time when it had reached an elevation equal to that from which it fell. Soft air expanding gives gradually the death-carrying velocity to the can- non-ball ; and soft air, or cotton, or wool, resisting in a close strong tube,-if he bullet could be directed exactly into it—would again gradually annihilate the motion. Were the attempt made, however, to stop the ball suddenly, PRODUCTION OF GREAT VELOCITIES. 69 by a block ol true hardest granite, the block would instantly be riven by its force. Bales of cotton or thick masses of cork, attached round a ship, will receive cannon-balls, and bring them to rest, without themselves suffering much, while the naked firmer side of the ship would be penetrated. The cotton or cork offers an increasing resistance through a considerable space, while the oak opposes its hard front at once, and must instantly suffice or be destroyed. A hard body, that it may at once destroy such a motion as we are supposing., must be able to oppose as much force in perhaps the space of one-hundredth of an inch, that is, in the extent to which its elasticity will let it yield without breaking, as the moving cause gave, through a much greater space (a plate of steel will thus oppose a pistol-bullet;) and when it cannot do this, it must be broken or penetrated by the moving body. It is to be remarked, how- ever, that the continued opposition of a thick mass of wood, stone, or earth, to an entered bullet, brings it to rest at last as any elastic unbroken opposition would. Gunners have ascertained the exact depth in each substance to which a ball will penetrate ; and they call buildings bomb-proof or ball-proof which have a thickness or depth exceeding that. A hempen or silk rope supporting the scale of a weighing beam, would resist a greater weight falling into the scale than would be resisted by an iron chain which were even stronger than the rope for the purpose of bear- ing a quiescent weight: because the hemp or silk would yield by its elasticity, and continue its resistance through a considerable space and time, and thus would at last gradually overcome the momentum ; while the iron, by scarcely yielding at all, would require to be strong enough to stop the mass suddenly or would break. Yet for the same reason that iron is weakest in such a case as the last, it is stronger than hemp or rope when used as a cable for a ship, to withstand the sudden force of waves. This will be understood on consideririg, that the chain by its weight hangs as a curve or inverted arch in the water, while the rope, being nearly of the weight of water, is supported in it almost as a straight line from the anchor to the ship; therefore, when a great wave dashes against the ship, the bent chain will yield until it be drawn nearly straight, by which great extent of yielding, and consequent length of resistance, it will withstand a great shock ; whereas, the straight rope, as it can yield only by the elasticity of its material, and comparatively, therefore, a little way, will resist much less. A heavy ship moving quickly with the tide or wind, could not be stopped instantly by a short rope or chain of any magnitude: if the attempt were made to destroy at once so vast a momentum, something would certainly give way; but a rope of very moderate size, kept tight between the shore and the ship, and from time to time allowed to slip a little round a wooden block, when the tightness threatens its breaking, would accomplish the end very soon and easily. The following are farther proofs that forces are to be measured as much by the time or space through which they act, as by their difference of intensity or momentary power. A door standing open, and which would yield readily on its hinges to the gentle push of a finger, is not moved by a cannon-ball piercing through it. Now the ball really overcomes the whole force of cohesion among the atoms of tough wood : but that force is allowed to act or resist for so short a time, 6 70 MOTIONS AND FORCES. owing to the rapid passage of the ball, that it is not sufficient to affect the inertia of the door, in a degree to produce sensible motion. The cohesion of the circle in the door, cut out by the ball, would have borne a weight of more than a hundred pounds laid quietly upon it, but supposing the bullet to fly twelve hundred feet in a second, and the door to be one inch thick, the cohe- sion being allowed to act for only the 14,400th part of a second, its influence is not perceived. The following are other examples of the same kind. A leaden bullet pressed slowly against a pane of glass, breaks it irregu- larly,' where the strength happens to be least; but the same bullet shot at it from a pistol, makes only a small round hole. It has been amusingly said of such a case, that the particles struck and carried away, have not time to warn their neighbours of what is happening. A cannon-ball, having very great velocity, passes through a ship's side, and leaves but a little mark; while one Avith less speed splinters and breaks the wood to a considerable distance around. A near shot thus often injures a ship less than one from a greater distance. A sheet of paper standing edgeways on a table, is not driven down by a pistol-ball fired through it. The truth at present under consideration explains, with respect to gun-shot wounds, why the man often remains ignorant for a time of his misfortune, and why a rapid bullet only kills the parts which it touches, while a spent ball may bruise and injure all around. In many cases of injury, popularly attributed to the wind of a ball, the ball itself has really touched the part. A man lying down and receiving the blow of a great hammer on his chest, would be killed by it; but if a heavy anvil be first laid upon the chest, and the blow then received upon the anvil, the man bears it with impunity. Here the quantity of motion in the hammer being diffused through the great mass of the anvil, produces but a trifling velocity, which the elasticity of the chest, in its slow yielding, easily overcomes. A circular plate of soft iron, made to turn with extreme rapidity, will cut through the hardest steel file, almost as a knife cuts through a carrot. In cases where a soft powder suffices to polish a hard body, it acts partly like this plate, by the motion or velocity given to the wearing particles. " There is no motion or action in the universe, without a concomitant and opposite action of equal amount." (See the Analysis.) This truth has otherwise been expressed—" action and reaction are equal and contrary."—It is evident, that if no action or movement takes place on earth but in consequence of either Attraction or Repulsion,—and this has now been shown—there must always be two objects or masses concerned, and each must be attracted or repelled just as much as the other, although one will have less velocity than the other, as it maybe itself greater, or fixed to another mass. If a man in one boat pull at a rope attached to another, the two boats will approach. If they be of equal size and load, they will both move at the same rate, m whichever of the boats the man may be; and if there be a difference in the sizes, and resistances, there will be a corresponding differ- ence in the velocities, the smaller boat moving the fastest. A magnet and a piece of iron attract each other equally, whatever dispro- portion there is between the masses. If either be balanced in a scale, and the other be then brought within a certain distance beneath it, the very same counterpoise will be required to prevent their approach, whichever be in the ACTION AND REACTION EQUAL. 71 scale. If the two were hanging near each other as pendulums, they would approach and meet; but the little one would perform more of the journey in proportion to its littleness. A man in a boat pulling a rope attached to a large ship, seems only to move the boat: but he really moves the ship a little, for, supposing the resistance of the ship to be just a thousand times greater than that of the boat, a thousand men in a thousand boats, pulling simultaneously in the same manner would make the ship meet them half way. A pound of lead and the earth attract each other with equal force, but that force makes the lead approach sixteen feet in a second towards the earth, while the contrary motion of the earth is of course as much less than this as the earth is weightier than one pound,—and is therefore unnoticed. Speak- ing strictly, it is true, that even a feather falling lifts the earth towards it, and that a man jumping kicks the earth away. A spring unbending between two equal bodies, throws them off with equal velocity; if between bodies of different magnitudes, the velocity of the smaller body is greater in proportion to its smallness. On firing a cannon, the gun recoils with even more motion or momentum in it than the ball has, for it suffers the reaction of the expelled gunpowder as well as of the ball; but the momentum in the gun being diffused through a greater mass, the velocity is small, and easily checked. The recoil of a light fowling-piece will hurt the shoulder, if the piece be not held close to it. A ship in chase, by firing her bow guns, retards her motion; by firing from her stern she quickens it. A ship firing a broadside, heels or inclines to the opposite side. A vessel of water suspended by a cord hangs perpendicularly: but if a hole be opened on one side, so as to allow the water to jet out there, the vessel will be pushed to the other side by the reaction of the jet, and will so remain while it flows. If the hole be oblique, the vessel will constantly turn round. A vessel of water placed upon a floating piece of plank, and allowed to. throw out a jet, as in the last case, moves the plank in the opposite direction. A steamboat may be driven by making the engine pump or squirt wrater from the stern, instead of making it, as usual, move paddle-wheels. There is a loss of power, however, in this mode of applying it, as will be explained under the head of "Hydraulics." A mam floating in a small boat, and blowing strongly with a bellows towards the stern, pushes himself onwards with the same force with which the air issues from the bellows-pipe. A sky-rocket ascends, because, after it is lighted, the lower part is always producing a large quantity of aeriform fluid, which, in expanding, presses not only on the air below, but also on the rocket above, and thus lifts it. The ascent is aided also by the recoil of the rocket from the part of its sub- stance, which is constantly bursting downwards. He was a foolish man who thought he had found the means of command- ing always a fair wind for his pleasure-boat, by erecting an immense belknvs in the stern. The bellows and sails acted against each other, and there was no motion; indeed, in a perfect calm, there would be a little backward motion, because the sail would not catch all the wind from the bellows. A man supported on a floating plank, by walking towards one end of it gives it a motion in the direction opposite. 72 MOTIONS AND FORCES. A man using an oar, or a steam-engine turning paddle-wheels, advances exactly with the force that drives the water astern. A swimmer pressing the water downwards and backwards with his hands, is sent forwards and upwards with the same force, by the reaction of the water. And a bird flying, is upheld with exactly the force with which it strikes the air in the opposite direction. A man pushing against the ground with a stick, may be considered as compressing a spring between the earth and the end of his stick, which spring is therefore pushing him up as much as he pushes down: and if, at the time, he were balanced in the scale of a weighing beam, he would find that he weighed just as much less as he was pressing with his stick. Thus an invalid, on a spring plank or chair, who, by a trifling downward pressure of his hand on a staff or on a table, causes his body to rise and fall through a great range, and thus obtains the advantage of almost passive exer- cise, is really lifting himself while he presses downward. When a boy cries on knocking his head against a table or pane of glass, he is commonly told, and truly, that he has given as hard a blow as he has received; although his philosophy probably, looking chiefly to results, blames the table for his head hurt, and his head for the glass broken. The difference of momentum acquired in a fall of one foot or of several, is well known: the corresponding intensities of reaction are unpleasantly experienced by a man who sits down in an easy chair, or who, in sitting down where he supposed a chair to be, unexpectedly reaches the floor. What motion the wind has given to a ship it has itself lost, that is to say, the ship has reacted on the moving air: as is seen when one vessel is be- calmed under the lee of another. When one billiard-ball strikes directly another ball of equal size, it stops, and the second ball proceeds with the whole velocity which the first had— the action which imparts the new motion being equal to the reaction which destroys the old. Although the transference of motion, in such a case, seems to be instantaneous, the change is really progressive, and as follows. The approaching ball, at a certain point of time, has just given half of its motion to the other equal ball, and if both were of soft clay, they would then proceed together with half the original velocity; but, as they are elastic, the touching parts at the moment supposed are compressed like a spring between the balls, and by then expanding, and exerting force equally both ways, they double the velocity of the foremost ball, and destroy altogether the motion of that behind. If a billiard-ball be propelled against the nearest one of a row of balls equal to itself, it comes to rest as in the last case described, while the farthest bail of the row darts off with its velocity,—the intermediate balls having each received and transmitted the motion in a twinkling, without appearing themselves to move. As farther illustrative of the truths, that action and reaction are equal and contrary, and that in every case of hard bodies striking each other, they may oe regarded as compressing a very small strong spring between them, we may mention that when any elastic body, as a billiard-ball, strikes another body larger than itself, and rebounds, it gives to that other, not only all the motion which it original y possessed, this being done at the .moment when o3S ? ?if ' *? addltional quantity, equal to that with whichit recoils -owing to the equal action in both directions of the repulsion or spring ACTION AND REACTION EQUAL. 73 which causes the recoil. When the difference of size between the bodies is very great, the returning velocity of the smaller is nearly as great as its advancing motion was, and thus it gives a momentum to the body struck nearly double of what it originally itself possessed. This phenomenon con- stitutes the paradoxical case of an effect being greater than its cause, and has led persons, imperfectly acquainted with the subject, to seek from the prin- ciple, a perpetuum mobile. A hammer on rebounding from an anvil has given a blow nearly double the force which it had itself, for the anvil felt its full original force while stopping it, and then, equally with itself, was affected by the repulsion which caused its return. Many other interesting facts might be adduced as examples of equal action and reaction, but these will suffice. This second section of the work has now explained the nature of inertia in matter, and has shown that the infinitely varied phenomena of motion, which the universe exhibits, are only attraction and repulsion, acting on inertia of atoms separate or conjoined, under diversified circumstances.— And such is the sublime simplicity of the whole scheme of nature. APPENDIX. APPENDIX TO PART I. —SECTION II. BY THE AMERICAN EDITOR. The attentive perusal of the preceding section will prepare the reader to understand the following propositions. Definitions. Prop. 1.—When a body is successively changing its place it is said to be in motion, p. 42. , The idea of motion involves those of space, time, velocity, direction, the quantity of matter and momentum. Prop. 2.—The space described is the distance passed over by a body during its motion ; and is measured by the number of units of length, as a foot, a yard, a mile, &c. contained in this distance. Prop. 3.—The time consists of a certain number of units of time adopted as its measure, as a second, a minute, &c, which have elapsed during the motion of a body. Prop. 4.—The velocity of a body is the rate at which it moves, or the number of these assumed units of space that it passes over during the as- sumed unit of time. All the above measures may be represented graphically by lines that are proportioned to them, p. 65. Prop. 5.—The direction of a body may be straight or curved: when straight or rectilinear, it is the angle which its path makes with any straight line in the same plane, adopted as an axis; when the path of a body is a curve, its direction at any point is the angle which the tangent to the curve at the point makes with the fixed axis. Prop. 6.—The momentum of a body is its quantity of motion, both the mass and velocity being taken into consideration, and its proper measure is the product of the mass into the velocity, pp. 53, 54. Prop. 7.—A body is said to have a uniform motion when its velocity remains constant, that is, when it describes equal spaces in equal successive intervals of time, p. 47. Prop. 8.—Every motion that is not uniform is said to be varied, and is called accelerated or retarded as the velocity increases or decreases. Prop. 9.—When the velocity constantly increases or decreases in the direct ratio of the time that the body has been moved, the motion is said to be uniformly accelerated or retarded, pp. 43, 58, 59, 60. Prop. 10.—Whatever is capable of producing or destroying the motion of a body is called/orce. APPENDIX. 75 Prop. 11.—A force that produces its effect instantaneously, and then ceases to act, is called an impulsive force. Prop. 12.—A force that acts continually and equally is termed a constant force. Prop. 13.—When the constant force acts in lines directed towards a single point or centre, it is called centripetal, and the path of the body its orbit, p. 59. Prop. 14.—That part of the impulsive force which tends to make a body move directly from the centre, is termed the centrifugal force, p. 49. Prop. 15.—A force that is capable of destroying motion without being able, under any circumstances, to produce motion, is termed a passive force. Prop. 16.—The state of rest produced by the action of opposite forces is termed equilibrium. Prop. 17.—When a body is struck, its particles yield to the impulse, and the form of the body is changed. When the body possesses the inherent power, when thus changed, of restoring its form, it is said to be elastic; when it has not this power, it is called non-elastic, p. 37. Prop. 18.—A body oscillating below a point to which it is in any way attached, is termed a pendulum, p. 60. Laws of Motion. Prop. 19.—1st. If a body be at rest it will continue at rest, and if in motion, it will continue to advance uniformly in a right line, unless com- pelled to change its state by some external force, pp. 47, 49. Prop. 20.—2d. The motion of a body is in the direction of the force that produces it and is proportional to that force, pp. 53, 55. Prop. 21.—3d. Action and reaction are always equal and opposed to each other; or when a body communicates motion to another, it loses of its own momentum as much as it gives to the other body, pp. 70, 72. Of Impulsive force and Rectilinear motion. Prop. 22.—The effect of an impulsive force is to produce uniform rec- tilinear motion, p. 49. For during the moment of its action on any body, it must set it in motion with a certain velocity ; and by the first law of motion, the body must con- tinue to advance in a straight line with that velocity. Prop. 23.—In rectilinear motion the space is as the velocity multiplied into the time. / For if a body move with the velocity of three feet per second, it is evi- dent, that it will move over 6 feet in two seconds, i. e. 3x2 ; and 9 feet in 3 seconds, i. e. 3x3, and 12 feet in 4 seconds, &c. &c. Prop. 24.—The time is as the space divided by the velocity. For if a body passes over 12 feet for instance, when its velocity is 3 feet per second, it is evident, that in order to find the number of seconds, which the body has employed in passing over 12 feet of space, we need only divide 12 by 3, (i. e., the space by the velocity) and. the quotient 4, is the time sought. Prop. 25.—The velocity is as the space divided by the time. For if a body move over 12 feet in 4 seconds, its velocity is evidently 3 feet per second or 12-*-4. The velocities of two bodies may be compared, in the same manner : the velocities of two bodies A and B, for instance, of which A moves over 54 76 APPENDIX. feet in 9 seconds, and B, 96 feet in 6 seconds; their velocities will be as 6 (54-=-9) to 16 (96-=-6.*) Of a constant force and uniformly ^accelerated motion. , pr0p, 26.—The effect of a constant force acting upon a body, is to pro- duce in it a uniformly accelerated motion, p. 58. For since the effect of force is to produce velocity, a constant force must, in successive instants of time, afford continual and equal additions to the velo- city of the body it has set in motion; that is, the velocity will increase in the direct ratio that the body has been moving, which is the definition of uniformly accelerated motion. Prop. 27.—In uniformly accelerated motion the space described is as the square of the time, pp. 58, 59. Thus it is found by experiment, that if a body move with a gradually and constantly increasing velocity that would carry it through a mile in one minute, that at the end of this time it has acquired such a velocity as would carry it through two miles the next minute, if the force that communicated its motion ceased to act at the end of the first minute; but if the force con- tinues to act, it acquires a velocity that would carry it over an additional mile, so that it will pass over three miles the second minute, or four miles in two minutes. At the end of the second minute it has acquired a velocity that will carry it over double the space in the third minute that it moved over in the first two minutes, or a velocity of 8 miles in 2 minutes, or 4 miles a minute. But the force still continuing to act, it will move a mile farther or five miles in the third minute. Hence, if a body acted upon by a continued force move a mile the first minute, it would move 3 miles the second, 5 the 3d, 7 the 4th, 9 the 5th, &c. Thus the spaces described in successive equal parts of time, by uniformly accelerated motion, are always as the odd numbers 1* 3, 5, 7, 9, &c, and consequently the whole spaces are as the squares of the times or of the last- acquired velocities. For the continued addition of the odd numbers yields the squares of all numbers from unity upwards. Thus 1 is the first odd number and the square of 1 is 1; 3 is the second odd number, and this added to one makes 4, the square of 2;—5 is the third odd number and this added to 4 makes 9, the square of three ; and so on for ever. Since, therefore, the times and velocities proceed evenly and constantly as 1,2, 3, 4, &c, but the spaces described in equal times are as 1,3, 5,7, &c, it is evident that the space described, In 1 minute will be - 1 = square of 1 In 2 " « - . l_|-3=4= " 2 \nS " " - - 1+3+5=9= " 3 In4 " " - -1+3+5+7=16= « 4 «&c. * For the benefit of those who are acquainted with algebra, we subjoin the following equation, which expresses all the circumstances of uniform motion. Let *«=the time of motion, s=the space described in the time t, v= the velocity : . Then, s=vt from which we obtain s t s and *=— APPENDIX. 77 Of Gravity. Prop. 28.—The force which causes bodies to fall to the earth is of the kind named constant, and is called gravity, p. 58. Prop. 29.—The direction of gravity is in lines perpendicular to the earth's surface. Prop. 30.—The force of gravity is directly proportional to the mass of the body. For however small the parts into which we divide a body, we find them all affected by gravity, since this force must act upon all the particles of a body. Hence, in an unresisting medium, all bodies setting out from a state of. rest, fall through the same space in the same time, because the force of gravity acting upon them increases in proportion to the mass to be moved. Prop. 31.—The force of gravity decreases, as the square of the distance from the attracting body increases. This is proved by astronomical observations. Motion produced by joint forces. Prop. 32.—When a body is acted upon at the same moment by a plurality of forces, each of these forces produces its full effect; and the place of the body at the end of any given time is the same as it would have been if the forces had acted in succession each during that time, pp. 55, 56, 57. Thus let A B represent the direction of a force that would move a body, A, the distance Fig- !8. from A to B in a certain interval of time, (a second for example,) and A C the direction of a force that would propel the same body from A to C in the same interval of time. Suppose the first force acted alone it would move the body from A to B in one second ; if the force A C then acted at B, by drawing B R equal and parallel to A C, B R will represent the direction and velocity of the force A C, and R the position in which the body would be in at the end of the second interval of time. Unite A and R and the line A R will represent the* course of the body A if acted upon at the same moment by the two forces A B and A C, and R the position of the body at the end of the first interval of time. In the same manner the action of any num- Fig. 19, ber of forces may be represented. Thus hit A B, A C, A D, A E, represent the separate effects of four different forces acting in the same plane, capable of moving a body the distances A B, A C, A D, A E, in a given interval of time. Draw B c, c d, d R, equal and parallel to A C, A D, A E respectively, and join A R, A B c d R will represent the path of the, body . if these forces had acted successively each during one interval of time, and A R the path of the body if they all act together^ and R the position of the body at the end of the first interval of time. Prop. 33.—The line A R in the figures given to illustrate the preceding proposition represents the direction and measure of a single force, equivalent to all the others in each figure ; and hence the process by which it is deter- mined is called the composition of forces, pp. 55, 56, 57. 78 APPENDIX. prop 34 —Any force may be decomposed into any number of other forces, that shall be equivalent to it, by the reverse of the foregoing operation. This process is called the Resolution of forces, p. 57. Thus the force A R, fig. 18, may be separated into two forces A B, A C, and the force A R, fig. 19, into four forces, A B, A C, A D, and A E. Prop. 35.—When the forces act in the same right line, we have only, in order to ascertain the spaces described by their combined action, to add or subtract the spaces which would be described by their separate action, ac- cording as these forces act in the same or opposite directions. Equilibrium. Prop. 36.—A body acted upon by a plurality of forces, in opposite direc- tions, will remain at rest, or in equilibrio ; when these forces were supposed to act in succession each during the same interval of time, the body would arrive at its point of departure. The simplest and most evident case of equilibrium is that in which a body is acted upon by two equal and opposite forces. On the joint action of an impulsive and a constant force. A. When these forces act in the same right line. Prop. 37.1—When the forces act in the same direction, the place of the body at the end of any given time, may be determined, as in the problem of the composition of forces, by supposing, first, that the impulsive force acts during that time, and'then that the action of the constant force commences and acts alone during the same time ; the spaces added altogether will give the space passed over by the joint action of these forces during the assumed time. Prop. 38.—When the forces act in opposite directions, the place of the body may be ascertained by a similar process ; in this case, however, the spaces are to be subtracted one from the other, pp. 58, 59. When a constant force is acting in a direction contrary to that of a moving body set in motion by an impulsive force, the retardation that the former produces may be determined by comparing the motion with that of a body moved by the same force. The degrees by which an ascending body loses its motion, are the same as those by which it is again accelerated at the same points, when it has acquired its greatest height and again descends, for the velocities at the corre- sponding parts of the ascent and descent are equal. Thus we may calculate to what height a body will rise when projected upwards by an impulsive force, gunpowder, for instance, and retarded by the force of gravity. Since the force of gravitation produces or destroys a velocity of 32 feet in every second, a velocity of 320 feet will be destroyed in 10 seconds ; and according to what has been premised, a body will fall in 10 seconds through a hundred times 16 feet or 1600 feet, which is therefore the height to which a velocity of 320 feet in a second will carry a ball projected, without resistance from other cause than gravity, in a vertical direction, p. 60. B. When these forces act in different directions. * When the successive directions of the constant forces are parallel Prop. 39.—If the constant force be that of gravity, the successive direc- APPENDIX. 79 Fig. 20. tions of which are assumed to be parallel, the investigation of the effects produced, constitutes the doctrine of projectiles; a projectile being a body thrown in any direction by an impulsive force and at the same time acted upon by the force of gravity, pp. 59, 60. Prop. 40.—The place of a projectile at the end of any given time may be determined, as in the problem of the composition of forces, by supposing first that the impulsive force alone has acted during that time, and then that the. action of gravity commences, and acts alone during the same time. Thus let A H represent a hori- zontal plane, and A B, the initial direction and velocity of a body projected from the point A in the same plane. If the impul- sive force alone acted on the body it would describe the path ABB' B" B"'&c. with uniform velocity. But as the force of gravity acts from the moment of projection, the body will be drawn downwards from the line A B'" so as to be found after the successive intervals of time, at the points g g' g", &c, and as the force of gravity produces a velocity which increases as the squares of the distances, if the distances A B, B B', B' B", B" B'" be equal, B g, B' g', B" g",B'" g'", &c, will be as the squares of these distances, and the path of the projectile through the points g g' g" g'" will be a curve, and this curve mathematicians have called a parabola. Fig. 21. H ** When the successive directions of the constant force tend to a common centre. Prop. 41.—This case constitutes the doctrine of central forces, see prop. 13, p. 75. Prop. 42.—The place of the body at the end of any given time may be determined here also by the problem of the resolution of forces. Thus, suppose A represent a body impelled towards H with such a force, as by itself, would enable it to run over the equal spaces A B, B F, F G, &c, in equal portions of time: suppose like- wise that it is acted upon at the same time by con- stant force which would enable it to pass over the unequal spaces A I, I K, K L, &c. in the same equal portions of time. It is evident, that the joint action of both these forces would compel the body A to pass over the curvilinear path A N O P, &c. Through B draw the line B C, (viz. in the centre of attraction;) through I draw IN paral- lel to A B; and at the end of the first portion of time the body will be found at N, whence it would proceed in the straight direction N R, (by the first law,of motion) if the constant force then ceased 80 APPENDIX. to act But as this force continues to act, the body at the end of the second portion of time will be found in O; for the like reason, at the end of the third portion of timeit will be found in P, and so on. The course then, A N 0 P, is not straight out consists of the lines A N, N O, O P, forming certain angles with each other. Now it will not be difficult to conceive that, because the attractive force acts not by intervals but constantly and unremitted^, the real path of the body must be a polygonal course, consisting of an infinite number of sides; or more justly speaking, a continuate curved line, which passes through the points A, N, O, P, &c. as is shown by the dotted line. Prop. 43.—Should the action of the centripetal force cease at any instant, the body would proceed straight forward, p. 49. The portion of the impulsive force by which this is affected is called the centrifugal, prop. 14. Prop. 44.—Whilst the distance from the centre remains unchanged, as when the body moves in a circular orbit, the centripetal and centrifugal forces are equal. Laws of Central forces. Prop. 45.—When bodies revolve in equal circles, their centrifugal forces are proportional to the squares of their velocities. Prop. 46.—When two bodies revolve with equal velocities at different dis- tances, the centrifugal forces are inversely as the distances. Consequently (prop. 45,46,) the centrifugal forces are in all cases, directly as the squares of the velocities, and inversely as the distances. Prop. 47.—When two bodies revolve in equal times at different distances, their centripetal forces are simply as their distances. In general the centripetal forces are as the distances directly and as the squares or the times of revolution inversely. Prop. 48.—When the forces vary inversely as the squares of the distances, as in the case of gravitation, the squares of the times of revolution are pro- portional to the cubes of the distances. Thus, if the distance of one body be four times as great as that of another, the cube of 4 being 64, which is the square of 8, the times of its revolution will be 8 times as great as that of the first body. Prop. 49.—Where the orbit deviates more or less from a circular form, a right line joining the revolving body and its centre of attraction, always de- scribes equal areas in equal times, and the velocity of the body is therefore always inversely as the perpendicular drawn from the centre to the tangent; and the velocity at any point less than three-eighths, greater than that neces- sary to make the body describe a circle. Prop. 50.—To propel a body in an elliptical orbit, the force directed to its focus must be inversely as the square of the distance. This is proved by astronomical observations, but we have no other proof of it. The motion of the planets round the sun in the solar system is governed by the laws of central forces, the centripetal force in this case being that of gravity. On the joint effect of active and inactive forces. A. When they have opposite directions. Prop. 51.—The effect of passive forces is to restrain and modify the action of other forces so as to confine the motion of a body to a particular course or path, and the direction of the passive force affecting a body at any moment APPENDIX. 81 is the line perpendicular to that part of this path at which the body is found at this moment. If the direction of the active force be also perpendicular to this path, the body must evidently remain at rest, since no part of this force can be resolverl into the direction of the path in which alone the body can move. B. Wlien they have different directions. General rule. Prop. 52.—Resolve the active force into two, one perpendicular, and the other a tangent to the path of the body, the effect of the former force will be entirely destroyed (prop. 51,) and the body will advance by the latter alone. * On the motion of a body impelled obliquely against a plain. Prop. 53.—Let M N represent the plane, and A B the direction and velocity from the impulsive force, resolve A B into the forces A C perpendicular to the plane and C B in its direction, then by the general rule (prop. 52) the body will move along the plane with a velocity of which C B is the measure. Fig. 22. ** On the motion of a body impelled obliquely against a curved surface. Prop. 54.—Let M N represent the curve and Fig. 23. A B the direction and velocity from the impul- sive force. Resolve A B into two forces, C B perpendicular to the curve at B, and B D (equal to A C) a tangent to the curve at the same point. Then B D will represent the velocity at the point B. Prop. 55.—If the curve be interrupted at any point, or change the direction of its concavity, the body will advance with its last velocity in a tangent to the curve at that point. *** On the descent of a body along an inclined plane. Prop. 56.—Let M N represent an in- Fig. 24. clined plane and A B (perpendicular to the horizontal base H N) the force of gravity as measured by the distance which it would cause a body to descend in the first second of time. Resolve A B into two, A C, per- pendicular to the plane, and C B in its di- rection, then the body will be urged down the plane by a constant force measured by C B. Laws of the descent of bodies down inclined planes. Prop. 57.—1st. The motion of a body down an inclined plane is uni- formly accelerated. Prop. 58.—2d. The velocity acquired is proportional to the perpendicular g2 APPENDIX. descent, so that a body falling from M to H has the same velocity at H as one descending the whole length of the plane at JN. Prop 59.-3d. The times of descent down plains of the same heights aT/>roph60.-4th.SThe times of descent down all planes which are cords drawn to the lowest point of the same circle, are equal. a Thus, if the balls A, B, C, be placed at different Fig 25. points of the circle and suffered to descend at the same instant along as many planes which meet at the lowest point of the circle, they will arrive there at the same time. Or it may be enunciated in the following terms: the times of descent down all the cords drawn from the same point or circumference of a circle will be the same. This will be made evident by supposing the above figure inverted, D being made the upper point and the balls allowed to fall from that point to A, B, and C* **** On the descent of a body down the vertical curved line. Propr. 61.__The times of descent down the cords of different circles are to each other as the square roots of their diameters. Prop. 62.—If a body fall from a state of rest down a curve, the velocity acquired is equal to that which it would have by falling through the same perpendicular height. For if the curve be considered as made up of an infinite number of conti- guous planes, it is evident that the angle of inclination of any two of these adjacent planes is infinitely small, or nothing, and consequently there is no velocity lost by a change of direction in passing from one to the other. Therefore, as the effect of gravity is not impeded, the truth of the proposi- tion becomes evident. Prop. 63.—If a body be projected up a curve, the perpendicular height to which it will rise is equal to that through which it must fall to acquire the velocity of projection. For the body in its ascent will be retarded in the ,same degree that it was accelerated in its descent. Thus let B A B' be a curve in which the lowest Fig. 26. point is A, and the parts A B, A B' are similar; a body in falling down B A will acquire a velocity that will carry it to B', and since the velocities in all equal altitudes in the ascent and descent are equal, the times of ascent and descent are equal. The foregoing proposition is equally true whe- ther the body actually move over a solid surface or be retained in its path by a string which is in every part perpendicular to it. Of the simple Pendulum. Prop. 64.—The simple pendulum is conceived to be a mere material point suspended by an imponderable and inextensible thread, p. 60. Prop. 65.—If the simple pendulum vibrates through very small arcs, these may, without sensible error, be conceived to coincide with theii chords, and we may derive from this consideration the following theorems: 1st. As the times of descent of the body down different chords of the APPENDIX. 83 same vertical circle are equal (prop. 60) the vibrations of the same pendu- lum, although performed through unequal arcs, will be very nearly equal, p. 61. 2d. The times of vibrations of different pendulums will be to each other as the square roots of the lengths of these pendulums, or which is the same thing, their lengths are proportioned to the squares of the times of vibration, p. 61. The times of descent down the chords of different circles are the same as would be occupied in descending vertically through their diameters, and are consequently proportional to the square roots of these diameters. Of the impact of bodies. Prop. 66.—When a body in motion strikes directly another body, it always communicates motion to the second body, and loses part of its own, and from the third law of motion it is evident that the momentum gained by the second body is exactly equal to that lost by the first. Prop. 67.—When one non-elastic body strikes against another, the two bodies will move on together since there is no force to separate them ; and as one of the bodies gains all the momentum which the other loses, the momen- tum after impact will be equal to the sum of the momenta before impact. Prop. 68.—When one elastic body strikes against another, the second is impelled forward with double the momentum which it would have received under the same circumstances if non-elastic. For at the moment of impact the form of the body struck is changed by a force equivalent to the momentum which it receives from the striking body, and if this body be perfectly elastic, its form will be restored to it by'a force exactly equal to that by which it was changed, and this force (which we have just seen to be equal to the original impulse,) will be exerted in driving the body forward. The body thus receives, besides its original impulse, the equal force of the rebound. Prop. 69.—The striking body when elastic, is also acted upon by the rebound, and loses twice as much momentum as it would have lost if non- elastic. In this case, as in the former, the sum of the momenta is the same after impact as before it; but the bodies after impact do not move on together. Prop. 70.—If an elastic body strike against a firm plane, the angle of reflection will be equal to the angle of incidence, p. 66. 84 MECHANICS. PART II. PHENOMENA OF SOLIDS. THE FOUR FUNDAMENTAL TRUTHS USED TO EXPLAIN THE PECULIARITIES OF STATE AND MOTION WHICH DEPEND ON THE SOLID FORM OF BODIES: A DEPARTMENT COMMONLY CALLED MECHANICS. ANALYSIS OF THE CHAPTER.* A force, which moves part of a solid body, must affect the whole or break off the part. If the force be directed towards a certain central point in the mass, it will affect the whole equally, whether simply to support the mass, or to move it or to stop it when in motion. The point,' according to circumstances, is called the centre of gravity of inertia, or of action. In solid bodies moving about an axis, as exemplified in a wheel or weigh- ing beam, the various parts describe circles or move through spaces which are greater in proportion to their respective distances from the centre of motion. Hence forces differing as to speed, may still, through a solid medium, be brought exactly to co-operate or to oppose one another; a slow force counter-balancing or being equivalent to a quicker'one, pro- vided that it be more intense in proportion as it is slower. The simple machines, or mechanical media, called lever, wheel and axle, pul- ley, inclined plane, wedge, screw, Sfc, are so many arrangements of solid parts, by which forces of different velocities and intensities may be thus connected or opposed, or may be conveniently substituted one for another. By solid connecting parts also the direction of any existing motion or forte may be changed, as when the straight motion of running water is con- verted into the rotary motion of a water-wheel, <^c. Hence arises an end- less variety of complex machines. In all machines, an important circumstance to be considered is the resist- ance among moving parts which arises from friction :—and in solid structures generally, the forms and positions of parts have to be adjusted to the strength of the materials, and to the strains which the parts have to bear. " Solid" is»the term applied to a mass in which the mutual attraction of the atoms is so strong, that the mass may be moved about as one body, with- out the relative positions of the component parts being thereby disturbed. " Force moving part of a solid must affect the whole or break off the part." This is a necessary consequence of the description or definition of a solid just given. And it follows that in all cases of breaking, the cohesion of the reader should here re-peruse the general table or synopsis at page 19. CENTRE OF GRAVITY. 85 atoms at the fractured part must have been less strong than the weight of the remaining mass, or its inertia resisting the degree of change attempted, or the force fixing it to its place, or than some combination of these particulars. The sharp blow of a hammer given to an ivory ball, causes it to dart off swiftly, but does not injure it, because the cohesion among the atoms struck is stronger than the opposing inertia of the mass, even under a rapid change: but the blow of the hammer on a large elephant's tusk indents or breaks the part, because the opposing inertia of the larger mass is stronger than the cohesion of the atoms which receive the blow. A vessel of pottery-ware may be safely suspended by its handle ; proving that the cohesion which fixes the handle to it is stronger than the weight of the vessel; but if the attempt be made to lift the vessel quickly, the handle may rise and leave the body behind; because then the weight and inertia are acting together to destroy the cohesion. Thus servants attempting to lift too quickly the loaded stone-ware dishes at a dinner-table, often break off the part by which they take hold. Centre of Gravity or Inertia. If any uniform beam or rod be supported by its middle, like a weighing beam, the two ends will just balance each other. This is in accordance with the general truth or law of attraction already explained; for as there is just as much similarly situated matter on one side of the support as on the other, there will also be just as much attraction, and therefore no reason why the matter on one side should overpower that on the other. If equal weights be afterwards attached in corresponding situations on the two arms of the beam. the balance will not be thereby disturbed; and the operation of adding weights that counterpoise, above and below,,and near and far from the centre may be continued, until a bulky mass is built up upon the beam—and instead of a beam a wheel may be used—yet the whole will remain perfectly supported and in equilibrium about the original centre. In the pages now to follow, it will be shown that, in every body or mass, or system of connected masses, in the universe, there is a point of this kind about which all the parts balance or have equilibrium, and it is this point which is called the centre of gravity or of inertia. Although in any mass, therefore, every atom has its separate gravity and inertia, and the weight and inertia of the whole are really diffused through the whole, still by supporting this one point, either from above or from below, the whole mass is equally supported; by lifting it, the whole is lifted; by stopping it,the whole is brought to rest; and when it rises or falls, the general mass is really rising or falling. Thus, for many purposes, a body however large, may be considered as compressed into or existing only in the single point called its centre of gravity or of inertia. This centre in a mass of regular shape and of uniform substance, as a ball or cube of metal, is easily found, because it is the evident centre of the form; but in bodies that are irregular, either as to density or form, it must be found by rules of calculation hereafter explained. • To say that the centre of gravity will always take the lowest situation which the support of the body will allow, is only to repeat, that bodies tend by their gravity towards the centre of the earth. In a suspended body, therefore, as the lowest situation which the centre of gravity can find is, when it is imme- diately under the point of suspension, all bodies hanging freely must have their centre of gravity directly under that point. A plummet is an interest- ing example of this; and the truth furnishes, in many cases of irregular masses j a very simple practical mode of finding the centre. 7 86 MECHANICS. Fig. 27. Fig. 28. Thus if an irregular piece of plank or of pasteboard, represented here by the figure aebd, be suspended from any point, as a, and the cord of a plummet a g be attached at the same point, the centre of gravity of the board must be somewhere in the direction of the plummet, and a chalk line left on the board where the cord touched it, must pass over the centre of gravity. If the board be then suspended by another point, as d, and another chalk line d e be made m the same man- ner the place c, where the two lines cross or cut each other, will indicate the centre of gravity; and the board when sup- ported by a cord attached there, will hang evenly balanced. The following cases farther illustrate the truth, that the centre of gravity always seeks the lowest place. They seem at first to be exceptions to the law; but when more fully con- sidered, are interesting proofs of it. A wooden cylinder or roller e d c, placed on a slope or inclined plane a b, will naturally descend, because its centre of gravity is thereby approaching the earth; but if there be a heavy mass of lead c introduced at one side, which must rise before the roller can descend, the rise of the mass being contrary to gravity, the motion will be arrested. Indeed, if the roller were placed on the plane with the lead in the position d, the lead would fall down to the position c, and so would move the roller towards b, exhibit- ing the singular phenomenon of a body rolling up hill by the action of its weight. If a billiard-ball be placed upon the small ends of two billiard sticks or cues a b and c d, laid on a table with their points c and a in contact, but with the larger ends b and d so far apart that there may be just room for the ball to touch the table be- tween them, the ball will roll along between the cues, sinking gradu- ally from its high situation near their points, to its lower situation near b. To a careless observer, it would then have the appearance of rolling upwards, because the cues on which it rests are thicker towards the ends d and b; but it would really be descending in obedience to gravity. If a double cone, as represented at /, were substituted for the ball, it would similarly roll from c to e, and with still more of the fallacious appearance of rolling upwards, because its ends would always be resting on the upper and rising surfaces of the cues. The board or stick c d resting on the edge of the table a b would naturally fall if left to itself, because more than half of it is beyond the edge of the table; but strange to say, an additional weight e attached to its projecting part as at b by the. cord b e, instead of pulling it down fast- er, shall fix or steady it on the table, provided the weight be pushed inwards a little by a rod d e resting against it and against a niche in the stick at d. It is evident that the stick c d, in falling, must turn round the edge of the table at Fig. 29. Fig. 30. CENTRE OF GRAVITY. 87 b: but in so doing, after the arrangement now supposed, it must lift the weight e along the path ef— which rise, as the weight is heavier than the stick (that is to say, as «he common centre of gravity of the connected objects is near e,) gravity forbids, and therefore the stick and weight will both remain supported by the table. An umbrella or walking cane, hanging on the edge of a table by a crooked handle, is another instance of the same kind. And the common toy of a little man standing on tiptoe upon the top of a pillar, and supporting two leaden bulletsby wires descending from his hands, is another combination of parts which places the centre of gravity of the whole below the support, making the combination a kind of pendulum. By attending to the centre of gravity of the bodies around us on earth, we are enabled to explain why, from the influence of gravity, some of them are stable or firmly fixed, others tottering, others falling. If we find that a body, from its form or position, cannot be overturned with- out its centre of gravity being lifted,—knowing now that the general mass is then lifted in the same degree, we see why a weak cause cannot effect the change. The rise of the centre of gravity, or body, in any case of falling over, where the centre of gravity is over the middle of the sustaining base, will be proportioned to the breadth of the base of the body, compared with the height of the centre of gravity above the base. This is shown in the annexed figures, in which the two particulars of base and height are combined in a Fig. 31. series of proportions. In the figures, the dot c marks the place of the centre of gravity, and the curved line beginning from the dot marks the path of the centre of gravity, when the body is overturned. This curved line is a por- tion of a circle which has the edge or extremity of the base (b, in fig. A) as a centre, because the body in turning must rest upon such extremity or cor- ner as the centre of its motion. The farther inwards, therefore, from this extremity that the centre of gravity is, as marked by where a plumb-line as p, hanging from it, crosses the base, the farther, of course, is the centre of gravity from the top of the circle which it has to describe in moving, and the steeper, consequently, will be its commencing path ; and as in the case of bodies made to roll up slopes, the steeper the ascent, the greater will be the force necessary to give motion.—The line of a plummet hanging from the centre of gravity is called the line of direction of the centre, or that in which it tends naturally to descend to the earth. In fig. A, which has a broad base and little height of the centre of gravity, we see that the centre must rise almost perpendicularly before it can fall over, and the resistance to overturning is therefore nearly equal to the whole weight of the body. Hence the firmness of a pyramid. In figures B, C and D, progressively, the commencing path of the centre is less steep, because the base is narrower, and hence the bodies are so much the less stable. B may represent an ordinary house, C a tall narrow house, and D a lofty chimney. g3 MECHANICS. Fig. E shows a tottering position, for the centre of gravity being directly over a base which is a mere point, the least inclination places it on a descend- ing slope, and the body must fall. « Fig. 32. In F the position is tottering on one side, and stable on the other. This explains how the least inclination of a standing body virtually narrows, in one direction, its sustaining base. In G, which represents a ball upon a level plane, the whole mass is sup- ported on a single point as in E, yet the body has no tendency to move, because, in any other possible position, the centre would still be as far from the sustaining plane. In moving, the centre describes the straight level line a b. In H the ball is on an inclined plane, and rolls down, the centre of gravity describing the oblique line b a. In I, which is an oval body resting on a level plane, when the body is moved to either side, the centre of gravity must rise, as in the case of a pendulum. Hence an oval body on a level wfll rock or vibrate like a pendulum. K is a true pendulum whose centre of gravity describes the curve here shown, as explained in Section II., at page 60. The importance of the subject of the centre of gravity will be farther judged of by the facts which are now to be reviewed. A cart loaded with metal or stone may go safely along a road of which one side is higher than the other, as here shown, but were the same cart loaded with wool or hay it would be overturned: because, although the sustaining base be the same in the two cases, the line of direction falls much within it from the low centre of gravity of the metal at c, but falls very near the wheel at P, or altogether on the outside, from the high centre of the wool at a, and in the latter case the centre has offered to it a descending path. This explains why lofty stage coaches or vans are so dangerous, and particularly when heavy luggage is placed on the top, and why lofty gigs and curricles have led to so many fatal accidents. As regards any of these, a defect of smoothness or of level in the road, or even, in a case of quick driving, a slight lateral bend, often suf- fices to produce the catastrophe. The safety-coaches of late times are made with the wheels far apart to give a broad base, and with the luggage receptacles and seats for outside passengers placed low down 'before and behind the body of the carnage, instead of on the top as formerly. The feet of tripods are generally expanded below to give a broad base. lhe same is true of our common chairs ; but a thoughtless child often leans so Jar over the back of a chair, that he causes the line of the general centre of gravity to fall beyond the base, and the chair with its load is overturned. Fig. 33. CENTRE OF GRAVITY. 89 The small lofty chairs made to raise children to the parent's elbow at the dinner-table, are very dangerous if the feet are not made to spread much. Pillar-and-claw tables, candle-sticks, table-lamps, and many other articles of household furniture, have stability given in the same manner. The least inclination of a standing body virtually narrows the supporting base. This truth is explained by fig. F. It shows the necessity of building the thin walls and tall chimneys of modern houses perfectly upright. And hence the extreme importance and utility of that simple instrument, the plummet or plumb-line, which, when applied to a body, is a visible indication of the fine of its centre of gravity. The mason and many other workmen cannot pro- ceed a step without their guiding plummet. The brick walls of ordinary houses are so thin that, to have standing strength, they require to rest against one another ; and hence they occasion- ally exhibit the kind of stability which belongs to a child's house built of cards. As contrasted with the masses of masonry which remain to us from antiquity, resting on firm-spreading basements, they are examples of what is truly ephe- meral, in comparison with that which has partaken of the permanency of nature's own works, covering regions with mighty ruins. What magnifi- cent illustrations of strength and durability dependent on proportions, are those ancient pyramids and temples, which still lance A, and, with one grain more, ^^r7^ would descend to the plane e, one inch ^^*^i<===i^<7* ' below; then a second ball of one pound i7.:-.-...^7^......................klL.Q©^®-. would occupy the second shelf, and ''0*^c ■ 7^~- would descend in the same way, to be /.. .......e followed by a third, and afterwards by /-■■ a fourth; and when the whole four had fallen from d to e, they would just have lifted the four-pound mass, at the other end of the lever, one inch. So that, although one pound was seen here lifting four pounds, it would only have lifted them one-fourth part as far as it fell itself, and the sum of the phenomena would be, that four pounds, by falling one inch at the long end of the lever, had raised four pounds through the same distance of one inch at the short end. No mechanical power or machine generates force more than the level does in this case. It appears, then, from all this, that as the quantity of motion in a body is measured by its velocity and the number of atoms in it conjointly, so the quantity of force exerted in any case, is measured by the intensity of the force conjointly with the space through which it moves. A clear mode, therefore, of comparing forces, is to state the lengths and the intensities— for instance, to speak of ten feet of one-pound force, as equal to one foot of ten-pound force, &c. A horse pulling with the force of fifty pounds goes generally at the rate of six miles an hour; the steam-engine piston is generally made to move at the rate of two hundred feet per minute, bearing a pressure of steam of about twenty pounds to each square inch of its surface; a particular mill-stream may have a force of one hundred pounds, with a velocity of a hundred and fifty feet per minute:—now it is easy, by simple arithmetic, and the rule of length and intensify above explained, to compare all these and other forces as applicable to any given work. We must warn the reader, however, that there are many important considerations connected with the practical employ- ment of forces, according to their respective nature and that of the resistance to be overcome, which cannot be entered upon in this elementary work. In very many cases there is a great waste or unavoidable loss of force, because the resistance, in yielding, runs away or escapes from the force: as when a ship runs away from the wind which is driving her, or the floats of a quick moving water-wheel, from the stream which turns it. Horses drawing boats or carriages at the rate of five miles an hour, might exert great force, but to have a speed exceeding twelve miles they might require their whole effort to move their own bodies. As a general rule, although equal quantities of force balance each other when applied to parts of a lever or wheel altogether or nearly at rest, still when a force is made to act near its axis or fulcrum, to produce considerable velocity in a more distant part of the machinery, much of it is wasted in pressure against the fixed fulcrum. What an infinity of vain schemes—yet some of them displaying great ingenuity—for perpetual motion, and new mechanical engines of power, &c, 98 MECHANICS. would have been checked at once, had the great truth been generally under- stood, that no form or combination of machinery ever did or ever can increase, in the slightest degree, the quantity of power applied. Ignorance of this is the hinge on which most of the dreams of mechanical projectors have turned. No year passes, even now, in which many patents are not taken out for such supposed discoveries; and the deluded individuals,after selling perhaps even their household necessaries to obtain the means of securing the expected advantages, often sink into despair, when their attempts, instead of bringing riches and happiness to their families, end in disappointment and ruin. The frequency, and eagerness, and obstinacy, with which even talented individuals, owing to their imperfect knowledge of this part of natural philosophy, have engaged in such undertakings, is a remarkable phenomenon in human nature. Examples of such schemes will be noticed in different parts of this wrork, where they may serve to illustrate points under consideration. "Lever, wheel and axle, 4*c." (Read the Analysis, at page.84.) These are the simplest of the contrivances which the circumstance of solidity in masses has enabled man to adopt, for the purpose of connecting or opposing forces and resistances of different intensities. We proceed to describe them, and to explain some of their useful applications. "Lever." A beam or rod of any kind, resting at one part on a prop or axis, which becomes its centre of motion, is a lever; and it has been so called, probably, because such a contrivance was first employed for lifting weights. This figure represents a lever employed to move a block of stone: a is the end to which the power ox force is applied, /"is the prop or fulcrum, and the mass b is the weight or resistance. According to the rule already given and explained at page 96, the power may be Fig- 40. as much less intense than the resistance as it is farther from the fulcrum, or moving through a greater space. A man at a, there- fore, twice as far from the prop as the centre of gravity of the stone b, will be able to lift a stone twice as heavy as himself; but he will lift it only one inch for every two inches that he descends: and two men would be required, acting at half the dis-< tance, to do the same work. There is no limit to the difference, as to intensity, of forces which may be made to balance each other by the lever, except the length and strength of the material of which levers have to be formed. Archimedes said, "Give me a lever long enough, and a prop strong enough, and with my own weight I would lift the world." But he would have required to move with the velocity of a cannon-ball for millions of years, to alter the position of the earth by a small part of an inch. As stated in a former part of the volume, this feat of Archimedes is, jn mathematical truth, performed by every man who leaps from the ground; he kicks the world away from him when he rises, and attracts it again when he falls back. To calculate the effect of a lever, in practice, we must always take into account the weight of the lever itself, and the fact of its bending more or less; but in expounding the theory of the lever, it is usual to consider, first, SIMPLE MACHINES. 99 what would be the result, if the lever were a rod without weight and without flexibility. The rule for the lever, that the opposing forces, to balance each other, must be more or less intense, exactly as they act nearer to or farther from the centre, holds in all cases, whether the forces be on different sides of the prop or both on the same side, and whether the force nearest to the prop have the office of power or of resistance ; it holds, also, whether the lever be straight or crooked. The following are examples of levers Avith the prop between the forces. The handspike, represented in page 98, is a lever moving a block of stone. The same form, when made of iron, with the extremity formed into claws, is called a crow-bar. Both kinds are used by gunners, in working cannon dur- ing battle : they are also used generally for lifting and moving heavy masses through small spaces, as the materials of the mason, the ship-builder, the warehouse-man, &c. A short crow-bar is the instrument of house-breakers, for wrenching open locks or bolts, tearing off hinges, &c. The common claw-hammer, for drawing nails, is another example. A boy who cannot exert a direct force of fifty pounds, may yet, by means of this kind of hammer, extract a nail to which half a ton might be quietly sus- pended,—because his hand moves through, perhaps, eight inches, to make the nail rise one-quarter of an inch. The claw-hammer also proves, that it is of no consequence whether the lever be straight or crooked, provided it produces the required difference of velocity between power and resistance. The part of the hammer resting on the plank is the fulcrum. A pincers or forceps consists of two levers, of which the hinge is the common prop or fulcrum. In drawing a nail with steel forceps or nippers, we have a good example of the advantages of using a tool: 1, the nail is seized by the teeth of steel instead of by the soft fingers ; 2, instead of the griping force of the extreme fingers only, there is the force of the whole hand conveyed through the handles of the nippers ; 3, the force is rendered, perhaps, six times more effective by the lever-length of the handles ; *id 4, by making the nippers, in drawing the nail, rest on one shoulder as a ful- crum, it acquires all the advantages of the lever or claw-hammer for the same purpose. . Common scissors are also double levers, and those stronger shears with which, under the power of a steam-engine, bars and plates of iron are now cut as readily as paper is cut by the force of the hand. The common fire-poker is a lever. It rests on the bar of the grate as its prop, and displaces or breaks the caked coal behind as the resistance. The mast of a ship, with sails set upon it, may be regarded as a long lever, having the sails as the power, turning upon the centre of buoyancy of the vessel as the fulcrum, and lifting the ballast or centre of gravity as the resistance. For this reason lofty sails make a ship heel or lean over greatly, and if used in open boats, are dangerous. In some of the islands in the Eastern and Pacific Oceans, for the sake of sailing sAviftly, boats are used so extremely narrow and sharp, that to counteract the overturning tendency of their large sails, they have an outrigger or projecting plank to wind- ward, on the extremity of which one or more of the crew may sit as a ba- lance, i r • Perhaps no instance of the lever, with the prop between the forces, is more interesting than the weighing-beam ; whether with equal arms, forrn- incr the common scale-beam ; or with unequal arms, forming the steel-yard. 100 MECHANICS. We have seen why quantities of matter attached at equal distances from the prop, must be equal to each other in order to balance. A lever, there- fore, which enables us to place quantities thus exactly in opposition to each other, and which turns easily on its axis, becomes a weighing beam. Of this the annexed figure shows a common form. Fig. 41. The axis or pivot at c is sharpened below, wedge-like, that the beam may turn easily, and that its centre of motion may be nicely determined ;—in a delicate balance for philo- sophical purposes, the axis is almost as sharp as a knife edge, and rests on some hard smooth surface of support, so as to turn with the weight of a small part of a grain. The scales also of a weighing beam are suspended on sharp edges to facilitate motion, and to determine nicely the points of suspension. If the two arms of a beam be not of perfectly equal length, a smaller weight at the end of the longer will balance a greater weight at the end of the shorter. An excess of half an inch in the length of a beam-arm, to which merchandize is attached, where the arm should be eight inches long, would cheat the buyer of exactly one ounce in every pound. This case might be detected instantly, by changing the places of the two things balanced ; for so, the lightest would be at the short arm, and would then appear doubly too light. A beam intended for delicate purposes, and required, therefore, to turn easily, must have its centre of gravity very near the axis on which the beam turns ; for if otherwise, the beam will be in the predicament of a ship with the ballast too high or too low: in the former case, when once inclined, it would fall over, and not to recover itself; in the latter, it would tend to remain horizontal, and therefore would be less free to move. The proper situation of the centre of gravity is a little below the axis or line of support, that the beam may return with sufficient readiness from any state of inclination, to its horizontal position of rest. There is a mode of arriving at ver3r accurate results, even with a weigh- ing b*eam which is not itself accurately made, provided it has very free motion, viz., first, very nicely to balance in one scale the substance, to be weighed, and then to remove it, and to put weights into the same scale, until a perfect balance is produced. Such weights must be the exact equiva- lent or weight of the substance, however unlike to each other the arms of the balance may be. A projecting rod, or plank, or branch of a tree, may thus be made to answer the purpose of a weighing beam, by attaching any substance to its extremity and observing minutely how far such substance bends it, and then trying what weights would bend it as much. The steel-yard is a lever with unequal arms, and any weight, as b, on the long arm, will balance as much more Fig 42. weight as a on the short arm, as the for- 0 mer is supported farther from the fulcrum ____V° ±2j >/ ,j G than the latter. Thus, if the hook at the (q. f ' ' ' !,y£—*—'•' s*lort en(* -°e one inch from the centre of [L Qfc support, c, a pouijd weight b, on the long y arm at four inches, will balance four Qa pounds, a, at the short arm. This sup- poses, however, that the steel-yard when bare, hangs horizontally, from having a greater mass of matter in the short arm to counterbalance the long slender SIMPLE MACHINES. 101 arm from which the shifting weight hangs. When this is not the case, a corresponding allowance has to be made. The Chinese, who are so remarkable for the simplicity to which they have reduced all their common implements, weigh any small objects by a delicate pocket steel-yard. It is a rod of wood or ivory, about six inches long, with a silk cord passing through it at a particular part, to serve as a fulcrum, and with a sliding weight on the long arm, and a small scale attached to the short one. The following are examples of levers with both forces on the same side of the prop, and where the more distant force acts as the power. A common wheel-barrow is a lever, in using which a man bears as much less than the whole weight of the load as the centre of gravity of the load is nearer to the axle of the wheel than to his hands. When two porters carry a load placed midway between them, on a pole, they share it equally, that is to say, each bears a half, for the pole becomes a, lever, of which each porter is a fulcrum, as regards the other; but if the load be nearer to one end than to the other, he to whom it is nearest bears proportionably more of its weight. Fig. 43. A load at c is equally borne by a porter at a and -, by one at b ; but a load at d gives three-quarters of its weight to the man at a, and only one-quarter to him at b. Two horses drawing a plough, act from the ends of a cross-bar, of which the middle usually is hooked to the plough. The horses must thus pull equally, to keep the bar directly across. When on heavy land, three horses are yoked, and two of them are made to draw from one end of the bar, it must be attached to the plough by a hook, not at its mid- dle but half as far from one end of it as from the other. The oar of a boat is a lever of this kind, where singularly the purpose of ful- crum is served by the unstable water. The common nut-crackers furnish another instance, by the lever power of which a person can break a shell many times stronger than he could break with the bare fingers. The consideration of this kind of lever explains why a finger caught near the hinge of a shutting door is so much injured. The momentum of the door acts by a comparatively long lever, upon a resistance placed very near the fulcrum. Children pinching their fingers near the hinge of a door, or of the fire-tongs, Avhich furnishes a similar case—wonder why the bite is so keen. The phenomenon of the branch of a tree giving way, when in autumn overloaded with fruit, or in winter with snow, also exhibits the action of this kind of lever. The resistance is the cohesion of the upper side of the branch to the tree, and the fulcrum is the part below which is last broken. The following are examples of the lever, where the two forces are on the same side of the pivot*? but where that nearest to the pivot acts as the power. In this kind, the power is more intense than the resistance. The hand of a man who pushes open a gate while standing near the hinges, moves throuo-h much less space than the end of the gate, and hence must act with great force. When a man uses the common fire-tongs, the ends move much farther than 8 0Q 102 MECHANICS. his fingers, and therefore with less strength. No one fears a pinch with the ends of the fire-tongs. The most beautiful and remarkable instances of this modification of lever are in the limbs of animals. The object in these was to give to the extremi- ties great range and freedom of motion, without clumsiness of form; and it has been attained most perfectly by the tendons or ropes which move them, being attached near to the joints, which are the pivots or fulcra of the bone levers. In the human arm, the deltoid muscle, which forms the cushion of the shoulder, by contracting its fibres less than an inch, raises the elbow twenty inches, and of course, if it overcome a force of fifty pounds at the elbow, it must itself be acting with a force at least twenty times as intense, or of one thousand pounds.—What extraordinary strength of muscle, then, is displayed by a man who lifts another at the end of his extended arm; yet this feat is frequently accomplished, and even on both sides of the person at once. How powerful again must be the wing-muscles of birds, which, by this kind of action, sustain themselves in the sky for many hours together. The great albatross, with wings extended fourteen feet or more, is seen in the stormy solitudes of the Southern Ocean, accompanying ships for whole days, without ever resting on the waves. A little contraction of the glutaei muscles of the hips gives to the human step a length of four feet. While the erroneous opinion prevailed, that machines increased power, instead of, as they do, merely accommodating forces to purposes, this last kind of lever, where a great force acting through a short distance is made to gain great extent of motion and other benefits, was regretted by many as a most unprofitable contrivance, and was called the losing lever. It is almost unnecessary to say, that the same rule of comparative velocities ascertains the relations required between power and resistance, where a com- bination of levers is used, as where there is only one. If a lever which makes one balance four, be applied to work a second lever which does the same, one pound at the long arm of the first will balance sixteen pounds at the short arm of the second, and would balance sixty-four at the short arm of a third such, &c. The general rule for the lever, that a force may be less intense the farther it is from the pivot, supposes always that the force acts at right angles, or directly across the lever; for if there be any obliquity, there is a correspond- ing diminution of effect, as explained under the head of resolution of forces, at page 57. For instance, one pound at b on the end of the long arm of the bent lever b d a, because its weight does not act FiS* 44< directly across b d, has influence only as if it were rI ,t, acting directly at the end of a shorter horizontal arm elf; and the two-pound weight at a acts only as if it were on a horizontal arm at e; now c being only half as far from the centre as/, two pounds at a, in the position of the lever here shown, would just balance the one pound at b. In every case, the exact influence of weights is known by referring them to places directly above or below them, on a supposed horizontal lever ef. What is called a bent-lever balance, is made on the principle here explained. It has on one side a heavy weight as at a, and on the other side a scale attached at b; and the weight of any thing put into the scale is indicated by the posi- SIMPLE MACHINES. 103 tion then assumed by the lever, marked by the point at which it cuts an arc of divisions placed behind it. In any common weigh-beam, the point of sus- pension of the scales being a little below the axis of motion of the beam, there is a degree of the property of the bent-lever balance, and enough to require notice in very nice experiments. " The Wheel and Axle" is the next to be mentioned of the simple machines. The letter d here marks a wheel, and e an axle affixed to it; and we see that in turning together, the wheel would take up or throw off as much more rope than the axle, as its circumference Fig. 45. or diameter were greater than that of the axle. If the proportions were as four to one, one pound at b, hanging from the circumference of the wheel, would balance four pounds at a, hanging from the opposite side of the axle. The proportions are equally indicated, and are usually expressed by comparison of the diame- ters of the wheel and the axle. This figure represents the same object as the last, viewed endways. It explains why the wheel with its axle has been called a perpetual lever; for the two weights hanging in opposition, on the wheel at a, and on the axle at b, are always as if they were connected by a horizontal lever at a c b, of which the arms are respectively Fig. 46. the diameters of the wheel and the axle, turning on the centre c as the prop; and while a simple lever could only lift through a small space, it is evident that this construction will lift as long as there is rope to be wound up. A common crane for raising weights, consists of an axle to wind up or receive the rope which carries the weight, and of a large wheel at the circumference of which the power is applied. The power may be animal effort exerted on the rim or outside of the wheel, or the weight of a man or beast walking within it, and moving it as a squirrel moves the cylinder of his cage. The capstan used on board of ships, is merely a large upright axle or spin- dle b, which by turning, pulls the cable or rope at a b c; and it is moved by the Fig. 47. men pushing at the capstan-bars d e f, &c, which for the time are stuck into holes made for them in the broader part or drum, usually appearing above the deck at the top of the spindle. These bars may be considered as the spokes of a large wheel, and the effect produced by a man working at one of them is in pro- portion to his distance from the centre. The capstan is chiefly used on board ships for lifting the anchor, and for doing any other very heavy work; but it is also applied to certain purposes on shore. The common winch (represented as attached to the wheel and axle at the letter c,) with which a grindstone is turned, or a crane worked, or a 104 MECHANICS. watch wound up, is really in principle a wheel: for the hand of the worker describes a circle, and there is no difference in the result whether an entire wheel be turning with the hand or only a single spoke of a wheel. That part of a common watch called the fusee is as beautiful an illustra- tion of the principle of the wheel and axle now under consideration, as it is a useful and ingenious contri- Fig. 48. vance. The spring of a watch, immediately after winding up, —-^- —---- ;f - ■ ^ being more strained, is acting I---------j -^l more powerfully than after- j^^SSSr- ^TTZZTX, wards when slacker, and if a. there were no means of equal- =%£ izing its action, it would de- ■" stroy the wished-for uniform- J ity in the motion of the time- piece. The fusee is this means. It may be considered as a barrel or spindle, gradually diminishing from its large end b, to its small end a, with the surface cut into a spiral groove to receive the chain, by pulling at which the spring in the box c moves the watch. Now when the watch has been wound up, by a key applied on the axis of the fusee, the fusee is covered with the chain up to the small end a, and the newly bent and strong spring begins to pull by this small end or short lever; and afterwards, exactly as the spring becomes relaxed and weaker, it is pulling at a larger and larger part of the fusee-barrel, and so keeps up an equal effect on the general movement. A large fusee in place of a common cylindrical axle, is often used with a winch, for drawing water by bucket and rope from very deep wells. When the bucket is near the bottom of the well, and the labourer has to overcome the weight of the long rope, in addition to that of the bucket and water, he does so more easily by beginning to wind the rope on a small axle, that is to say, on the small end of the fusee; and in proportion as the length of rope dimi- nishes, he lifts by a larger axle. By the double axle a b, very unequal intensities of force may be balanced. We see that in turning it, a rope unwinding Fig. 49. from the small end a is taken up by the large end b, turn for turn, and that the rope below must be shortened at each turn by the differ- ence between the circumference of the ends a and b. If the weight rise half an inch only, while the handle of the winch describes a circle of fifty inches, one pound force at the winch would balance one hundred pounds at d. By means of a wheel, which is very large in proportion to its axle, forces of very dif- ferent intensities may be balanced, but the machine becomes of inconvenient proportions. It is found preferable, therefore, when such an end is desired, to use a combination of wheels of moderate size. In the adjoining figure, three wheels are seen thus connected. Teeth on the axle d, of the first wheel c, acting on six times the number of teeth in the circumference of the second wheel g, turn it only once for every six times that c turns; and in the same manner the second wheel, by turning six times, turns the SIMPLE MACHINES. 105 third wheel h once ; the first wheel, there- fore, turns thirty-six times for one turn of the last; and as the diameter of the wheel c, to which the power is applied, is three times as great as that of the axle /, which has the resistance, three times thirty-six, or one hundred and eight, is the difference of velocity, and therefore of intensity, be- tween weights or forces that will balance here.—An axle with teeth upon it, as d or e, is called a pinion. On the principle of combined wheels, cranes are made, by which one man can lift many tons. It is even possible to make an engine, by means of which a little windmill, of a few inches in diameter, should tear up the strongest oak by the roots ; but of course it would require a very long time for its work. The most familiar instances of wheel-work are in our clocks and watches. One turn of the axle on which the watch-key is fixed, is rendered equiva- lent, by the train of wheels, to about four hundred turns or beats of the balance-wheel; and thus the exertion during a few seconds, of the hand which winds up, gives motion for twenty-four or thirty hours. By increas- ing the number of wheels, time-pieces are made which go for a year: if the material would last, they might easily be made to go for a hundred or a thousand years. Wheels may be connected by bands as Fig. 51. well as by teeth. This is seen in the com- mon spinning-wheel, turning-lathes, grind- stones, &c. &c. A spinning-wheel as a c, of thirty inches in circumference, turns by its band a pirn or spindle of half an inch, b, sixty times for every turn? of itself. l# " The Inclined Plane" is the third means which we shall describe, of balancing, by solid media, forces of different intensities. A force push- ing a weight from c to d, only raises it Fig. 52. through the perpendicular height e d, by acting along the whole length of the plane c d ; and if the plane be twice as long as it is high, one pound at b acting over the pully d, would balance two pounds at a, or anywhere on the plain: and so of all other quantities and proportions, as already ex- plained under the head of " Resolution of forces," at page 86. A horse drawing on a road where there is a rise of one foot in twenty, is really lifting one-twentieth of the load, as well as overcoming the friction and other resistance of the carriage. Hence the importance of making roads as level as possible ; and hence our forefathers often erred in carrying their roads directly over hills, for the sake of straightness considered vertically, where by going round the bases of the hills they would scarcely have had greater distance, and would have avoided all rising and falling. Hence, also, 106 MECHANICS. a road up a very steep hill must be made to wind or zig-zag all the way; for to reach a given height, the ease of the pull to the horses is greater exactly as the road is made longer. This rule of road-making is exhibited remark- ably in various parts of the world, where hills with almost perpendicular faces, have very safe and commodious roads upon them, leading to forts or residences near their summits. An intelligent driver, in ascending a steep hill on which there is a broad road, winds from side to side of the road all the way to save his horses a little. The railways of modern times offer a beautiful illustration of the subject. They are made generally quite level, so that the drawing-horse or steam- engine has only to overcome the friction of the carriage ; or where heavy loads are passing only in one direction, as from mines, they are made to slope a very little, leaving to the horse or other power only the office of regulating the movement. A hogshead of merchandize, which twenty men could not lift directly, is often seen moved into or out of a wagon, by one or two men, who have the assistance of an inclined plane. In some canals, or rather particular situa- tions on canals, the loaded boats are drawn up by machinery or inclined planes instead of being raised by water in locks, as is the usual mode. It is supposed that the ancients (the Egyptians particularly) must have used the inclined plane, to assist in elevating and placing those immense masses of stone, which still remain from their times, specimens of their gigantic architecture. ' Our common stairs are inclined planes in principle ; but being so steep, are cut into horizontal and perpendicular surfaces, called steps, that they may afford a firm footing. We may here recall, that a body falling freely, in obedience to gravity, descends about sixteen feet in the first second, and that if made to descend on an inclined plane, it moves just as much less quickly (besides the loss from the friction and the turning produced) as the length of the plane is greater than the height. On a plane sloping one foot in sixteen of its length, a body would descend only one foot in the first secAnd. The descent of a pendulum in its arc is investigated mathematically by the laws of the inclined plane. And the laws of the inclined plane itself are mathematically examined by the principle of the resolution of forces, ex- plained at p. 57. " The Wedge" is merely an inclined plane forced in between resistance to separate or over- come them, instead of, as in the last case, being stationary while the resistance is moved along its surface. The same rule as to mechanical advantage has been applied to the wedge as to other simple machines ; the force acting on a wedge being considered as moving through its length c d, while the resistance yields to the extent of its breadth a b. But this rule is far from ex- plaining the extraordinary power of a wedge. During the tremor produced by the blow of the driving-hammer, the wedge insinuates itself, and advances much more quickly than the above rule anticipates. The wedge is used for many purposes, as for splitting blocks of stone and wood; for squeezing strongly, as in the oil-press ; for lifting great weights, as when a ship of war, in dock, is raised by wedges driven under the keel, &c. An engineer in London, who had built a very lofty and w SIMPLE MACHINES. 107 heavy chimney, common to all his steam-engines and furnaces, found after a time that, owing to a defect in the foundation, it was beginning to incline. However, by driving wedges under one side of it, he succeeded°in restoring it to perfect perpendicularity. Nails, awls, needles, &c, are examples of the wedge ; as are also all our cutting instruments, knives, razors, the axe, &c. These latter are often used somewhat in the manner of a saw—which is a series of small wedges, —by pulling them lengthwise at the same time that they are pressed directly forward against the object. They themselves, indeed, when viewed through a microscope, are seen to be but finer saws. It appears that the vibration°of the particles produced by the drawing of a saw, enables its edge to insinuate itself more easily. The sharpest razor may be pressed directly against the hand with considerable force, and will not enter, but if then drawn along ever so little, it starts into the flesh. " The Screw" is another of the simple machines. It may be called a winding wedge, for it has the same relation to a straight wedge that a road winding up a hill or tower has to a straight FiS- 54* road of the same length and acclivity. A screw may be described as a spindle a d, with a thread wound spirally round it,—turning or work- ing in a nut c, which has a corresponding spiral fur- row fitted to receive the thread. The nut is some- times called the female screw. Every turn of the screw carries it forward in a fixed nut, or draws a moveable nut along upon it, by exactly the distance between two turns of its thread : this distance, there- fore, is the space passed through by the resistance, while the force moves in the circumference of the circle described by the handle of the screw, as at/ in the figure. The disparity between these lengths or spaces is often as a hundred or more to one ; hence the prodigious effects which a screw enables a small force to produce. Screws are much used in presses of all kinds ; as in those for squeezing oil and juices from such vegetable bodies, as linseed, rapeseed, almonds, apples, grapes, sugar-cane, &c. : they are used also — in the cotton press, which reduces a great spongy bale, of which a few, comparatively, would fill a ship, to a compact package, heavy enough to sink in water ;—also, in the common printing-press, which has to force the paper strongly against the types :—a screw is the great agent in our coining machinery,—and in letter- copying machines:—it is a screw which draws together the iron jaws of a smith's vice, &c. The screw, although producing so much friction as to con- sume a considerable part of the force used in working it, is an exceedingly useful contrivance. As a screw can easily be made with a hundred turns of its thread in the space of an inch, at perfectly equal distances from each other, it enables the mathematical instrument maker to mark divisions on his work, with a minute- ness and accuracy quite extraordinary. If we suppose such a screw to be pulling forward a plate of metal, or pulling round the edge of a circle, over which a sharp-pointed steel marker can be let down perpendicularly, always in the same place, the marker, if let down once for every turn of the screw, will make just as many lines on the plate as the screw makes turns ; but if 103 MECHANICS. made to mark at every hundredth or a thousandth of a turn of the screw, which it will do with equal accuracy, it may draw a hundred thousand dis- tinct lines in one inch. The instruments called micrometers, by which the sizes of the heavenly bodies and of microscopic objects are ascertained, are worked by fine screws. A perpetual screw is the name given where a screw acts on the teeth of a wheel, so as to produce a continued rotation of the wheel. A common cork-screw is the thread of a screw without the spindle, and is used, not to connect opposing forces, but merely to enter and fix itself in the cork. Complicated cork-screws are now made, which draw the cork by the action of a second screw, or of a toothed rod or rack and pinion. " The Pulley" is another simple machine, by which forces of different intensities may be balanced. A simple pulley consists of a wheel as a b, which rests with its grooved circumference on the bend of a rope, c ab d, and to the axis of which the weight or resistance is attached, as at e. In such a construction, it is evident that the. weight (let it be supposed ten pounds) is equally supported by each end of the rope, and that a man holding up one end, only bears half of the weight, or five pounds ; but to raise the weight one foot, he must draw up two feet of rope ; therefore, with the pulley he is as if lifting five pounds two feet, where, without the pulley, he would have to lift ten pounds one foot. Many wheels may be combined together, and in many ways to form compound pulleys. Wher- ever there is but one rope running through the whole, as shown here, the relation of power and resistance is known by the number of folds of the rope which support the weight. Here there are four supporting folds, and a power of one hundred pounds would balance a resistance of four hundred. As persons using pulleys generally find it more conveni- ent to stand upon the ground than to go up and apply their force directly to one of the supporting ropes, the last of these is commonly made to pass over a wheel above, and to come down apart from the others, as shown here. This portion not being directly connected with the weight, adds convenience to the pulley, but is not to be counted with the others, in estimating the relation of the power and resistance. Infixed pulleys, like those shown at a and c, p. 109, there is no mechanical advantage, for the weight just moves as fast as the power; yet such pulleys are of great use in changing the direction of forces. A sailor without mov- ing from the deck of his ship, by means of such a pulley, may hoist the sail or the signal-flag to the top of the loftiest mast. And in the building of lofty edifices, where heavy loads of material are to be sent up every few minutes, a horse, trotting away with the end of the rope Fig. 56. ' 5> id ijvJi! ■i! SIMPLE MACHINES. 109 from d, in a level courtyard, causes the charged basket b to ascend to the summit of the building as effectually as if he had the power of climbing, at the same rate, the per- Fig. 57. pendicular wall. _ There is a case, however, in which a fixed > pulley may seem a balancer of different intensi- ties of force ; viz., where one end of a rope is attached to a man's body, and the other is carried oyer a pulley above, and brought down again to his hands;—for safety this end also should be -, attached to his body. By using the hands then to pull with force equal to half his weight, he supports himself, and may easily raise himself to the pulley. A man, by a pulley thus employed, may let himself down into a deep well, or from the brow of a cliff, with assurance of being able easily to return, although no one be near to help him; and cases have often occurred where, by such means, a fellow-creature's life might have been saved, or other import- ant objects attained. How easily, for instance, might persons either reach or escape from the elevated windows of a house on fire, by such a pulley, which might readily be found and used where ladders could not be obtained ! This kind of pulley furnishes a convenient means of taking a bath from a ship's stern windows, &c. The chief use of the pulley is on ship-board. It is there called a block, although, strictly speaking, the block is only the wooden mass which sur- rounds the wheel or wheels of the pulley. It aidii so powerfully in over- coming the heavy strains of placing the anchor, hoisting the mass and sails, &c, that, by means of it, a smaller number of sailors are rendered equal to the duties of the ship. Pulleys are also used on shore, instead of cranes and capstans, for lifting weights, and overcoming other resistances. Surgeons, in former days, when they trusted rather to force than to the address which better information gives, used pulleys much to help in the re- ductions of luxations,—but often hurtfully, from not understanding the force of the pulley. A good surgeon now rarely needs a pulley, and he who should ignorantly stretch his patient on the rack, would be well requited by similar treatment. The cranks of bell-wires, seen in the corners of our rooms, are bent levers nearly equivalent to fixed pulleys. There is no reason, but old usage, why the appellation of mechanical power should be confined to the six contrivances now explained, for those of which the account is yet to follow equally deserve it; and, as will be seen under hydrostatics and pneumatics, the most powerful mechanical engines do not belong to solids at all. Engine of oblique action, is a title which may include a considerable variety of contrivances for connecting different velocities. Suppose c a and c b to represent two strong rods connected together, like a carpenter's folding rule, by a hinge or joint at c. If the distant ends be made to bear against notches in two obstacles, at a and b, and by force then applied to c, either to, push or to pull, the joint c be straightened or carried towards d, the joint c will move through a much greater space than the simul- ffi- 7 f ,t 110 MECHANICS. Fig. 58. Fig. 59. taneous increase of distance produced between a and b; and, in proportion to the disparity, the power applied at c will overcome a more intense resisteince at the extremities. The mechanical power of this contrivance increases rapidly, the nearer the jointed rods approach to straightness. If we suppose the end a to be steadied by a hinge on frame-work, and the end b to bear upon that part of a printing-press which carries the paper against the types, we have imagined the simple press called, from its contriver, the Russell-press. A man's force, at d, at the moment when the rods are drawn nearly to a straight line, becomes equivalent to a pressure of many tons. For the same reason, that by urging c towards d, in the last figure, the extremities a and b are separated with great force, so by urging c in the con- trary direction, the extremities would be drawn together with corresponding force : and if we suppose a c b to be part of a rope coming through pulleys at a and b, to one end of which rope beyond a, great resistance is attached, one man, by pulling at c, may move a weight or resistance many times greater than he could move by his direct power. The following is another mode of connecting an oblique and a direct force so as to balance them, although of different inten- sities.—If to turn a wheel (represented here by the circle,) a weight be suspended from d, it is act- ing directly, for it descends just as fast as the cir- cumference of the wheel moves, and would, there- fore, be impelling with its whole strength: but if it were suspended from the point e, it would then be acting obliquely to the motion of that part of the wheel, and from not descending so fast as if at d, it would have as much less effect on the wheel, than if there, as the line e b is shorter than the line d c. The reason of this will be understood by referring to the subjects of resolution of forces and of bent levers, in former parts of the work. For the same reason, if such a wheel Avere used in lifting weights, a man turning it could lift as much more attached at the point e than at the point d, as the line d c is longer than e b. A man turning this wheel in the direction from e to a, with a Aveight hanging at e, would be lifting that weight exactly as if he Avere rolling it up the inclined plane or curve e a. This figure is useful in explaining the varying intensity of the ac- tion of a crank or winch, in different parts of its revolution, and of the combination of levers used in the Stanhope printing-press, in their different positions: it explains also the degrees of strength and support afforded by oblique stays in buildings and in ships' rigging, and many other kindred matters. The arrangement of cross-jointed wires, re- presented here, connects different velocities, and therefore, is really a mechanic power. It has Fig. 60. XxX* SIMPLE MACHINES. x 111 been applied to some curious purposes, but to none of much utility. By pressing the ends a and b towards each other, the wires, from being in the position represented in the upper figure, immediately assume the position represented in the lower: so that the end c darts outwards much farther than the ends a and b approximate. Different intensities of force are balanced, although not simultaneously, by the following means; which, therefore, according to the old idea, have some claim to the name of mechanic powers. ' A man may have a purpose to effect, which a forcible downward push would accomplish: but his body being too weak to give that push directly, he may employ a certain time in carrying a weight to such an elevation, above his work, that when let fall its momentum may do what is required. Here the continued effort of the man in lifting the weight, to a height of perhaps thirty feet, may be just sufficient to produce a blow which will cause a stake or pile to sink into the earth one inch; and the contrivance has therefore balanced forces, of which the relation as to intensity is marked by the spaces thirty feet and an inch. So also hammers, clubs, battering-rams, slings, &c, are machines which enable a continued moderate effort to overcome a great but short resistance. The fly-wheel, Avhich, by persons ignorant of natural philosophy, has often been accounted a positive power, in common cases merely equalizes the effect of an irregular force. . In using a winch to turn a mill, for instance, a man does not act Avith equal force all around the circle: but a heavy wheel fixed on the axis mode- rates acceleration, and receives or absorbs momentum, while his action is above par, and returns it again, giving it to the machine, while his action is below par, thus equalizing the movement. And in the common instances of circular motion produced by a crank, as when, by the pressure of the foot on a treadle, we turn a lathe or grind-stone, or spinning-wheel, the force is only applied during a small part of the revolution, or in the form of inter- rupted pushes; yet the motion goes on steadily, because the turning grmd- stone, or wheel, or lathe, becomes a fly and reservoir, equalizing the effect of the force. In a steam-engine which moves machinery by a crank, the upward and dowmvard pushes of the piston are converted, by means of a heavy fly-wheel, into a very steady rotatory motion. A 'heavy wheel, however, has sometimes been used as a concentrator ol force or a mechanic power. By means of a winch, or a weight, or other- wise, motion or momentum being gradually accumulated in the wheel, is then made to expend itself in producing some sudden and proportionally great effect. Thus, a man may lift a very heavy weight by first, in any way living motion to a fly-wheel, and then suddenly hooking a rope from the weio-ht to the axle of the wheel, which rope being wound upon the axle, lilts the Aveight. . . , ~ A fly-wheel moved in the same manner, and containing the result ot a man's action during perhaps one hundred seconds, if made to impel a screw- press, will, with one bloAV or punch, stamp a perfect medal, or from a rough flat plate of silver will form a finished spoon, or other utensil. A spring in the same sense, may become a mechanical power. A person may expend some minutes in bending it, and may then let fly its accumulated cneW m an instantaneous blow. A gun-lock shows this phenomenon on a small scale. The slow bending of a bow, which afterwards shoots its arrow with such velocity, is another instance. 112 MECHANICS. These, then, are the principal means which the solid state of bodies affords us of balancing forces of different intensities. We shall find other such means or mechanic powers belonging to liquids and airs. All of them are of inesti- mable value to man, by enabling him to accommodate the forces which he can command to any kind of work which he has to perform. Thus he makes his millstone turn Avith the same velocity, whether it be moved by the slow exertion of a horse or bullock, walking in a ring, or by the quicker motion of a river gliding under the wheel, or by the rapid gush of a water-fall, or by the invisible swiftness of the Avind. And again each of these forces he can equally apply to turn the heavy millstone or to twist a cotton thread. The Avants of men seem first to have led them to use the simple machines for the purposes of raising great weights, or overcoming great resistances, and hence the name long used of mechanic powers—particularly for the Lever, Wheel and Axle, Plane, Wedge, Screw, and Pulley: but the term conveys to the uninformed a false idea of their real nature, and has begotten the common prejudice with respect to them, that they generate force, or have a sort of innate power for saving labour. Now so far is this from being true that in using them in any case, even more labour or bodily exertion is ex- pended than would suffice to do the work without them. This assertion is intentionally rendered paradoxical to arrest attention, but its truth Avill appear from the following considerations. One man may be able, with a tackle of pulleys having ten plies of the rope, to raise a weight which it would require ten men to raise at once without pulleys. But if the weight is to be raised a yard, the ten men will raise it by pulling at a single rope and walking one yard, while the one man at his tackle, must walk until he has shortened all the ten plies of rope of one yard each; that is, he must walk ten yards, or ten times as far as the ten men did. In both cases, therefore, to accomplish the same end, we have just the same quantity of man's work expended, in the first, performed by ten men in one minute, in the second, by one man in ten minutes; and if the work were of a nature to continue longer, let us say a whole day for the ten men, it would last ten days for the single man, and there Avould be ten days' wages of a man to pay in both cases: there is, therefore, no direct saving of human effort from using pulleys; indeed, there is a loss, because of the great friction which has to be overcome. Now exactly the same is true of all other simple ma- chines, or mechanic powers ; none of them save labour, in a strict sense of the phrase; they only allow a small force to take its time to produce any requisite magnitude of effect, at the expense of additionally overcoming a certain amount of friction or other such resistance. The real advantages of these machines are such as the following: That one man's effort, or any small power, which is always at command, by working proportionally longer, will ansAver the purpose of the sudden effort of many men, even of hundreds or thousands, whom it might be most inconvenient and expensive, or even impossible, to bring together. A ship's company of a few individuals easily weighs a heavy anchor by means of the capstan. A solitary workman, with his screw or other engine, can press a sheet of paper against types, so as to take off a clear impression; to do which Avithout the press, the direct push of fifty men would scarcely be sufficient: and these fifty men Avould be idle and superfluous except just at the instants of pressing, Ayhich occur only now and then. In this way the screw may be said'to do the Avork of fifty men, for it is as useful. A man with a crow-bar may move a great log of wood to a convenient COMPLEX MACHINES. H3 place, Avhere twenty men Avould have been required to move it Avithout the croAv-bar ; and although the single man takes twenty minutes, perhaps, to do what the many men would have done in one minute, as the twenty might not have been wanted again for the rest of the day, the crow-bar may really be as useful as the twenty men. It is so important to have correct notions on the subject of the simple machines or mechanical powers, that more space has been here allotted to the explanation of the general principle, than has been usual in such works. After the examination which it has now undergone, hoAvever, the author hopes that none of his readers will have difficulty in conceiving clearly, that " whatever, through a machine, is gained in power, is lost in speed or in time, and vice versa"—or will have difficulty in detecting immediately any common fallacy connected with the subject; — as that of supposing, for instance, that a lever, or great pendulum, or spring, or heavy fly-wheel, &c, can never exert more force than has passed into it from some source of motion. " By solid connecting parts, also, the direction of any existing motion or force may be changed. Hence the endless variety of complex machines." (Read the Analysis at p. 84.) It is in this power of changing the direction of motion, added to the power of connecting and adjusting various intensities of force and resistance by the simple machines last described, which has enabled man to make complex machines, rivaling in their performances the nicest work of human hands. It would be endless to attempt the enumeration of the modes in which the directions of motions may thus be changed, for it would be to enumerate and describe the whole apparatus of the arts and sciences ; but we shall advert to a feAv as specimens. Straight motion changed into rotatory.—The straight motion of Avind or water becomes rotatory in Avind or water-wheels.—The straight-dowmvard pressure of the human foot, acting at intervals on a treadle and crank, turns round the grindstone, and common lathe, and spinning-wheel.—The alter- nate rising and falling of the piston of a steam-engine is made, by means of a crank, to turn the great fly-wheel and any other wheels which a steam-engine may move. Rotatory motion into straight.—An axle in turning will wind up a rope, and lift a weight in a-straight line.—A crank on a turning axle, if connected with a pump-rod, will work the piston up and down ; or it will work a saw.— Pallets or teeth on a turning-wheel act on the handle of a great forge ham- mer, so that every one in passing lifts the hammer and produces a blow. We need not multiply instances. By a visit to great manufacturing towns, or, indeed, by simply directing the eyes to what is passing around, in any part of the civilized world, we discover miracles of mechanic art:—machines driven by wind, water or steam for grinding corn;—machines for sawing wood and giving it various forms;—machines in which rods of metal are seized betAveen great rollers, and are flattened at once into thin plates, as if they were of clay, and these plates again are slit into bars or ribbons— spinning machines, which perform their delicate office even more uniformly than human hands, forming thousands of threads at once, in obedience to the impulse of a single steam-engine ;—weaving machines, which accomplish their difficult task Avith the most admirable perfection;—paper-making engines, which convert Avorn-out and apparently useless remnants of our apparel, into 114 MECHANICS. the uniform and beautiful texture of paper, a texture which, with the farther assistance of the pen, or types, or engraved plate, becomes a magic conserva- tory of mind, shutting up among its folds the brightest effusions of genius, and ready, at any instant, to disclose them again to the delighted student, nothing changed after revolving centuries ;—coining machinery, which from a bar or plate of metal cuts out and stamps thousands of beautiful medals in an hour, and keeps an exact record of its work ;—cranes,—pile-engines,— turning-lathes,—time-pieces,—all the implements of agriculture, of mining, of navigation, &c. &c. If Aristotle deemed the title or definition of tool-using animal appropriate to man two thousand years ago, what title should be given now ? In many of the complex machines, several of the simple ones are found as elements ; and in the same machine may be comprised many of the means of changing the direction of motion. "Friction." (Read the Analysis, p. 84.) In estimating the effects of mechanical contrivances, by the rule of compara- tive velocities of the power and resistance, there is an important correction to be made, on account of the mutual friction of the moving parts. In the steam-engine, where the rubbing parts are numerous, the loss of power from friction often amounts to one-third of the whole. Impediment from friction seems to be owing to two causes : 1st, a degree of cohesive attraction between the touching substances ; 2d, the roughness of these surfaces, even where, to the naked eye, they appear smooth. It is supposed to be, because the roughness, or little projections and cavi- ties, in pieces of the same or of homogeneous substances mutually fit each other, as the teeth of similar saws Avould, so as to allow the bodies, in a degree to enter into each other, that the friction is greater betAveen such than between pieces of different or of heterogeneous substances with dissimilar grain. The friction of one piece of iron, wood, brick, stone, &c, on another piece of the same substance, has been measured by using the second piece as an inclined plane, and then gradually lifting one end of it until the upper mass began to slide, — the inclination of the plane, just before the sliding com- mences, is called the angle of repose. This angle, different for different sub- stances, is found to be, for metals, generally such as to mark that the force required to overcome the friction between small pieces of them is equal to about a fourth of the weight of the moving piece, and for woods it is about a half. But for large piepes or great pressures, the friction is proportionably much less. It is this angle in the substances concerned, which determines the degrees of acclivity which can exist in the sides of hills composed of sand, gravel, earth, &c, in the banks of canals, rivers, &c. If the thread of a screw winds round the spindle with an angle less than this, the screw can never recoil or shde back from force acting against its point. But for friction, men walking on the ground or paVement would always be as if Avalking on ice ; and our rivers, that now flow so calmly, Avould all be frightful torrents. Friction is, therefore, in these cases of great use to men. Friction is useful, also, when it enables men, out of the comparatively short fibres of cotton, flax, or hemp, to form their lengthened Avebs and cordage,—for it is friction alone, consequent upon the interweaving and FRICTION. 115 tAvisting of the fibres and threads, which keeps the material of these fabrics together. The folloAving means are used to diminish friction between rubbing sur- faces ; and they are used singly or in combination, according to circum- stances. 1. Making the rubbing surfaces smooth ;—but this must be done Avithin certain limits, for great smoothness allows the bodies to approach so near that a degree of cohesion takes place. 2. Letting the substances which are to rub on each other be of different kinds. Axles are made of steel, for instance, and the parts on which they bear are made of brass : in small machines, as time-keepers, the steel axles often play in agate or diamond. The sAviftness of a skater depends much on the great dissimilarity between steel and ice. 3. Interposing some lubricating substance between the rubbing parts ; as oils for the metals, soap, grease, black-lead, &c, for the woods. Thgre is a laughable illustration of this in the holiday sport of soaping a lively pig's tail, and then offering him as the prize of the clever fellow who can catch and hold him fast by his slippery appendix. 4. Diminishing the extent of the touching surfaces ; as in making the rub- bing axis of a wheel very small. 5. Using wheels, as in wheel-carriages, instead of dragging a rubbing load along the ground. Castors on household furniture are miniature Avheels. 6. Using what is called friction-wheels ;•—Avhich still farther diminish the friction even of a smooth Fig. 61. axis, by allowing it to rest on their circumferences, which turn with it. Here a represents the end of an axis, resting on the exteriors of two friction- wheels, b and c. 7. Placing the thing to be moved on rollers or balls, as when a log of wood is drawn along the ground upon rounded pieces of wood ; or when a cannon, Avith a flat circular base to its carriage, turns round by rolling on cannon-balls laid on a hard level bed. In these two cases, there is hardly any friction, and the resistance is merely from the obstacles which the rollers or balls may have to pass over. Of all rubbing parts, the joints of animals, considering the strength, fre- quency and rapidity of their movements, are those which have the least fric- tion. The rubbing surfaces in these are covered, first, with a layer of elastic cartilage, and then with an exceedingly smooth membrane, over Avhich there is constantly poured from the glands around, a fluid called synovia, more emol- lient and lubricating than any oil, and which is renewed constantly as may be required. We study and admire the perfection of animal joints, Avithout being able very closely to imitate it. Wheel carriages merit notice here, as illustrating many of the circumstances connected with friction; and moreover as being among the most common of machines. Wheel carriages have three advantages over the sledges for Avhich they are the substitutes: 1. The rubbing or friction, instead of being between an iron shoe and the stones and irregularities of the road, is betAveen the axle and its bush, of Avhich the surfaces are smoothed and fitted to each other, and well lubricated. J16 MECHANICS. 2. While the carriage moves forward, perhaps fifteen feet, by one revolu- tion of its AA-heel, the rubbing part, viz., the axle, passes over only a few inches of the internal surface of its smooth greased bush. 3. The wheel surmounts and abrupt obstacle on the road by the axle describing a gently rising slope Fig. 62. or curve, — as shown in this , figure, where a represents an obstacle, and where the curve from c, of which the beginning has the direction shoAvn by the line c e, represents the path of the axle in surmounting it. The Avheel is as if rising on an inclined plane, and gives to the draAving animal the relief which such a plane Avould bring. This kind of advantage is greater in a large wheel, for evidently the smaller wheel here represented, in having to surmount the same size of obstacles, has to rise in the steeper curve beginning at d,—but the difference of advantage, in this respect, is not so great as the difference of size. It is true again, that a small wheel would sink to the bottom of a hole, where a larger one would rest on the edges as a bridge, and Avould sink less. The fore-wheels of car- riages are usually made small, because such construction, by allowing the wheel to go under the body of the carriage, facilitates the turning of the car- riage. It is not true, however, according to the popular prejudice, that the large hind-wheels of coaches, wagons, &c, help to push on the little wheels before them, as if the carriage were on an inclined plane resting on theAvheels; but there is the accidental advantage, that in ascending a hill, Avhen the horses have to put forth their strength, the load rests chiefly on the hind-wheels, and in descending, Avhen an increased resistance is desirable, the load falls chiefly on the fore-wheels. From the. causes mentioned in the last paragraphs, the difference in per- forming the same journey of a mile, by a sledge and by a wheel-carriage, is that while the former has to rub over every roughness in the road and to be jolted by every irregularity, the rubbing part of the latter, the axle, glides very slowly over about thirty yards of a smooth oiled surface, in a gently waving line. Thus, by wheels, the resistance is reduced to about the hun- dredth part of Avhat it is for a sledge. On hilly roads, in descending, it is common to lock or fix one of the wheels of a carriage, and the horses have then to pull nearly as much as on a level road Avith the wheel free ; showing the effect of a little increase of friction. The Avheel of a carriage, simple as, from our extreme familiarity Avith it, it noAy appears to us, is a thing of very nice workmanship, and which has exercised much ingenuity.—It acquires astonishing strength, indeed, that of the arch, from what is called its dished form, seen here in the wheel c, as contrasted with the flat wheel a. In a wheel of this form, the extremity of a spoke cannot be displaced inwards, or towards the car- riage, unless the rim of the wheel be enlarged, or all the other spokes yield at the same time, and it cannot be displaced outwards, or away from the car- riage, unless the rim be diminished, or the other spokes yield in the opposite direction ;—now the Fig. 63. FRICTION. 117 rim being strongly bound by a ring, or tire of iron, cannot suffer either increase or diminution, and the strength of all the spokes is thus by it conferred on each individually. In a flat wheel a given degree of displacement outAvards or inwards of the extremities of a spoke, would less affect the magnitude of the circumference, and therefore the rim of such a Avheel secures much less firmly. A watch-glass and a round piece of egg-shell are stronger than flat pieces of like substances, for the same reason that a dished Avheel is stronger than a flat wheel.—The dished form of a wheel is farther useful by leaving more room between the wheels for the body of the carriage, and is useful also in this, that when the carriage is on an inclined road, and more of the weight consequently falls upon the wheel of the lower side, the inferior spokes of that wheel become nearly perpendicular, and thereby support the increased weight more safely. The strongest form of Avheel is the doubly dished, that is, a wheel having half of the spokes passing from within to the rim, as from c to d, fig. 63, and the other half similarly from without. This form is adopted in the wheel recently constructed entirely of iron, in Avhich there is the farther peculiarity that the load is supported more by hanging by the upper spokes than by resting on the lower.—When wheels, instead of stand- ing upright, like b and d shoAvn, fig. 63, are made to incline outwards, as is common, owing to the ends of the axletree being bent down a little to give a security against the accident of the Avbeels falling off, the pull to the horses in deep or sandy roads is much increased; for an inclining wheel would naturally describe a curved and outward path, as is seen when a hoop or wheelbarrow inclines; and the horses, therefore, in draAving straight for- ward, have constantly to overcome the deviating tendency in all inclining wheels. This cause of resistance is still more remarkable when the wheels have broad rims. Such Avheels must be conical, that is, of smaller diameter at the outer than at the inner edge, as the end of a cask is smaller than its middle, and then, as the iron hoops or tires which cover the different parts cannot all, by an equal number of turns, truly measure the same length of road, there will be a constant rubbing or grinding forward of the lesser rings, and a grinding backAvard of the larger, injuring the road, rapidly wearing the iron, and exhausting the strength of the pulling animals. Such wheels rolling free Avould describe a circular path, as is exemplified Avhen a thimble, or drinking glass, or sugar-loaf, which also are conical, is pushed forward on any plane surface. The application of springs to carriages, which is an improA'ement of com- paratively recent date, not only renders them soft moving vehicles on rough roads, but much lessens the pull to the horses. When there is no spring, the whole load must rise with every rising of the road, and if time be given, must sink with every depression, and the depression costs as much labour as the rising, because the wheel must be draAvn up again from the bottom of it; but in a spring-carriage moving rapidly along, only the parts beloAV the springs are moved in correspondence with the road-surface, while all above, by the inertia of the matter, have a soft and even advance. Hence arises the-superiority of those modern carriages, furnished Avith Avhat are called undcr-springs, Avhich insulate from the effect of shocks, all the parts, except- ing the wheels and axletrees themselves. When only the body of the car- riage is on springs, the horses have still to rattle the heavy frame-AA-ork below it over all irregularities, and then the wheels as well as the structure generally require to be of much greater strength and weight to bear the consequent shocks. 9 f jig MECHANICS. The subject of wheel carriages is interesting to medical men, from their having often to direct in transporting the sick or wounded. It is perhaps difficult to conceive any thing more elegant and perfect than the carriages of modern refinement; and therefore a man, who sees them gliding swiftly along the prepared levels and slopes of our present landscapes, and thinks of the clumsy vehicles on the bad roads of former times, may readily imagine that absolute perfection is at last attained. Yet we are per- haps now on the eve of a farther change which, for many purposes, will be of greater importance than all that has yet been achieved—viz., the general adoption of rail-roads, with neAv-fashioned carriages to suit them. To all who study such subjects, it is now known, that to drag a loaded wagon up one inconsiderable hill, costs more force than to send it thirty or forty miles along a level rail-way; and the conclusion is obvious, that although the origi- nal expense of forming the level line might considerably exceed that of mak- ing an ordinary road, still, in situations of great traffic, the difference would soon be paid for by the savings, and when once paid, the savings would be as a profit for ever. To readers conversant with political economy, it would be superfluous to speak here of the advantages of any greater facility of intercourse, but to those Avho are not, the following reflections may be interesting. In reviewing the history of the human race, we find that every remarkable increase in civilization has taken place very much in proportion to the facili- ties of intercourse offered in the particular situation. First, therefore, civili- zation grew along the banks of great rivers, as the Nile, the Euphrates and the Ganges; or along the shores of inland seas and archipelagos, as in the Mediterranean and the numerous islands of Greece; or over fertile and ex- tended plains, as in many parts of India. When the situation thus bound a great number of individuals into one body, the useful new thought or action of any one unusually gifted, and which, in the insulated state, would soon have been forgotten and lost, extended its influence immediately to the whole body, and became the thought or action of all who could benefit by it, besides that it was recorded for ever, as part of the growing science of art of the com- munity. And in a numerous society, such useful thought and acts would naturally be more frequent, because persons feeling that they had the eyes of a multitude upon them, and that the rewards of excellence would be propor- tionally great, would be excited to emulation in all the pursuits that could contribute to the well-being of the society. Men soon learned to estimate aright these and many other advantages of easy intercourse, and after having possessed themselves with avidity of the stations naturally fitted for their purposes, they began to improve the old and to make ne\y stations. They created rivers and shores, and plains of their own, that is, they constructed canals, and basins, and roads; and so connected artificially regions which nature seemed to have separated for ever.—In the British isles, whose fa- voured children have taken so remarkable a lead in showing Avhat prodigies a wise policy may effect, the advantages arising from certain lines of canal and road first executed, soon led to numberless similar enterprizes, and within half a century the empire has been thus bound together in all directions: and it seems as if the noble work was noAV to be crowned by the substitution of level railways for many of the common roads and canals.* Several rail- * These observations were first published (the substance had been written long before,) soon after the Darlington rail-road, the first of any note intended for passengers, was opened. The Manchester and Liverpool rail-road has since then admirably verified the anticipations. STRENGTH OF MATERIAL. 119 roads of short extent have already been established, and although they and the carriages upon them are far from having the perfection which philosophy says they will admit, the results have been very satisfactory. If we sup- pose the progress to continue, and the price of transporting things and persons to be thus reduced to a fourth of the present charge—and in many cases it may be less—and if we suppose the time of journeying with safety also to be reduced in some considerable degree,—of which there can be as little doubt—the general adoption of such roads would operate an extraordinary revolution and improvement in the state of society. Without in reality changing the distances of places, it would in effect bring all places nearer to each other, and would give to every spot in the kingdom the conveniences of the whole,—of town and country, of sea-coast and of highland district. A man, wherever residing, might consider himself virtually near to any other part, Avhen, at the expense of time and money now expended in travelling a short way, he might travel very far, and he would thus find remarkably ex- tended, the sphere both of his business and of his pleasures. The over- crowded and unhealthy parts of towns would scatter their inhabitants into the country; for the man of business could be as conveniently at his post from a distance of several miles, as he is now from an adjoining street. The present heavy charges for bringing distant produce to market being nearly saved, the buyer everywhere would purchase cheaper, and the producer would be still better remunerated. In a word, such a change would be effected, as if by magic the whole of Britain had been compressed into a circle of a few miles in diameter, yet without any part losing aught of its magnitude or beauties.—All this may appear visionary ; but it is less so than seventy years ago it would have been to anticipate much of Avhat, in respect to travelling, has really come to pass,—as, that the common time of passing from London to Edinburgh would be forty-six hours. At the recent opening (in 1825) of the rail-road near Darlington, a train of loaded carriages was dragged by one little steam- engine a distance of twenty-five miles within two hours; and in some parts of the journey the speed was more than twenty miles an hour: the load was equal to a regiment of soldiers, and the coal expended was not of the value of a crown. An island with such roads would be an impregnable fortress; for in less time than an enemy Avould require to disembark on any part of the coast, the forces of the country might be concentrated to de- fend it. " Strength depends on the magnitude, form, and position of bodies, as well as on the degree of cohesion in the material." (Read the Analysis, page 84.) The minute details connected with this branch of the subject belong to the practical engineer, but there are some of the general truths Avhich should be familiar to every body. Of similar bodies the largest is proportionally the weakest. Suppose two blocks of stone left projecting from a hewn rock, of which blocks one, as d, p. 120, is twice as long, and deep, and broad as the other, b. The larger one will by no means support at its end as much more Aveight than the smaller, as its mass is greater, and for two reasons. 1st. In the larger, each particle of the surface of attachment at c, in helping to bear 120 MECHANICS. o the weight of the block itself, has to support by Fig. 64. its cohesion tAvice as many particles beyond it in the double extent of projection, as a particle has to support in the shorter block at a; and 2dly, both the additional substance, and any thing ap- ^1 j, pended at its outer extremity, are acting with a s\ double lever advantage to break it, that is, to de- V stroy the cohesion at c. Hence, if any such mass d be made to project very far, it will be broken off, or will fall by its own weight alone. And what is thus true of a block supported at one end, is equally true of a block supported at both ends, and indeed of all masses, however supported, and of whatever forms, if they have projecting parts. It is to be observed also that masses, like an abso- lutely perpendicular cliff, which have no projecting or overhanging parts, are still limited as to size by the degree of cohesive force among their particles, for the upper part of such a mass tends to crush or break down the lower. A lofty pillar cannot be formed of soft clay. That a large body, therefore, may have proportionate strength to a smaller, it must be still thicker and more clumsy than it is longer: and beyond a cer- tain limit no proportions whatever will keep it together, in opposition merely to the force of its own weight. This great truth limits the size and modifies the shape of most productions of nature and of art;—of hills, trees, animals, architectural or mechanical structures, &c. Hills. Very strong or cohesive material may constitute hills of sublime elevation, with very projecting cliffs and very lofty perpendicular precipices; and such accordingly are seen where the hard granite protrudes from the bowels of the earth, as in the Andes of America, the Alps of Europe, the Himalayas of Asia, and the Mountains of the Moon in Central Africa.— But material of inferior strength exhibits more humble risings and more rounded surfaces. The gradation is so striking and constant, from granite mountains, down to those of chalk, or gravel, or sand, that the geologist can often tell the substance of Avhich a hill is composed by observing the pecu- liarities of its shape. Even in granite itself, which is the strongest of rocks, there is a limit to height and projection ; and if an instance of either, much more remarkable than now remains on earth, were by any chance to be produced again, the lawAvhich we are considering would prune the monstrosity. The grotesque figures of rocks and mountains seen in the paintings of the Chinese,—or actually formed in miniature for the gardens, to express their notions of perfect sublimity and beauty,—are caricatures of nature for which originals can never have existed. Some of the smaller islands in the Eastern Ocean, however, and some of the mountains of the chains seen in the voyage towards China, along the coasts of Borneo and Palawan, exhibit, perhaps, the A*ery limits of possibility in singular shapes. In the moon, Avhere the Aveight or gravity of bodies is less than on earth, on account of her smaller size, mountains of a given material might be many times higher than on earth—and observation proves that the lunar mountains are in fact very high. STRENGTH OF MATERIAL. 121 By the action of winds, rains, currents, and frost, upon the mineral masses around us, there is unceasingly going on an undermining and wasting of supports, so that every now and then immense rocks, or almost hills, are torn by gravity from the station which they have held since the earth received its present form, and fall in obedience to the law now explained. The size of vegetables, of course, is obedient to the same law. We have no ttees reaching a height of three hundred feet, even when perfectly per- pendicular, and sheltered in forests that have been unmolested from the be- ginning of time: and oblique or horizontal branches are kept within com- paratively narrow limits by the great strength required to support them. The truth, that to have proper strength, the breadth or diameter of bodies must increase more quickly than the length, is well illustrated by the contrast existing between the delicate and slender proportions of a young oak or elm, yet in the seedsman's nursery, and the sturdy form of one which has braved for centuries all the winds of heaven, and has become the monarch of the park or forest. Animals furnish other interesting illustrations of this law. How massive and clumsy are the limbs of the elephant, the rhinoceros, the heavy ox, compared with the slender forms of the stag, antelope, and grayhound ! And unless the bones were made of stronger material than now, an animal much larger than the elephant would fall to pieces owing to its weight alone. The whale is the largest of animals, but feels not its enor- mous weight, because lying constantly in the liquid support of the ocean. A cat may fall with impunity from a greater height than Avould suffice to dash the bones of an elephant or ox to pieces. For the reason which we are now considering, the giants of the heathen mythology could not have existed upon this earth ; although, on our moon, where, as already stated, weight is much less, such beings might be. In the planet Jupiter, again, which is many times larger than the earth, an ordinary man from hence would be carrying in the simple weight of his body, a load sufficient to crush the limbs which supported him. The phrase a little com- pact man, points to the fact that such a person is stronger in proportion to his size than a taller man. The same law limits the height and breadth of architectural structures. In the houses of fourteen stories, which formerly stood for protection, close under the Castle of Edinburgh, there was danger of the superincumbent wall crush- ing the foundation. Roofs. Westminster Hall approaches the limit of Avidth that is possible without either very inconvenient proportions or central supports ; and the dome of the church of St. Peter in Rome is in the same predicament. Arches of a bridge. A stone arch, much larger than those of the magnifi- cent bridges in London, would be in danger of crushing or splintering its material. Ships. The ribs or timbers of a boat have scarcely a hundredth part of the bulk of the timbers of a ship only ten times longer than the boat. A ship's yard of ninety feet contains, perhaps, twenty times as much wood as a yard of thirty feet, and even then is not so strong in proportion. If ten men may do the work of a three-hundred-ton ship, many more than three times that number will be required to manage a ship three times as large. Very large ships, such as the two built in Canada, in the year 1825, which carried each nearly ten thousand tons of timber, are Aveak from their size alone ; and the loss of these first two specimens of gigantic magnitude aa-M not encourage to the building of others. 122 MECHANICS. a The degree in which the strength of structure is dependent on the form and position of their parts, will be illustrated by considering the two cases of longitudinal ana transverse compression. And the rule for giving strength to any structure will be found to be, to cause the force tending to destroy it, to act, as equally as possible, on the whole resisting mass at once, and with as little mechanical advantage as possible. i In longitudinal compression, as produced by a body a, on the atoms of the support b, the weight, Avhile the support remains straight, can only destroy the support, by crushing it in opposition to the repulsion and impenetrabihty of all its atoms. Hence a very small pillar, if Fig. 65. kept perfectly straight, supports a very great C 7> ___ weight; but a pillar originally crooked, or be- ^----I ginning to bend, resists Avith only part of its strength ; for, as seen in c d, the whole weight above is supported chiefly on the atoms of the concave side, which are therefore in greater danger of being oppressed and crushed, while those on the convex side, separated from their natural helpmates, are in the opposite danger of being torn asunder. The atoms near the centre in such a case are almost neutral, and might be absent without the strength of the pillar being much lessened. Long pillars or supports are weaker than short pillars of the same diameter, because they are more easily bent; and they are more easily bent I----------------------1 because a very inconsiderable, and therefore easily effected yielding between each adjoining two of their many atoms, makes a considerable bend in the whole; while in a very short pillar there cannot be much bend- ing without a great change in the relation F«g. 66. of proximate atoms, and such as can be effected only by great force. The weight resting on any pillar, and bending it, may \ be considered as acting (with obliquity \ dependent on the degree of bending) at \ the end of a long lever which reaches \ from the extremity to the centre of the \ pillar, against the strength resisting always \ directly at a short lever reaching from the ■-■dr-j side d to the centre: the strength of the pillar, therefore, has relation to the differ- ence between these levers and to the degree / of bending. Shortness, then, or any stay / or projection, as a e b, which, by making the resisting lever longer, opposes bending, really increases the strength of a pillar. A column with ridges projecting from it, is on this account stronger than one that is perfectly smooth. A hollow tube of metal is stronger than the same quantity of metal as a solid rod, because its substance standing farther from the centre resists bend- STRENGTH OF MATERIAL. 123 ing Avith a longer lever. Hence pillars of cast-iron are generally made hollow, that they may have strength with as little metal as possible. In the most perfect weighing-beams for delicate purposes, that there may be the least possible Aveight with the required strength, the arms, instead of being of solid metal, are hollow cones, of which the substance is not much thicker than writing paper. Masts and yards for ships have been made holloAv in accordance with the same principle. In Nature's works we have to admire numerous illustrations of the same kind. The stems of many vegetables, instead of being round externally, are ribbed or angular and fluted, that they may have strength to resist bending. Many also are hollow, as corn-stalks, the elder, the bamboo of tropical climates, &c, thereby combining lightness with their strength.—A person who has visited the countries where the bamboo grows, cannot but admire the almost endless uses to the inhabitants, which its straightness, lightness and hollow- ness, fit it to serve. Being found of all sizes, it has merely to be cut into pieces of the lengths required for any purpose, and nature has already been the turner, and the polisher, and the borer, &c. In many of the Eastern Islands it is the chief material, both of the dAvellings, and of the furniture; there are the bamboo huts and bungalows, and then the fanciful chairs, couches, beds, &c.; flutes and other wind instruments there, are merely pieces of the reed with holes bored at the requisite distances: conduits for AA-ater are pipes of bamboo; bottles and casks for preserving liquids are single joints of larger bamboo with the natural partitions remaining; and bamboo split into threads is twisted into rope, &c. From the animal kingdom also we have illustrations of our present subject: —as in the hollow stiffness of the quills of birds; the hollow bones of birds; the bones of animals, generally—strong and hard, and often angular exter- nally, with light cellular texture within, &c. Transverse Pressure. When a horizontal beam is support- ed at its extremities, as at a and b, its Fig. 67. weight bends its middle down more «£\_ ^--^X^ or less, as here shown, the particles Q^^-~~~~^^l^^ on the upper side being compressed, ^^^^--^ | -~^^Z-^^ while the parts below are distended; " ^ and the bending and tendency to break are greater, according as the beam is longer and its thickness or depth IS J.6SS 'The danger of breaking, in a beam so situated, is judged of, by consider- ino- the destroying force as acting by a long lever reaching from an end of the beam to the centre, and the resisting force or strength as acting only by a short lever from the side d to the centre: Avhile only a little of the sub- stance of a beam on the under side is allowed to resist at all. This last cir- cumstance is so remarkable, that the scratch of a pin on the under side of a plank resting, as here supposed, will sometimes suffice to begin the fracture. Because the resisting lever is small in proportion as the beam is thinner, a plank bends and breaks more readily than a beam, and a beam resting on its side bears less weight than if resting on its edge. Where a single beam can- 124 MECHANICS. not be found deep or broad enough to have the strength required in any par- ticular case, as for supporting the roof of a house, several beams are joined together, and in a great variety of Avays,»as is seen in house-rafters, &c, which, although consisting of three or more pieces, may be considered as one very broad beam, with those parts cut out which would contribute least to the strength. The arched form, resting against immovable abutments, bears transverse pressure so admirably because by means of it the force that would destroy, is made to compress, not one side only, but all the atoms or parts of both sides nearly in the same degree. By Fig. 69. comparing this figure with the last, we see that the atoms on the under side of an arch, must be compressed about as much as those on the upper side, and are therefore in no danger of being torn, or overcome separately. The whole substance of the arch therefore resists, nearly like that of a straight pillar under a weight, and is nearly as strong. An error, which lias been frequently committed by bridge-builders, is the neglecting to consider sufficiently the effect of the horizontal thrust of the arch on its piers. Each arch is an engine of oblique force (see page 56), pushing the pier away from it. In some instances, one arch of a bridge fall- ing, has allowed the adjoining piers to be pushed down towards it, by the thrust, no longer balanced, of the arches beyond, and the whole structure has given way at once like a child's house or bridge built of cards. It is not known at what time the arch was invented, but it was in com- paratively modern times. The hint may have been taken from nature, for there are instances in Alpine countries of natural arches, where rocks have fallen between rocks, and have there been arrested and suspended, or Avhere burrowing Avater has at last formed a wide passage under masses of rock, and has left them balanced among themselves as an arch above the stream. No- thing can surpass the strength and beauty of some modern stone bridges;— those, for instance, which span the Thames, as it winds through London. Iron bridges have been made with arches twice as large as those of stone; the material being more tenacious and easily moulded, is calculated to form a lighter whole. The bridge of three fine arches lately built between the city of London and Southwark, is a noble specimen, and compared with those erected in the preceding century, appears almost a fairy structure of lightness and grace. The great domes of churches, as those of St. Peter's in Rome and St. Paul's in London, have strength on the same principle as simple arches. They are in general strongly bound at the bottom Avith chains and iron-bars, to aid the masonry in counteracting the horizontal thrust of the superstruc- ture. The Gothic arch is a pointed arch, and is calculated to bear the chief weight on its summit or key-stone. Its use, therefore, is not properly to span rivers as a bridge, but to enter into the composition of varied pieces of architecture. With what effect it does this, is seen in the truly sublime Gothic structures which still adorn so many parts of Europe. The following are instances, in smaller bodies, of strength obtained by the arched form.—A thin watch-glass bears a very hard push ;—a dished or arched Avheel for a carriage is many times stronger to resist all kinds of shocks than a perfectly flat wheel;—a full cask may fall with impunity, where a STRENGTH OF MATERIAL. 125 strong square box would be dashed to pieces ;—a very thin globular flask or glass, corked and sent down many fathoms into the sea, will resist the pres- sure of water around it, where a square bottle, with sides of almost any thickness, would be crushed to pieces. . We have, from the animal frame, an illustration of the arched form giving strength, in the cranium or skull, and particularly in the skull of man, which is the largest in proportion to its thickness:—the brain required the most perfect security, and in the arched form of the skull has obtained it with little weight. — The common egg-shell is another example of the same class: what hard blows of the spoon or knife are often required to penetrate this wonderful defence of a dormant life ! The weakness of a similar substance not arched, is seen in a scale from a piece of freestone so readily crumbling between the fingers. To determine, for particular cases, the best forms and positions of beams and joists, and of arches, domes, &c, is the business of strict calculation, and belongs therefore to mathematics, or the science of measures. It was a beautiful problem of this kind, Avhich Mr. Smeaton, the English engineer, solved so perfectly, in the construction of the far-famed Eddy- stone light-house. He had to determine the form and dimensions of a building, which should stand firm on a sunken rock, in the channel of a swift ocean tide, and exposed to the fury of tempests from every quarter. Only the man who has himself been driven before the irresistible storm in the darkness of night, and in the midst of dangers, and whose eyes have watched the steady ray from the light-house which saved him, can appreciate fully the importance of the studies which bring such useful results ; or can feel how happy he is to have fellow men, Avhose talents, although exerted usually for individual good, are yet, by God's providence, made to accom- plish the most philanthropic ends, and to bind the whole of human kind into one great society of helping brotherhood. [For Animal and Medical Mechanics, see Part V. Sec. 1.] 126 HYDROSTATICS. PART III. THE PHENOMENA OF FLUIDS.* SECTION I.—HYDROSTATICS. ANALYSIS OF THE SECTION. The particles of a fluid mass are freely movable among one another, so as to yield to the least disturbing force ; and if bearing force at all, can be at rest only when equally forced in all directions. Hence: I. In a mass of fluid submitted to compression, the whole is equally affected, and equally in all directions. A given pressure, for instance, made by a plug forced inwards upon a square inch of the surface of a fluid filling a vessel, is suddenly communicated to every square inch of the vessels surface, however large, and to every inch of the surface of any body immersed in the fluid. 2. In any fluid, the particles that are below bear the weight of those that are above, and there is, therefore, within the mass, a pressure increasing exactly with the perpendicular depth, and not influenced by the size, or shape, or position of the containing vessel. 3. The open surface of a fluid is level; and if various pipes or vessels communicate with each other, any fluid admitted to them will rise to the same level in all. 4. A body immersed in a fluid displaces exactly its own bulk of it, which quantity having been just supported by the fluid around, the body is pressed upwards, or supported, with a force exactly equal to the weight of the fluid displaced, and must sink or swim according as its own weight is greater or less than this. By comparing, therefore, the weight of a body with the force ivhich holds it up in a fluid, the comparative weights or specific gravities are found. "Fluid." It Avas explained in Part I., that the same atoms may exist in the form of a solid or of a fluid ; and as a fluid, they may either constitute a dense liquid like water, or a light elastic mass like air. A pound of ice, or a pound of water, or a pound of steam, differs only in the particles being more or less distant from each other, owing to the different quantities of heat among them. In the ice, they are comparatively near, and are held together by attraction, as if they were spitted or glued to each other ; in the water, the repulsion of heat seems nearly to balance attraction, and to leave the par- • Read again the Synopsis, page 20. FLUIDS. 127 tides at liberty to glide about among each other almost without friction ; and in the steam, the repulsion altogether overcomes the attraction, and the par- ticles separate to a great distance, as if held apart by some bulky elastic medium. The few facts not evidently reconcilable with this simple and satisfactory explanation of so many phenomena,—as that water in freezing, and even in cooling down from forty degrees to the freezing point, increases in volume, instead of contracting, like things in general, and like itself in cooling at other temperatures,—and that baked clay, in proportion as it is more heated, contracts instead of dilating,—are treated of in other parts of our work. Whether matter be in the solid or fluid form, the properties of the indi- vidual atoms remain unchanged, that is, the atoms always exist in accord- ance with the " general truths ;" but as, in the chapter on Mechanics, we found so many important modifications of effect produced by the circum- stance of the attraction being in the degree which produces solid cohesion among the particles, in this chapter on fluids we shall find as many important results springing from the circumstance of non-cohesion or fluidity. In a liquid the particles, although comparatively near to one another, seem not to be in actual contact; for the mass may be condensed indefinitely by pressure. The force required, however, to change the volume of a liquid in any sensible degree, is so great, that until improved means of experiment, recently contrived, liquids were accounted absolutely incompressible. In aeriform fluids, on the contrary, each particle, under common circumstances, has about two thousand times as much space to itself as when forming part of a liquid or solid; and hence it is that these fluids are so extensively com- pressible and dilatable—or elastic, as they are called. On account of this elasticity, they exhibit so many important phenomena, in addition to those of mere fluidity, that the consideration of them requires to be gone into apart, and forms the branch of the subject called pneumatics, from a Greek word, signifying " spirit" or " breath !" " In a quantity of fluid submitted to compression, the whole mass is equally affected, and similarly in all directions. A given pressure, therefore, made upon an inch of the surface of a fluid confined in a vessel, as by a plug forced inwards, is suddenly borne by every inch of the surface of the vessel, however large, and by every inch of the surface of any body immersed in thefluid." This truth is of great importance, both from its explaining so many remarkable phenomena of nature, and from the useful applications of it in the construction of machinery. When a man compresses in his hands a bladder full of air, he readily conceives that the air immediately under his fingers is not at all more compressed than that in every other part of the bladder; and of course that every part of the bladder's surface must be pressing the air as much as those parts of it on which his fingers rest, and must be bearing a reaction or resistance of the air in an equal degree ; and that every single particle of air must be acted upon equally on every side, so that if a small opening were made in the bladder anyAvhere, the air would issue from it with equal readiness. This is in accordance with the characteristic of fluidity, " that the particles glide about among one another almost without friction, so that a particle can never be at rest unless Avhen equally urged in all directions." 128 HYDROSTATICS. Fig. 69. In like manner, if a close vessel B be filled Avith Avater, and into the top of it a tube a c be screwed, and if then, by means of a cork or movable plug in the tube at c, the surface of the Avater in the vessel be pressed upon Avith a force of one pound, the water throughout the Avhole will be squeezed or condensed in proportion to the pressure, and every other portion of the vessel B, of equal surface with c, will be keeping up the con- densation just as much as c, and will be bearing the resistance or elasticity of the Avater to the extent of one pound. And if there were another similar tube, b, also with a plug, screwed into the top of the box B, the force of one pound depressing the plug c would be pushing up the plug b, with the same force. And if there were many other similar tubes and plugs, by acting on one, all would be equally affected; and a plug or piston of double size would be twice as much affected as the smaller one ; and a plug d, of ten times the size, would be lifted with a force of ten pounds. Hence it appears that, through the medium of confined fluid, a force of one pound, acting upon an inch square of the fluid surface in a vessel, may become a bursting force of ten, or a hundred, or a thousand pounds, according to the size of the vessel, or may be used as a mechanical power to overcome a force much more intense than itself. It will be explained below that the well-known hydrostatic press is merely a large plug or piston as here described, forced up against the substance to be pressed by the action of a smaller piston in another barrel. If, in the above figure, the tube a were such as to contain just one pound of water, on the plug c being withdrawn from it, and water being poured in to fill it, the same pressure or condensation would take place in the box B as when the plug Avas pressed with the force of one pound; and of course ex- actly the same effects would follow on the sides of the vessel and on the other pistons ; and if, in the other tubes also, water were substituted for the pistons, it is evident that, to effect a balance in all, it Avould require to stand as high in every one as in the tube a c, producing the same level in all, whatever their size. The fact, that the Aveight of one pound of Avater, or any other force of one pound similarly applied, may be made, through the medium of extended fluid surface to produce a pressure of hundreds or of thousands of pounds,' has been called the " hydrostatic paradox," yet there is nothing in reality more paradoxical in it than that one pound at the long end of the lever should balance ten pounds at the short end: indeed it is but another means, like the contrivances usually called mechanical powers, and described in the last chapter, of balancing different intensities of force, by applying them to parts of an apparatus moving Avith different velocities. Here the tube a being ten times smaller than the tube e, the piston in a must descend ten inches to raise the greater piston in e one inch. This laAv of fluid pressure is rendered very striking in the experiment, of bursting a strong cask by the weight or action of a few ounces of Avater. Suppose a cask a already filled Avith Avater, and that a long small tube b c is screwed tightly into its top, which tube will contain only a few ounces Fig. 70. fl b FLUIDS. 129 of water; by pouring these few ounces into the tube, the cask will be burst. In explanation, it is unnecessary to say more than that if the tube have an area of a fortieth of an inch, and contain, Avhen filled, half a pound of water, that AA*ater Avould produce a pressure of half a pound upon every fortieth of an inch all over the interior of the cask, or nearly 2,000 lbs. on the square foot, —a pressure greater than a common cask can bear. A similar effect is seen in what is called the hydrostatic bellows. This consists of a long small tube a b, into which water is poured to enter the body of the apparatus at c, which resembles the common bellows, in having wooden boards above and below, and strong leather connecting them. If the tube a b holds an ounce of water, and has itself only one-thousandth of the area of the top of the bellows, an ounce of water in it will balance weights of a thou- sand ounces placed on the top of the bellows at d. If mercury Avere substi- tuted in this machine for water, the effect would be fourteen times greater, Fig. 71. fl a hundred because mercury is fourteen times heavier in the same bulk. And if a man stand on a large bellows of the kind, he may raise himself by blowing into the tube with his mouth. The annexed cut will give an idea of Mr. Bramah's singularly powerful and useful hydrostatic or hydrau- lic press; which, if compared with the bellows, exhi- bits merely a strong forcing-pump instead of the lofty tube, and a barrel with its piston instead of the leather and boards. The letter e points out the piston of the forcing pump worked by the handle d, and driv- ing Avater along the horizontal tube into the space f under the large solid piston c, which last, with its spreading top, is urged against the object to be com- pressed. If the small pump have only one-thousandth of the area of the large barrel, and if a man, by means of its lever-handle d, press its piston down Avith a force of five pounds, the piston of the great barrel will rise with a force of one thousand times five hun- dred pounds, or more than two hundred tons. Scarcely any resistance can withstand the pow- er of such a press; with it the hand of an infant can break a strong iron bar; and it is used to condense 'substances, as cotton or hay for sea voyages, to raise great weights, to uproot trees, to tear things asunder, &c. The Dilater is a surgical instrument of extensive applicability, of which the action depends on the principle of the communication of fluid pressure. It was proposed by the author some years ago, and was brought to great practical perfection by his brother, Dr. James Arnott, (now superintendent surgeon in the service of the Hon. East India Company,) in Avhose publica- tion^ is minutely treated of. Many professional men in this country doubted of its power, from not being aAvare of the nature of fluid action; but it is in reality a kind of hydraulic press, allowing the operator to act with the most gentle or most energetic force. Farther remarks are made upon it in the medical section which follows this chapter. 130 HYDROSTATICS. "In any fluid, the particles that are below, bear the weight of those that are above, and there is therefore a pressure among them increasing in exact proportion to the perpendicular depth, and not influenced by the size, or shape, or position of the containing vessel." The atoms of matter having gravity, it is evident that the upper layer of any mass of fluid must be supported by the second, and this with its load by the third, and the third Avith its double load by the fourth, and so on. This truth is experimentally proved by putting different heights of liquid into an upright tube, of which the bottom is closed by a flap having a spring or lever to support it, and to indicate the force acting on it. And what is true of the entire column of water in the tube, may be considered true of any single line of atoms; just as it would be true of a line of bricks piled one above another. A tube of which the area is an inch square, holds, in two feet of its length, nearly a pound of water; hence, the general truth, well Avorth recollecting, that the pressure of water, at any depth, whether on the side of a vessel or on its bottom, or on any body immersed, is nearly one pound on the square inch for every two feet of depth. The striking effects from the increase of pressure in a fluid, at great depths, are of course most commonly exhibited at sea. The following instances will illustrate them. If a strong square glass bottle, empty, and firmly corked, be sunk in water, its sides are generally crushed inwards by the pressure before it reaches a depth of ten fathoms. A chamber of air similarly let down Avith a man in it, would soon allow him to be drowned by the Avater bursting in upon him;—as really happened to an ignorant projector. When a ship founders in shallow water, the wreck, on breaking to pieces, generally comes to the surface, and is cast upon the beach; but when the accident happens in deep water, the great pressure at the bottom forces water into the pores of the wood, and makes it so heavy that no part can ever rise again to reveal her fate. A bubble of air or of steam, set at liberty*far below the surface of Avater, is small at first, and gradually enlarges as it rises. A man who dives deep, suffers much from the compression of his chest, as the elastic air within yields under the strong pressure. This limits the depth to which divers can safely go. It is not known whether there is a limit to the pressure which fishes can bear with impunity, but they are chiefly found living in the shallower Avaters on coasts, or on banks in the midst of the ocean, such as the banks of New- foundland, the Dogger-bank, and other fishing stations out at sea. In round- ing the Cape of Good Hope, at a considerable distance from land, ships pass over the bank of Lagullas, where a hook let down Avith a bit of red rag or almost any thing as a bait, immediately secures its codfish. By sending a vessel prepared for the purpose, down into the deep sea, we can readily prove the compressibility of water. Suppose the vessel to be made Avith only one entrance, and that a small round opening, into Avhich, instead of a cork, a sliding rod has been closely fitted. If, then, when filled Avith water, and having the rod inserted into the opening, it be allowed to sink in the sea, the pressure around will push the rod inwards, in a degree proportioned to the yielding or compression of the Avater within: and if there be on the rod a stiff sliding-ring, or other contrivance to indicate on the PRESSURE AS DEPTH. 131 return of the vessel how far the rod had been driven inwards, the apparatus will show the degree of compression at the greatest depth to which it has descended. Water a thousand fathoms beloAV the surface is less bulky by about one-twentieth part than when at the surface. The following are proofs of the pressure of weight in an open fluid, opera- ting in all directions, as any pressure does in the case of a confined fluid. A bottle-cork carried far under water, is not flattened as if it were pressed unequally, but is reduced in all its dimensions so as to appear a phial-cork of the usual form. If a corked empty bottle be sent down into the sea, the cork is generally forced inwards at a given depth, and equally so in whatever direction the mouth of the bottle may happen to point. If a vessel containing water have an opening in the side, covered by a valve or flap so contrived as to tell the force required to keep it shut, we find that the water tends to escape just as powerfully through such an opening as it Avould through one in the bottom, with the same elevation of water over its centre. And different equal openings in the side of a vessel require to be closed with forces exactly proportioned to the heights of liquid above their centres. _ In an open square-sided vessel full of water, the whole pressure on any upright side is just half the pressure on an equal extent of horizontal bottom ; for the centre of the side being just half as deep as the bottom, the pres- sure on any point there is only half as great as on a point at the bottom, and on points above the level of the centre is just as much less than half, as, at corresponding distances below, it is more than half, and so it amounts to an exact half in the whole. Considering that the pressure on every point be- low the central level is greater than on every point above it, we see the rea- son why, to support a sluice or flood-gate by a single stay on the outside, the point at which the pressure has to be made is below the central level. Cal- culation discovers that this point, called the centre of pressure, is at one-third from the bottom. The knowledge of such facts furnishes rules for the con- struction of large vessels for liquids, canal embankments, &c. The pressure on a given extent of the side of a narrow vessel is just as great as on the same extent of the side of a wide vessel, having the same depth of fluid : because, as now explained, it depends entirely on the extent of surface *»€ted upon and the depth of liquid. Hence a flood-gate or sluice which shuts out the ocean, as in docks open- ing to the sea, bears no more pressure than if it stood only against an equal depth of lake or river; or than if it were one of tAvo such flood-gates be- come the sides of a*'very narrow vessel, made to contain only a few hogs- heads of water. Hence, again, the fear is unfounded which has been expressed Avith refer- ence to the formation of a canal between the Red Sea and the Mediterra- nean,—that because the former, owing to the effects of easterly Avinds at its mouth, &c, is twenty feet higher than the latter, it might burst through the flood-gates, and carry devastation along its course. A deep crevice in a rock, when filled by a shower, is often the cause'of the rock being torn asunder, and of part being precipitated. Extensive Avails or faces of masonry, intended to confine banks of sand or earth, if no openings were left for water to escape from behind them, Avould be burst after a rain unless they had the strength of flood-gates of the same size. Ignorance of this danger has led to some extraordinary catas- trophes. 132 HYDROSTATICS. Other examples of the pressure in fluids being in all directions, and pro- portioned to the depth, are ;—the swelling and bursting of leaden pipes when filled from a very elevated source:—the tearing up of the coverings of sub- terranean drains or water courses, when, during a flood, any accident chokes them near their lower openings :—the violence with which water escapes by an opening near the bottom of any deep vessel, or enters by an opening or leak near the keel of a deep-floating ship :—the great strength required in the loAver hoops and securities of those enormous vessels of porter-breAvers, called Arats, some of which contain many thousand barrels of liquid. In speaking of the pressure of a fluid in all directions, some persons have difficulty in conceiving that there is an upward as Avell as a downward and a lateral pressure. But if, in a fluid mass, the particles below had not a ten- dency upwards equal to the weight or downward pressure of the fluid over them, they could not support that fluid, which entirely rests* upon them. Their tendency upward is owing to the pressure around them from which they are trying to escape. Accordingly, if a long tube, open at both ends, and with a sliding plug or piston in it near one end, be partially plunged into water by the plugged end, the water is found to press the plug upwards with force proportioned to the depth to Avhich it is carried, and exactly equal to the for-je with which water presses upon an equal extent of the bottom or side of any other vessel having in it the same depth ; or, with which, in the same vessel, it Avould press other plugs in other branches of the tube pro- jecting in various directions. On removing such a plug altogether, the up- ward pressure is visibly proved and measured by the column of water pushed into the tube from below, and supported there to the level of the water around. The pressure in a mass of fluid is proportioned to the perpendicular depth, and is not at all influenced by the size, shape, or position of the containing vessel. A body immersed in the water of a lake, one foot under the surface, is just as much pressed upon as if it were one foot under the surface of the sea, and no more than if it were one foot under the surface of a small cistern. Suppose vessels differing from each other in form and capacity, as sketched here at a, b, and c, but all having flat bottoms, F'g- 73. 0f exactly the same area; if fluid be poured into all to the same level or perpendicular height, as represented here by the dotted lines, although the quantity be very different in each, the pressure on the bottom will be the same in all. This truth is easily proved experimentally, by having the bottoms movable, and held to their places by weights or springs capable of measuring the pressure : or by letting the three vessels all communicate Avith the same vessel of water below them, and then observing that the water in all has still the same level___These results are other exemplifications of the truths, "pressure equal in all directions," "pressure as depth," and "pressure as the extent of surface" For as a column of the fluid, resting on the middle of each bottom, just presses with its Avhole Aveight, and therefore according to its altitude, this column could not remain at rest if there Avere any greater or less pressure than its own near it; then as the fluid really is at rest in all the cases, and in all a cen- tral column is of the same height, the pressure must be equal on all the bot- toms. The case of the largest vessel, a, is in a degree illustrated by sup- FLUID LEVEL. 133 posing the water in it to be suddenly converted into smooth upright small columns or rods of ice or glass ; then, evidently, only those pieces which rested on the bottom could press on it, while the others would be supported by the oblique sides of the vessel, and by the lateral resistance of the pieces around them. " Level surface of a Fluid." (Read the Analysis.) That the surface of a fluid must be level, follows from the facts of all the particles being equally attracted towards the centre of the earth, and being perfectly movable among themselves. The particles forming the surface may be regarded as the tops of so many columns of particles, supported at any given level below, by a uniform resistance or pressure ;—for no particle of an inferior level can be at rest unless equally urged in all directions, and therefore all the particles at such a level, and Avhich, by equally urging one another, keep themselves at rest, must all be bearing the weight of equal columns: thus a higher column must sink and a lower one must rise, until just balanced by those around; that is, until all become alike. Besides, just as a ball rolls down a slope or inclined plane, so do the particles of a fluid slide or move from any higher situation among themselves, to any lower unoccupied situation near them. The account now given explains why an accidental elevation or depression of a fluid surface, usually called a wave, continues to rise and fall, or to oscillate, for some time with gradually dimi- nishing force;—for when the mass is raised above the general level, it is not quite supported, and therefore soon sinks, but in sinking, like a falling pen- dulum, it acquires momentum which carries it below the general level, until opposed and arrested by a resistance greater than its Aveight, it then rises again, but by acquiring new momentum in its rise, it has to fall again, again to rise, and this alternation continues, until the lateral sliding of the parti- cles, and the friction among them, gradually destroy it. A perfectly level surface on earth really means one in Avhich every par- ticle is equi-distant from the centre of the earth, and it is therefore truly a spherical surface ; but so large is the sphere, that if a slice of it of two miles in diameter were cut off, and laid on a perfect plane, the centre of the slice Avould only be four inches higher than the edges. Any small portion of it, therefore, for all common purposes, may be accounted a perfect plane. So truly smooth does a fluid surface become, that it forms a perfect mirror; that is, it reflects or throws back the rays of light, Avhich fall upon it so exactly in the order which they had on leaving the object, that an eye which receiA*es them may fancy the object to be placed in the direction of the mir- ror.—-It Avas over the glassy surface of the fountain or the lake, that the shepherdesses of the young world bent themselves, to learn the charms which nature had bestowed on them. And a child contemplates with wonder and delight, through the window of a still pool or gliding stream, another sky below the ground, with its clouds, and sun or stars ; and another landscape, with inverted Avoods and mountains, the supposed dwelling of fairy beings. In the cutting of canals, the making of railways, and in many other ope- rations of engineering, it is of essential importance to determine the lever or horizontal direction at any Fig. 74. place ; and this is usually done by a tube or glass, a c, filled with spirit except one bubble of air b *L-----^,------£! and called a spirit level. When this tube is hori- ^—------------- zontal, the bubble has no tendency to move to either 10 134 HYDROSTATICS. end; but if the tube inclines ever so little, the bubble rises to the end which is highest; or to speak more correctly, the denser spirit falls down to the loAver end, and forces the light bubble away from it. Such a tube properly fixed in a frame, Avith a telescope attached to it, or simply with sight-holes to look through, becomes the engineer's guide in many of his most import- ant operations. A hoop surrounding the earth would bend away from a perfectly straight line four inches in a mile. In cutting a level canal, therefore, which may be considered as part of a hoop, there must be everywhere a falling from the straight line, called by geometers a tangent, in the proportion now de- scribed. All rivers also have the curvature of hoops applied to the surface of the earth. Canals leading from sea-ports to the interior of countries have generally to ascend; but as Avater cannot become stagnant in any channel which is not level, the canal is divided, by gates or sluices, into portions at different levels, like steps of a stair, the rising at the joinings being generally from six to tAvelve feet. The boats are raised or lowered from one level to another by the contrivance called a lock, which is merely a portion of the canal, of sufficient capacity for the boat to lie in, furnished with high walls, and with flood-gates at both ends ; so that when the gates below are shut, and water is gradually admitted from above, it becomes part of the high level, ready as such to deliver a boat, or receive one : and when the upper flood-gates are shut, and the water is gradually allowed to escape from the lock, it becomes a part of the low level, and a boat may enter it, or leave it by its loAver gates. The cutting of canals is one of the great items in the mass of modern improvement, which both mark and hasten the progress of civilization. Adverting to the importance of easy intercourse, as explained in a former section, we need only say here, that a horse which can draw only one ton on our best roads, can draw thirty with the same speed in a canal-boat. And what a glorious triumph to science and art it is, to be able to conduct * vessels of all kinds, even those originally intended for the ocean surge alone, through the quiet valleys of an interior country ! In Scotland, now, along the Caledonian canal, a noble frigate may be seen, wandering as it were among the inland solitudes, and displaying her grace and majesty to the asto- nished gaze of the mountain shepherd; and when she has traversed the king- dom, and visited the lonely lakes, whose waters until lately had borne only the skiff of the hunter, she descends again by the steps of her liquid stair, and safely resumes her place among the waves. It was lately in contemplation to lead a ship canal across the isthmus Avhich joins North and South America. The elevation to which the canal must reach, to surmount the central ridge, is considerable, and will increase the difficulty; but such important consequences would follow the accomplish- ment of the object, that, Avith the continuance of general peace, and the in- crease of political wisdom, it will probably be attained. If so, the loaded vessel, rising from the Atlantic, would soon be descried among the mountain heights, and, a few hours after, Avould be safely lodged in a port of the oppo- site sea; having performed, by a near cut, a voyage which at present costs months of delay and hazard, in a tedious navigation round the whole southern continent.—And if the Red Sea and Mediterranean were joined in the same way, as has also been proposed, the operation would, in effect, bring India nearer to Europe, and would more and more strengthen the bonds of mutual utility and brotherhood among the nations of the earth. Then, indeed, might I FLUID LEVEL. 135 it be said with truth, that the world is a vast garden, given to man for his abode, of which every spot has its peculiar SAveets and treasures ; but, because the cultivator of each may exchange a itshare of its produce for shares in re- turn, the same general result follows as if every field or farm contained within itself the climates and soils and capabilities of the whole. In a canal, the least deviation from the true level Avould immediately cause any water admitted into it to flow towards the lower end. This flux to a lower situation is Avhat is going on in the myriads of streams, which render the face of the earth a scene of such varied beauty and incessant change. As in the animal body, from every the minutest point, a little vein, endowed with living power, takes the blood which has just brought life and nutriment to the part, and delivers it into a larger vein, Avhence it passes into a larger still, until, at last, in the great reservoir of the heart, it meets the blood re- turned from every part of the body, so, in this terraqueous globe, where the magic moving power is simply fluid seeking its level, does the rain, Avhich falls to sustain vegetable and. animal life, and to renovate nature, glide from every point of the surface into a lower bed, and from thence into a lower still, until the countless streams, so formed, after every variety of course, combine to form the swelling rivers, Avhich return the accumulated Avaters into the common reservoir of the ocean. In the living body, the arteries carry back the blood with renewed vitality to every point Avhence the veins had with- draAvn it, and so complete the circulation ; and in what may be called the living universe, the circulation is completed by the action of heat and of the atmosphere, which, from the extended face of the ocean, raise a constant exhalation of watery vapour of invisible purity, Avhich the winds then carry away and deposit as rain or dew on every spot of the earth. A very slight declivity suffices to give the running motion to water. Three inches per mile, in a smooth straight channel, gives a velocity of about three miles per hour. The Ganges, Avhich gathers the waters of the Himalaya mountains, the loftiest in the world, is, at eighteen hundred miles from its mouth, only eight hundred feet above the level of the sea—that is, above twice the height of St. Paul's Church in London; and to fall these eight hundred feet, in its long course, the water takes nearly a month. The greater river Magdalena, in South America, whose channel, for a thousand miles, is between two ridges of the Andes, falls only five hundred feet in all that dis- tance. Above the commencement of the thousand miles, it is seen descending in rapids and cataracts from the mountains. The gigantic Rio de la Plata has so gentle a descent to the ocean, that, in Paraguay, fifteen hundred miles from its mouth, large ships arrive Avhich have sailed against the current all the way, by the force of the wind alone: that is to say, which on the beautifully inclined plane of the stream, have been gradually lifted by the soft wind, and even against the current, to an elevation greater than that of our loftiest spires. A small lake or extensive mill-pond, with uneven bottom, if suddenly emptied by a sluice, or opening at its lowest part, Avould exhibit a number of pits or pools of various size and shape left among the inequalities. But sup- posing rain to fall, and frequently to recur, the water seeking its level Avould soon effect a very remarkable change. In consequence of each pool dischar- ging over its lowest part, that is, sending out a streamlet either into another lower pool, or into a channel leading directly to the sluice or opening, there would be a constant wearing doAvn of the part or side of the pool over which the water was running, that is to say, a deepening of a breach or channel there, and the surface of Avater in the pool would be consequently becoming lower, Avhile, at the same time, the bottom Avould be rising, owing to the de- 136 HYDROSTATICS. posit of sand or mud AA'ashed down by the rain from the elevations around; and these two operations continuing, the pool would at last altogether disap- pear. And by this change going on in every pool through the whole of the emptied mill-pond, the general bottom would at last exhibit only a varied or undulated surface of dry land, with a beautiful arrangement of ramifying AA-ater channels, all sloping with a precision unattainable by art, to the general mouth or estuary.—The reason that, in the supposed case, and in every other, a watercourse soon becomes so singularly uniform, both as to dimension and descent, is, that any pits or holloAvs in it are filled up by the sand and mud carried along in the stream, and deposited where the current is slack; while any elevations are worn away by the action of the more rapid current which accompanies shallowness. The above paragraph describes, in miniature, what has been going on over the general face of our earth ever since that convulsion of nature which pro- duced its present form. In many places the phenomenon is already com- plete ; in others it is only in progress. The whole of what is now dryland, has at some period been under water, and much of it has evidently been a gradual deposition from water. By some extraordinary convulsion, therefore, our present continents and islands must have been thrown up from the bot- tom of an ocean, or an ocean must have subsided away from them ; and in either case the land must have merged as checkered and unsightly as the bottom of the emptied lake above supposed. And it is the gradual operation of water seeking its level which has at last converted the earth into the para- dise which we now behold. The marks of the former state of the world, and of the progressive change, are everywhere most strikingly evident to the enlightened eye of philosophy. The present kingdom of Bohemia, for instance, is the bottom of one of the great lakes formerly existing over Europe. It is a basin or amphitheatre, formed by a wall of mountains, and the only gate or opening to it, is that remarkable one by which the water now escapes from it, and which evidently has been gradually cut or formed by the action of the running stream. As the bottom became uncovered, owing to the sinking of the Avater, and the formation of a regular sloping channel from every part, the former lake was converted into a.fine and fertile country, a fit habitation for man; and the continued drain from it of the rains which fall over its surface, and either pass rapidly aAvay, or sink into the earth, and ooze again more gradually in the form of springs, is the beautiful river Avhich we now call the Elbe. In Switzerland, many of the valleys Avhich were formerly lakes, have the opening for the exit of water so narroAV, that, as happened in one of them a feAV years ago, a mass of snoAv or ice falling into it, converts the valley once more into a lake. On the occasion alluded to, the accumulation of water within was very rapid; and although, from the danger foreseen to the coun- try below, if the impediment should suddenly give way, every means Avas tried to remove the Avater gradually, the attempt had not succeeded when the frightful burst took place, and involved the inferior country in common ruin. lhe magnificent Danube is the drain of a chain of basins or lakes, which must, at one time, have discharged or run over one into another; but owing to the continued stream cutting a passage at last low enough to empty fl a I y are,now regions of fertility, occupied by civilized man, instead o the fishes Avlnch held them formerly. This operation is still going on in all the lakes of the earth. The Lake of Geneva, for instance, although con- hned by hard rock, is lowering its outlet, and the surface has consequently talfen within the period of accurate observation and records ; and as, at the FLUID LEVEL. 137 same time, the wearings of the neighbouring mountains, brought down by the winter torrents, are filling up its bed, if the town of Geneva last long enough, its inhabitants may have to speak of the river in the neighbouring valley, in- stead of the picturesque lake which now fills it. Already several towns and villages, which were close upon the lake a century ago, have fiolds and gar- dens'Spreading between them and the shore. Illustrating this subject, it is very interesting to observe the contrast between the pure blue water of the Rhone issuing from the lake of Geneva, and the turbid streams which joins its course a little farther down. The tor- rents Avhich fall into the lake all around, are equally charged with the debris or wearings of the mountains; but, having deposited all their load in the still bosom of the lake, the pure water alone escapes to form the river. The streams, however, coming to the Rhone directly from the Alps, and bringing with them their charge of broken-down earth, even after they have joined it, are long distinguishable by their muddy water. It is the mud deposited as here described, which is gradually filling up all lakes, and which has formed the vast regions of flat country seen about the mouths of great rivers. The greater part of Holland is deposition of this kind, the whole of lower Egypt, a great part of Bengal, &c, &c. There are some lakes on the face of the earth which have no outlet towards the sea,—all the water which falls into them, being again carried off by evapo- ration alone—and such lakes are never of fresh water, because every sub- stance, which, from the beginning of time, rain could dissolve in the regions around them, has necessarily been carried towards them by their feeding streams, and there has remained. The great majority of lakes, hoAvever, being basins Avith the water constantly running over at one part toAvards the sea, although all originally salt, have, in the course of time, become fresh, because their only supply, being directly from the clouds, or from rivers and springs fed by the clouds, is fresh, while Avhat runs away from them must always be carrying Avith it a proportion of any substance that remains dis- solved in them. We thus see how the face of the earth has been gradually washed to a state of purity and freshness fitting it for the uses of man, and why the great ocean necessarily contains in solution all the substances which originally existed near the surface of the earth, soluble in water:—viz., all the saline substances. The city of Mexico stands in the centre of a vast and beautiful plain, 7,000 feet above the level of the sea, and surrounded by sub- lime ridges of mountains, many of them snow-capped. One side of the plain is a little loAver than the other, and forms the bed of a lake, which is salt for the reasons stated above;—but the lake will not long be salt, for it now has an outlet. About 150 years ago, owing to unusual rains, an extraordinary increase of the Avater took place, and covered the pavements of the city. An artificial drain was then cut from the plain, at the distance of about sixty miles from the city, to the lower external country. This soon freed the city from the Avater, and since then, becoming every year deeper by the Avearing effects of the uninterrupted stream, it is still lowering the surface of the lake, is daily rendering the Avater less salt, and is com*erting the vast salt marshes, which formerly surrounded the city, into fresh and fertile fields. The vast continent of Australasia, or New Holland, (as large as Europe,) is supposed by some to have been formed at a different time from Avhat is called the Old World, so different and peculiar are many of its animal and vegetable productions; and the idea of a later formation receives countenance from the existence of immense tracts of marshy or imperfectly drained land 138 HYDROSTATICS. discovered in the interior, into Avhich rivers flow, but seem not yet to have worn down a sufficient outlet or discharging channel towards the ocean. Where the soil or bed of a country through which a water-track passes is not of a soft consistence, so as to alloAV readily the wearing down of higher parts, and th^ filling up of hollows by deposited sand, lakes, rapids and great irregularities of current remain. We have, for instance, the line of the lakes in North America, the rapids of the St. Lawrence, and the stupendous falls of Niagara, where at one leap the river gains a level lower-by a hundred and sixty feet. A softer barrier than the rock over which the river pours, would soon be cut through, and the line of lakes Avould be emptied. The contemplation of the fact, that water in seeking its level is constantly Avearing where its rubs, and carrying the abraded portions doAvn to lower levels, and ultimately to the bed of the ocean, brings irresistibly the awful idea, that this earthly abode of ours, owing to natural causes already in operation, can have but a limited existence in its present state. No shower falls that does not send portions of mountains and plain into the depths of the ocean, and thus cause a corresponding encroachment on the shores by the rising Avater; and with revolving ages, unless new convulsions of nature disturb the progress, or art succeed, as in Holland and elsewhere, in shutting out the ocean from extensive low tracks by means of sea dykes or embank- ments, the dry land must at last disappear, and another gradual deluge em- brace the globe. There is, perhaps, nothing which illustrates in a more striking manner the exact resemblances among nature's phenomena, or their accordance with the few general expressions or laws which describe them all, than the perfect level of the ocean as a liquid surface. The sea never rises or falls in any place, even one inch, but in obedience to fixed laws, and therefore its changes may generally be foreseen and allowed for. For instance, the eastern trade- winds and other causes force the water of the Indian Ocean towards the Afri- can coast, so as to keep the Red Sea about twenty feet above the general ocean level; and the Mediterranean is a little below that level, because the evaporation from it is greater than the supply of its rivers, causing it to receive an additional supply by the Strait of Gibraltar;—but in all such cases, the effect is as constant as the disturbing cause, and therefore can be calcu- lated upon Avith confidence. Were it not for this perfect exactness, in Avhat a precarious state would the inhabitants exist on the sea shores, and on the banks of low rivers ! Few of the inhabitants of London, perhaps, reflect, when standing by the side of their noble river, and gazing on the rapid flood-tide pouring inland through the bridges, that although sixty miles from the sea, the water there is, at the moment, loAver than the surface of the sea, which may at the time be heaving, moreover, in lofty waves, covered, perhaps, with wrecks and the drowning. The horrible destruction that Avould follow any alteration in the level of the ocean, may be judged of by the effects of occasional floods, produced by rains and melting snow in the interior of countries, or by these combined with winds and high tides on the coasts. The flood at St. Petersburg, in 1825, Avas dreadful, in which strong westerly winds had retarded the flow of the Neva so much, that the Avater rose forty feet (the height of an ordinary house) above its usual mark, covered all the low parts of the town, and drowned thousands of the people. In Holland, which is a low flat, formed chiefly by the mud and sand brought down by the Rhine and neighbouring rivers, much of the country is really below the level of the common spring-tides, and is only protected from FLUID LEVEL. 139 daily inundations by artificial dykes or ramparts, made strong enough to resist the ocean. On one occasion the water broke into such an enclosure, and drowned more than sixty thousand people. What awful uncertainty then would hang over the existence of the Dutch, if the level of the sea Avere subject to change : for while we know that its waters, owing to the centri- fugal force of the earth's rotation, are seventeen miles higher at the equator than at the poles, if the level, as now established, were from any cause to be suddenly changed but ten feet, millions of human beings would be the victims. Where inundation is regularly periodical, as in the Nile and many other rivers, the hurtful effects can be guarded against, and the occurrence may even become useful, by fertilizing the soil. Tracts of land in contact with rivers, of which land the surface lies be- tween the levels of ebb and flood-tide, if surrounded with dykes, may be kept constantly covered with water, by opening the sluices only at high Avater ; or may be kept constantly drained, by opening the sluices only at low water. A vast extent of rice fields, near the mouths of rivers in India and China, is managed in this way, the admission or exclusion of water being regulated by the age of the rice plant. A great part also of the rich sugar plantations of Demerara, Esequibo, &c, on the coast of South America, are in the same predicament; and another advantage which these have over the plantations on the West-India Islands, is the saving of the labour of transport effected by the canals which intersect all the fields. " If various tubes and vessels communicate with one another, fluid admitted to them will rise to the same level in all." (Read the Analysis, p. 84.) The folloAving sketch may represent a variety of tubes and vessels, fixed upon and opening into the cistern or box G. Water poured into any one would fill the box, and would then rise to the same level in all. The dotted lines from a to f, may represent the surfaces of the fluid in the different vessels. In the figure at p. 128, it was seen why, in all upright cylin- drical vessels, as a, b and c, the fluid rises to the same level; and the figure at page 132, explained why the shape of the vessel cannot affect the level. Al- though in the oblique vessel c, re- presented here, there is more water than in a, still there is the same pressure at the bottom of both, be- cause c supports part of the weight of its contained fluid on the principle of the inclined plane. If a tube twenty miles long, and rising and descending among the inequali- ties of a country, Avere filled with Avater, and could have its ends brought together for comparison, it would exhibit two liquid surfaces having precisely the same level; and on either end being raised, the fluid Avould sink in it to overfloAv from the other. An easy mode of determining a level line at any spot is to have an open tube, bent up at its ends, a and b, and nearly filled Avith liquid: by then looking along the tAvo liquid surfaces, or through floating sights resting on them, an observer looks in a line which is quite horizontal at the middle point be- tween them. Fig. 76. a^ J] 140 HYDROSTATICS. If there were two lakes on adjoining hills of different heights, a pipe of communication descending across the valley and connecting them, would soon bring them to the same level; or if one were much higher than the other, Avould empty that one into the other. A projector thought that the vessel of his contrivance, represented here, Avas to solve the renowned problem of the perpetual motion. It was goblet- shaped, lessening gradually towards the bottom until it became a tube, turned upwards at c, and pointing with an open extremity into the goblet again. He reasoned thus : A pint of Avater in the goblet a must more than counterbalance an ounce which the tube b will contain, and must there- Fig. 77. fore be constantly pushing the ounce forward into the vessel again, and keeping up a stream or circulation, ^=S^. which will cease only when the water dries up. He at...........\ \U was confounded when a trial showed him the same level f j I] always in a and in b. V J J J A glass tube inserted near the bottom of a cask or X. //' cistern of any sort, not air-tight above, which tube is V___' then bent upwards, to appear on the outside like a barometer tube, shows by the elevation of a fluid in it, the height of the greater mass of fluid within. In like manner a tube brought from a river into a neighbouring cellar or pit, will indicate the height of the water in the river. A knowledge of the truth, that Avater in pipes will always rise again to the height or level of its source, has enabled men in modern times to con- struct those admirable systems of iron pipes, which distribute water in great towns. The Avater brought to any elevated site, in or near the town, may be delivered from a reservoir there, by the effect of gravity alone, to every cistern which is under the level of the reservoir ; the result not being affected by the pipes having to rise over heights and to descend into valleys many times in their course. On the hill north of London, on which Pentonville stands, there is such a reservoir to which water is brought from Hertfordshire, by a channel cut for the purpose upwards of thirty miles in length, and called the New River. Another reservoir has lately been constructed, by the West Middlesex Water Company, at Primrose Hill, higher than any house in town. It is filled by operation of steam-engines at the Company's works, near Hammersmith, five miles off. It will supply water to the summits of all the houses con- nected with it, and is exceedingly useful in cases of fire. Many persons have believed that the ancients were ignorant of the law, that fluid in pipes rises to the level of its source, because, in all the ruins of their aqueducts, the channel is a regular slope. Some of the aqueducts, as works of magnitude, are not inferior to the great wall of China, or the Egyp- tian Pyramids ; yet, at the present day, a single pipe of cast-iron is made to answer the same purpose, and even more perfectly. It is now ascer- tained, however, that it was not ignorance of the principle, but want of fit material for making the pipes, which cost our forefathers such enormous labour. The supply and distribution of water in a large city, particularly since the steam-engine has been added to the apparatus, approach closely to the per- fection of nature's own work in the circulation of blood through the animal body. From the great pumps or a high reservoir, main pipes issue to the chief divisions of the tOAvn: these then send suitable branches to the streets, Avhich branches again divide for the lanes and alleys ; and at last subdivide FLUID LEVEL. 141 until every house has its small leaden conduit carrying its precious freight, if required, even into the separate apartments, and yielding it anywhere to the turning of a cock. A corresponding arrangement of drains and sewers, most carefully constructed in obedience to the law of level, receives the water again when it has answered its purposes, and sends it to be purified in the great laboratory of the ocean. And so admirably complete and perfect is this counter-system of sloping channels, that a heavy shower may fall, and after washing and purifying every superficial spot of the city, and sweeping out all the subterranean passages, may, within the space of an hour, form part of the river passing by. It is the recurrence of this almost miracle, of ex- tensive, sudden, and perfect purification, which makes modern London the most healthy, while it is the largest city in the Avorld. English citizens have now become so habituated to the blessing of a sup- ply of pure water, more than sufficient for all their purposes, that it no more surprises them than the regularly returning light of day or Avarmth of sum- mer. But a retrospect into past times may still awaken them to a sense of their obligation to advancing art. How much of the anxiety and labour of men in former times had relation to the supply of this precious element! How often, formerly, has periodical pestilence arisen from deficiency of water; and how often has fire devoured whole cities, which a timely supply of water might have saved ! Kings have received almost divine honours for constructing aqueducts,to lead the pure streams from the mountains into the peopled towns. In the present day, it is he who has travelled on the sandy plains of Asia or Africa, where a well is more prized than mines of gold, or who has spent months on ship-board, where the fresh water is often doled out with more Caution than the most precious product of the still, or who, in reading history, has vividly sympathized with the victims of siege or ship- wreck, spreading out their garments to catch the rain from heaven, and then, with mad eagerness, sucking the delicious moisture—it is he who can ap- preciate fully the blessing of that abundant supply which most of us now so thoughtlessly enjoy. The author of this work will long remember the intense momentary regret with which, on once approaching a beautiful land after months spent at sea, he saw a stream of fresh water gliding over a rock into the salt waves—it appeared to him as if a most precious essence, by some accident, were pouring out to waste. The subject of fluid level leads to the consideration of springs or Avells, and of the operation of boring for water. The water which falls from the clouds, and which must all ultimately return to the sea, may find its way to the rivers, either by running directly along the surface of soils which refuse it admittance; or by first sinking into porous earth, and again oozing out at lower situations in the form of springs. If a spring be as low as the bottom of the porous earth from which it issues, that is to say, as low as the surface of the impermeable clay or rock on which at some depth all such earth rests, it may drain the whole; but if not, the water will stand at a certain level among the earth as it would among bullets in a water-tight vessel. If a hole or pit be then dug in such earth, reaching below the level of the Avater lying in it, the pit will soon be filled with water up to the level, and will be called a well. In many places this water-level is very far below the surface of the ground; and in some places, by reason of the water having an easy drainage tOAvards the sea, or of the superficial soil being altogether impermeable to it, there is none to be found within an accessible depth. 142 HYDROSTATICS. A remarkable illustration of this subject occurred a few years ago, in Kent, on the occasion of cutting between Rochester and Gravesend the canal called the Thames and Medway Canal. This canal consists of but one cut or level, seven miles long, of which two are in a tunnel through the hill—which level is that of high water in the connected rivers; the intention having been to let the canal be filled always from the rivers at high water:—but as the level of the subterranean Avater in the surrounding land, and therefore of all the inhabitants' wells there, is, as might be anticipated, half-way between the levels of high and low tides, the salt water from the rivers was no sooner admitted to the canal, than it spread into the land on either side, Avh-ere the resisting internal water-level was lower, and destroyed all the wells. If the canal had been dug a feAV feet loAver, the mischief Avould not have occurred, and the company would have escaped paying the heavy damages, Avhich rendered their undertaking a very ungainful speculation. All the wells and springs in the world are merely the rain water Avhich has sunk into the earth, appearing again, and gradually escaping at lower places; nature thus admirably making the bowels of the earth an ever-stored reservoir of the substance most indispensable to the comfort and existence of man, and of all living creatures. It is worthy of remark here, that high cultivation or agricultural improvement of a country has a great effect on the quantity of spring-Avater in it. While the face of a country is rough, the rain-water remains long among its inequalities, slowly sinking into the earth to feed the springs, or slowly running away from the surface as from bogs and marshes towards the rivers. The rivers hence have a comparatively uniform and regular supply, even when rain has not fallen for a longtime:—but in a well- drained country, the rain, by a thousand prepared channels,'finds its way to the brooks and rivers almost immediately, producing often dangerous floods or inundations of the neighbouring low grounds. A friend of the author had a Avater-fall and mill in Surrey, which he formerly let for a rent of £1,200 a year ; but after agricultural improvements in the district from which the water came, the supply of water was generally either superabundant or deficient, and the value of the mill was reduced to one-half. The surface of our globe is formed of different strata or layers, as of clay, chalk, sand, gravel, &c. &c, which appear all to have been at former periods horizontal, formed under water, and to have been afterwards thrown up, by some convulsion or convulsions of nature, into every variety of position. In particular situations, the upper surface is now concave or basin-shaped, the different strata or layers, when water-tight, being like cups or basins placed one within another; and as water poured in, to fill the space between two basins so placed, would spring out to the height of its upper or level surface, through any hole made in the side of either, so on boring for water, through an innermost or superior water-tight stratum or basin of earth, the water often springs out and rises far above the surface of the ground. London stands in a hollow of which the first-met layer is a basin of clay, placed over chalk, and on boring through the clay (sometimes of three hundred feet thickness,') the Avater issues, and in many places will form a jet considerably above the surface of the ground; showing that there is a higher source or level some- Avhere—as among the hills of Surrey, or those north of London. When fluids of different kinds and of different weights under the same bulk, are made to oppose, or to balance each other in communicating vessels—as water, for instance, in one leg of the bent tube b d c, and oil in the other— the surfaces will not at all rest or settle at the same height or level, but that of the lighter fluid will be just as much higher than that of the other as it is FLUID SUPPORT. 143 lighter. Thus a column of oil must be of a length as d o, to balance a column of water d w ; and akohol, because lighter than oil, to balance the same water, would have to stand higher still, as at a; while mercury, because thirteen times weightier than water, Avould stand only about m. The shape, size or position of the vessels in Avhich the oppos- ing fluids might stand, would have no in- fluence on the relative heights of the surfaces; for if we suppose a larger vessel, such as is represented here by the dotted lines between the letters efrn, to be substituted for the leg c d of the tube, the various fluids to balance the water in b d, would have to stand just as high in it as in the smaller tube. " A body immersed in a fluid, displaces exactly its own bulk of it, which quantity having been just supported by the fluid around, the body is held up with force exactly equal to the weight of the fluid displaced, and must sink or swim according as its own weight is greater or less than this." A bladder full of air, and maintaining the bulk of a pound of water, requires a force of one pound (except a few grains, the weight of the air,) to plunge it under Avater. The same bulk of gold is held up in water with exactly the same force ; so that, if previously balanced at the end of a weighing beam, it appears on immersion to have lost one pound of its weight. And a piece of wood, ivory or any other substance, having exactly the same bulk, is opposed on entering the fluid by the same resistance. The reason of this is obvious, for the immersed body takes the place of water which weighed one pound and yet was supported, and Avhose pressure Avas necessary for the equilibrium of the rest. In a vessel of water represented here by the figure a b, let us attend to any por- tion of the water, a single column of particles for Fig. 79. instance, represented by the line c d: we know that each column is steadily supported in its place, because the particle of the liquid immedi- ately under it is tending upwards to escape from & the surrounding pressures, with force exactly equal to the weight of the column ; and what is true of a column of single particles, is true of any other portion, such as the larger column represented by the figure/hg. If such portion weighed exactly a pound, the surface under it Avould be tending upA\*ard Avith the force of a pound ; and if the portion, without changing its bulk or form, were to become ice, it would still be exactly supported by the surface below pressing upwards Avith force of a pound ; and farther, if a simi- lar column of wood, or stone, or metal, Avere there, the surrounding pressures Avould still be the same. Again, if we suppose only half the column to be solidified, the portion h g for instance, it would still be pressed upAvards with a force of one pound at g ; but its own Aveight of half a pound, and the Aveight of the half pound of Avater above it, would produce an exact balance and main- tain rest. Fig. 79. IV f cl cf ............c__ & U e ! ci 1 144 HYDROSTATICS. It is very important to have clear notions on this subject; and as different minds apprehend such matters with different degrees of facility, and in dif- ferent ways, we shall state the same general truth in other Avords. Let us consider a mass of fluid as consisting of a vast number of extremely minute columns of single particles standing side by side, where every particle supports those above it by the tendency upwards which it acquires through the pressure of the fluid surrounding it. Now if we suppose the particles of a portion of a fluid mass, of any shape, to stick together, or to become ice Avithout change of bulk or weight, that portion Avhen solid would still be between the same forces as when fluid, and therefore would be equally sup- ported, and would remain at rest. And if gold, or silver, or glass, or wood, having the same bulk, were substituted for the supposed ice, such neAv sub- stance would still be sustained with the same force ; so that a substance of exactly the same weight as the ice or water displaced, would have no ten- dency either to rise or to fall more than the water itself had ; but a substance heavier would sink, and one lighter would swim, and in either case Avith force exactly proportioned to the difference between its Aveight and that of an equal bulk of water. Few persons, in now reading the statement of this truth—in appearance so simple and obvious—would imagine that it had remained so long unknown, and that the discovery of it may be accounted one of the most important which human sagacity ever made,—but such is the case. We owe the dis- covery to one of the master-minds of antiquity—that of Archimedes. He caught the idea one day while his limbs were resting on the liquid support of a bath : and as his god-like intellect darted into futurity, and perceived many of the important uses to which the knowledge Avas applicable, he is said to have become so moved with admiration and delight, that he leapt from the water, and unconscious of his nakedness, pursued his way homewards, call- ing out "««•/£»**, «ug»**," I have found it. He was thinking chiefly of the ready means, thus obtained, of ascertaining in all cases what has since been called the specific gravity of bodies, viz., the comparative weights of equal bulks of different substances ; as of gold, or silver, or copper, or iron, com- pared with water ; and in the case of mixtures, as of gold with silver for instance, of declaring at once the proportion present of each—important problems, which, until then, could not be correctly solved. The hydrostatic law now explained, has since led to great advances in various arts. It may be regarded as a chief foundation of chemistry, for by it the chemist distinguishes one substance from another, distinguishes a pure from an impure substance, and discovers the nature of many mixtures or compounds. The merchant often judges by it of the worth of his merchan- dize. In any case it enables an inquirer to ascertain at once the exact size or solid bulk of a mass, however irregular—even of a bundle of twigs. It has become the cause of improvements in navigation, in marine architecture, and in many other arts. We shall now discuss more particularly the subject of comparative iveights or specific gravity. ■■ The force with which a body is held up in a fluid, being the exact weight of its bulk of that fluid, by ascertaining this force and comparing it with the weight of the body itself, the comparative weights or specific gravi- ties are found." (Read the Analysis, p. 126.) If any body, c, a mass of gold for instance, be suspended by a thread or FLUID SUPPORT —SPECIFIC GRAVITY. 145 Fig. 80. hair from the bottom of one scale b of a Ayeighing beam, and be balanced by \veights put kto the other scale a, and if a vessel of water be then lifted under it so that the water shall sur- round it, the body is pushed up or supported by the water with force equal to the weight of the water which it displaces; the weights, therefore, then required in the scale b to restore the balance, show truly the exact weight of the water displaced ; or of water equal in bulk to the body ; and the Aveights in the two opposite scales show the comparative weights of the body and of its bulk of water. In the supposed case, whatever weight the gold had in the air, it would seem to lose, when the water surrounded it, about a nineteenth part of such weight; that is, the water would support it with this force ; and gold Avould thus be proved to be about nineteen times as heavy as water. In making a table of specific gravities, it was necessary to select a common standard with which all other substances should be compared, and this has been done in choosing Avater ; the reason of preference being, that water can be so easily procured in a state of purity, and therefore of uniformity, in all situations. When we say, therefore, that gold is of the specific gravity 19, and copper 9, and cork 4, we mean that these substances are just so much heavier or lighter than their bulk of pure water in its densest state, viz., at the temperature of 40 degrees of Fahrenheit's thermometer. As the substances in nature differ as to form and other qualities, corre- sponding differences have to be made in the manner of ascertaining their specific gravities : the following cases are the most important. Solid bodies insoluble in wetter and heavier than it—as the metals, &c, are merely suspended by a thread or hair, having nearly the specific gravity of water, to one scale of the hydrostatic balance (simply a good weighing beam with a water-vessel below one of the scales ;) and the body being first balanced or weighed in the air, and then in water, as already described, the weight and the loss, represented, if the operator chooses, by the weights in the opposite scales, are the Aveights of equal bulks of the two substances ; and by finding, through the arithmetical operation of division, how often the weight of the water is contained in the weight of the solid, Ave find the specific gravity of the solid, or hoAV much it is weightier than its bulk of water.—It is almost superfluous to remark, that putting weights into the scale b, or taking them out of the scale a, are equivalent operations. We shall explain afterwards, that for very delicate purposes, bodies must be weighed first in a vacuum, instead of in air, or a suitable allowance must be made; for air itself supports a little any body immersed in it. Solids lighter than water, as cork, are weighed in it by attaching to them a mass of metal or glass heavy enough to sink them, and already ba- lanced in water for the purpose; or by making the line Avhich connects them with the Aveighing beams pass under a small pulley fixed at the bottom of the vessel, so that the rising of the end of the beam to which they are at- tached shall draw them down. 146 HYDROSTATICS. A solid soluble in water, as a crystal of any salt, may be protected during the operation of weighing in water, by previously dipping it in melted wax, so as to leave a thin covering on it; or it may be yeighed in some liquid which does not dissolve it, allowance being afterwards made for the difference betAveen the weight of such liquid and of water. Powders insoluble in water, such as gold dust, are weighed in a glass cup which has previously been balanced in water for the purpose. Powders soluble in water, must be weighed in some other liquid. Mr. Leslie, the highly endowed professor of natural philosophy in the University of Edinburgh, has lately suggested a novel and ingenious mode of ascertaining the specific gravities of pulverized or porous bodies ; but as it can be understood only by persons acquainted with the doctrines of pneu- matics, the consideration of it must come under that head. Other liquids may be compared with water in several ways. 1st. If a phial be made to hold exactly one thousand grains of distilled water, at the temperature of 40°, the weight of the same measure of any other liquid is found, by simply filling the phial, and Aveighing it. Of sulphuric acid, for instance, such a phial will contain nearly nineteen hundred grains, while of alcohol it will receive only about eight hundred. 2d. A bulb of glass, Avhich loses one thousand grains when weighed in Avater, (which thousand grains is therefore the weight of its bulk in water,) may be Aveighed in other liquids, and the difference of loss marks the specific gravity, as in the last case. The bulb for this purpose may be of any size, but one which loses in water exactly one thousand grains, is preferable, from the simplicity there- by given to the calculations :—This remark applies also to the phial last mentioned. 3d. A contrivance which renders the beam and scales altogether unnecessary, is a hollow floating bulb of glass or metal a, Avith a slender stalk rising from it to support the little scale or dish b, and with another stalk de- scending to carry the Aveight or weights at c, which serve as ballast to it. The whole is so adjusted that when displacing one thousand grains, or other known quantity of pure water, it shall float with a certain mark upon the upper stalk just at the surface of the water. By then immersing it in Fig. 81. other liquids and finding how much weight must be added to, or taken from it above or below, to make it float in them at the same elevation, the comparative weights of these other liquids and of water are found :—or the differ- ence of weight which makes it float at different elevations in water having been previously ascertained, it will only be necessary, in any other case, to note exactly its eleva- tion : an inch of the slender stalk may be equivalent to a difference of ten grains. This instrument is called an hydrometer. There are generally printed tables and di- rections accompanying all forms of it, telling the exact import of the several indications, and the allowances to be made for temperature, &c. It may be used for weigh- ing solids as well as liquids, for if any mass be put into the saucer b, weights exactly equal to the mass must be taken out of the saucer b, or from below at c, to restore the equilibrium of the instrument. The mass may be after- wards placed at c, and weighed in water. 4th. The shortest mode of ascer- taining the specific gravities of liquids, is to have a set or series of small glass bubbles of different specific gravities, so that Avhen they are thrown into any liquid, those heavier than it will sink, and those lighter will swim, Avhile that one which marks its specific gravity will remain merely suspended. FLUID SUPPORT—SPECIFIC GRAVITY. 147 The bubbles must, of course, be numbered, and the specific gravity of each be previously known. A common use of hydrometers is to ascertain the quality of the distilled spirits brought to market, as of rum, brandy, gin, &c. All these consist of alcohol more or less diluted with water ; and duty or tax is levied upon them in proportion to their strength, or the quantity of alcohol which they contain. A delicate hydrometer discovers this at once. A shop-keeper in China sold to the purser of a ship, a quantity of distilled spirit according to a sample shoAvn ; but not standing in awe of conscience, he afterwards, in the privacy of his store-house, added a certain quantity of water to each cask. The spirit having been delivered on board, and tried by the hydrometer, Avas discovered to be wanting in strength. When the vender was charged with the intended fraud, he at first denied it, for he knew of no human means Avhich could have made the discovery; but on the exact quantity of water which had been mixed being specified, a superstitious dread seized him, and, having confessed his roguery, he made ample amends. On the instrument of his detection being afterwards shoAvn to him, he offered any price, for what he foresaw might be turned to great account in his trade. The specific gravity of aeriform substances is ascertained by means of a glass flask of known size, furnished with a stop cock. It is first weighed Avhen emptied by the air-pump, and afterwards when filled successively with water and with different airs or gases. Comparison of the Aveights gives the specific gravities, as already described. The folloAving table sIioavs, in round numbers, the comparative Aveights or specific gravities of some common substances. Water is the standard kept in vieAV, and any equal bulk of another substance is heavier or lighter than water, according to the numbers severally attached to them: Platinum .... 22! Gold.....19j Mercury . . . .13s Copper .... 8! Steel and Iron ... 8 Diamond .... 3| Glass.....3 Common stones ... 2| Complete tables are found in systems of Dictionaries of Chemistry. A cubic foot of water happens to weigh very nearly one thousand ounces avoirdupois, or 02.t pounds. Hence, in the foregoing table, the figures de- noting the specific gravities tell hoAV many times a thousand ounces of the different substances a cubic foot contains. Of gold, for instance, a cubic foot contains more than nineteen thousand ounces, being worth in money about £63,000 sterling. A cubic foot of common air contains only a little more than one ounce ; and of hydrogen gas, the lightest of ponderable things, a cubic foot contains less than a drachm. , The following facts also are illustrations of the truth, that a body immersed in a fluid is held up, or has its entrance resisted, with force equal to the weight of the quantity of fluid which it displaces. A stone Avhich on land requires the strength of two men to lift it, may be lifted and carried in AA-ater by one man. There are cases, therefore, where Common Salt . * . .2 Brick .... 2 Alcohol .... ^Ether .... Cork .... Atmospheric Air Hydrogen Gas . . . T 148 HYDROSTATICS. the support of water thus rendered useful is equivalent to the assistance of an additional hand. A boy will often wonder why he can lift a certain stone to the surface of Avater, but no farther. The invention of the diving-bell in modern times, having enabled men, in the building of piers, bridges, &c, to work under water almost as freely as above, many have experience of this influence of water : but workmen are generally surprised at first, to find that below, they can move much larger and heavier stones than they can in the air. Some had supposed the fact accounted for by saying that the denser air of the diving-bell when received into the lungs gave greater strength. In recoA'ering property from a sunken ship by the diving-bell, every thing is found to be lighter in the proportion uoav stated. This law explains also why stones, gravel, sand, and mud, are so easily moved by waves and currents. Many people expressed astonishment, in March 1825, to learn that at the Plymouth Breakwater, the storm had dis- placed blocks of stones, of many tons weight; but Ave now see that the moving water had only to overcome about half the weight of the stone. When a person lies in a bath, the limbs are so nearly supported by the water as to require scarcely any exertion on the part of the individual. When this softest of all beds has been indulged in for half an hour or more, the person, on first lifting a limb out of the water, feels surprise at its great appa- rent weight. The workers about diving-bells always experience the sensa- tion now spoken of, on returning to the air. The bodies of most fishes are nearly of the specific gravity of water, and, therefore, if lying in it without making exertion, they neither sink nor rise very quickly. When this subject was less understood, many persons be- lieved that fishes had no weight in water ; and it is related as a joke at the expense of philosophers, that a king having once proposed to his men of science, to explain this extraordinary fact, many profound disquisitions came forth, but not one of the competitors thought of trying what really Avas the fact. It Avas beneath the dignity of science in those days to make an experi- ment. At last a simple man balanced a vessel of water in scales, and on putting a fish into the water, showed its scale preponderating just as much as if the fish had been weighed alone. In the sense now explained, water is said to have no weight in water. The least force will raise a bucket of water from the bottom of a well to the sur- face ; but if the bucket be lifted at all farther, its weight is felt just in propor- tion to the part of it which is above the surface. " A body lighter than its bulk of water will float, and with force propor- tioned to the difference." (Read the Analysis, p. 126.) The reason of this is clear. If any body, the cylinder a b c d for instance, be partially immersed in water, we know that the Fie. 82. upward pressure of the water on the bottom c d, is exactly what served to support the water displaced by the body, viz., water of the bulk, ef c d. The body, therefore, that it may remain out as far as here represented, must have exactly the weight of the Avater which the immersed part of it displaces ; and if it be lighter than this, it will rise farther; if heavier, it will sink farther until the exact balance be produced. FLUID SUPPORT —SWIMMING. 149 Hence of any body which floats in water, a pound weight displaces just a pound of water, whether the body be very fight in proportion to its bulk, as cork, or heavier, as a piece of dense wood. This is experimentally shown by putting such bodies to float in a vessel originally full of water. The water displaced by each must run over the sides of the vessel, and may be caught and measured. Hence a porcelain basin weighing four ounces will sink in water only as far as a similar wooden basin or bowl of the same Aveight; and the weight of either basin may be in the substance of which it is formed, or in any thing else put into it as a load. Hence a boat made of iron floats just as high out of water as a boat of simi- lar form and size made of wood, provided the iron be proportionately thinner than the wood, and therefore not heavier on the whole. An empty metallic pot or kettle is often seen floating with a great part of it above the surface of the water.—Prejudice for a long time prevented iron boats from being used, although, for various purposes, they are superior to others; and there are still people who would fear to go on board of a ship built of the strong and singu- larly durable Indian teak, because it is heavier than water, and in the form of a log, therefore, sinks in water. Many fine ships of the line, however, and East-Indiamen of fifteen hundred tons or more, are now built of teak. Hence a ship carrying a thousand tons weight will draw just as much water. or float to the same depth, whether her cargo be of cotton or of lead:—and the exact weight of any ship and her cargo may be determined by finding hoAv much water she displaces. In canal boats, which are generally of a simple form, this truth affords a ready rule for ascertaining the quantity of their load. The human body, in an ordinary healthy state Avith the chest full of air, is lighter than water. If this truth were generally and familiarly understood, it Avould lead to the saving of more lives, in cases of shipAvreck and in other accidents, than all the mechanical live-preservers which man's ingenuity will ever contrive. The human body with the chest full of air naturally floats with a bulk of about half the head above the Avater,—having then no more tendency to sink than a log of fir. That a person in water, therefore, may live and breathe it is only necessary to keep the face uppermost. The reason that in ordinary accidents so many people are droAvnedwho might easily be saved, are chiefly the following:— 1st. They believe that the body is heavier than water, and therefore that continued exertion is necessary to keep it from sinking; and hence, instead of lying quietly on the back, with the face upwards, and with the face only out of the Avater, they generally assume the position of a swimmer, in which the face is doAvnwards, and the whole head has to be kept out of the Avater to allovv of breathing. Now, as a man cannot retain this position but by continued exertion, he is soon exhausted, even if a swimmer, and if he is not, the unskilful attempt will scarcely secure for him even a few respira- tions. The body raised for a moment by exertion above the natural level, sinks as far below it when the exertion ceases; and the plunge, by appearing the commencement of a permanent sinking terrifies the unpractised indivi- dual, and renders him an easier victim to his fate.—To convince a person learning to SAvim of the natural buoyancy of his body, it is a good plan to throAV an egg into water about five feet deep, and then desire him to bring it up again. He discovers that instead of his body Avith the chest full of air 11 150 HYDROSTATICS. naturally sinking towards the egg, he has to force his way downwards, and is lifted again by the water as soon as he ceases his effort. 2d. They fear that water entering by the ears may droAvn, as if it entered by the nose or mouth, and they make a wasteful exertion of strength to pre- vent it; the truth being, however, that it can only fill the outer ear, as far as the membrane of the drum, where its presence is of no consequence. Every diver and swimmer has his ears thus filled Avith water, and cares not. 3d. Persons unaccustomed to the Avater, and in danger of being drowned, generally attempt in their struggle to keep their hands above the surface, from feeling as if their hands Avere imprisoned and useless Avhile below; but this act is most hurtful, because any part of the body held out of the water, in addition to the face Avhich must be out, requires an effort to support it, which the individual is supposed at the time ill able to afford. 4th. They do not reflect, that when a log of wood or a human body is floating upright, Avith a small portion above the surface, in rough water, as at sea, every Avave in passing must cover it completely for a little time, but will again leave its top projecting in the interval. The practised swimmer chooses this interval for breathing. 5th. They do not think of the importance of keeping the chest as full of air as possible ; the doing which has nearly the same effect as tying a blad- der of air to the neck, and Avithout other effort, will cause nearly the whole head to remain above the water. If the chest be once emptied, Avhile from the face being under water the person cannot inhale again, the body remains specifically heavier than water, and will sink. When a man dives far, the pressure of deep AA*ater compresses, or dimi- nishes the bulk of the air in his chest, so that, without losing any of that air, he yet becomes really heavier than Avater, and would not again rise, but for the exertion of swimming. The author of this Avork once saw a sailor (a fine-bodied West-India negro) fall into the calm sea from a yard-arm eighty feet high. The velocity on his reaching the water was so great, that he shot deep into it, and, of course, his chest Avas compressed as now explained: probably also the shock stunned him, for although he was an excellent SAvimmer, he only moved his arms feebly once or tAvice, and was then seen gradually sinking for a long time afterwards, until he appeared only as a black and distant speck, descending towards the unknown regions of the abyss. Every person needs not learn to SAA*im; but every one who makes voyages should have practised the easy lesson of resting in the water Avith the face out. The head, from the large quantity of bone in it, is a heavy part of the body, yet, owing to its proximity to the chest which is comparatively light, a little action of adjustment with the hands easily keeps it uppermost; and there is an accompanying motion of the feet, called treading the water, not difficult to learn, Avhich suffices to sustain the entire head above the surface. Many of the seventy passengers who Avere swallowed up on the sudden sinking of the Comet steam-boat near Greenock, in November, 1825, might have been saved by the boats, which so soon went to their assistance, had they known the truth which we are now explaining. A man having to SAvim far, may occasionally rest on his back for a time, and resume his labour when he is somewhat refreshed. So little is required to keep a swimmer's head above water, that many in- dividuals, although unacquainted Avith what regards swimming or floating, have been saved after shipwreck, by catching hold of a few floating chips or broken pieces of Avood. An oar will suffice as a support to half a dozen FLUID SUPPORT —STABILITY. 151 people, provided no one of the number attempts by it to keep more than his head out of the water ; but often, in cases where it might be thus serviceable, from each person Avishing to have as much of the security as possible, the number benefited is much less than it might be. The most common contrivances, called life-preservers, for preventing drowning, are strings of cork put round the chest or neck, or air-tight bags applied round the upper part of the body, and filled, when required by those who wear them blowing into them through valved pipes. On the great rivers in China, where thousands of people find it more con- venient to live in covered boats than in houses upon the shore, the younger children have a hollow ball of some light material attached constantly to their necks, so that, in their frequent falls overboard, they are not in danger. Life-boats have a large quantity of cork mixed in their structure, or of air-tight vessels of thin copper or tin plate: so that, even when the boats are filled Avith Avater, a considerable part still floats above the general surface. Swimming is much easier to. quadrupeds than to man, because the ordi- nary motion of their legs in AA-alking and in running is that which best supports them in SAvimming. Man is at first the most helpless of creatures in water. A horse while swimming can carry his rider with half the body out of the Avater. Dogs commonly sAA'im well on the first trial.—Swans, geese, and water-fowls in general, owing to the great thickness of feathers on the under part of their bodies, and the great volume of their lungs, and the holknvness of their bones, are so bulky and light, that they float upon the water like stately ships, moving themselves about by their webbed feet as oars. A water-fowl floating on plumage half as bulky as its naked body, has about half that body above the surface of the Avater; and similarly a man reclining" on a floating mattrass, as in the hydrostatic bed afterwards to be described, has nearly as much of his body above the level of the water-surface, as he forces of the mattrass under it. His position, therefore, depends on the thickness of the mattrass. A man Avalking in deep water may tread upon sharp flints or broken glass with impunity, because his weight is nearly supported by the water. But many men have been drowned in attempting to Avade across the fords of rivers, from forgetting that the body is so supported by the water, and * does not press on the bottom sufficiently to give a sure footing against a very trifling current. A man, therefore, carrying a weight on his head or in his hands held over his head as a soldier bearing his arms and knapsack, may safely pass a river, where, without a load, he would be carried doAvn the stream. There is a mode practised in China of catching wild ducks, Avhich requires that the catcher be Avell loaded or ballasted. Light grain being first strewed upon the surface of the water to tempt them, a man hides himself in the midst of it, under Avhat appears a gourd or basket drifting Avith the stream, and when a flock approaches and surrounds him, he quickly obtains a rich booty by snatching the creatures down one by one—adroitly making them disappear as if they were diving, and then securing them below. Each bird becomes as a piece of cork attached to his body. Fishes can change their specific gravity, by diminishing or increasing the size of a little air-bag contained in their body. It is because this bag is situated towards the under side of the body, that a dead fish floats with the belly uppermost. . Vnimal substances, in undergoing the process of putrefaction, give out much aeriform matter. Hence the bodies of persons droAvned and remaimeg 152 HYDROSTATICS. in the water, generally swell, after a time, and rise to the surface, again to sink when the still increasing quantity of air shall burst the containing parts. A floating body sinks to the same depth whether the mass of fluid support- ing it be great or small:—as is seen when a porcelain basin is placed first in [ a pond, and then in a second basin only so much larger than itself that a spoonful or two of water suffices to fill up the interval between them. One ounce of water in the latter way may float a thing weighing a pound or more, exhibiting another instance of "the hydrostatic paradox:—And if the largest ship of war were received into a dock, or case, so exactly fitting it that there were only half an inch of interval between it and the wall or side of the con- taining space, it would float as completely, when the few hogsheads of water required to fill this little interval up to its usual water-mark were poured in, as if it were on the high sea. In some canal locks, the boats just fit the place in which they have to rise and fall, and thus the expense of Avaterat the lock is diminished. The preceding examples of floating are all illustrations also of the truth that the pressure of a fluid on any immersed body is exactly proportioned to the depth and extent of the surface pressed upon. The lateral pressures just balanced one another, and the upward pressure has to be balanced by the weight of the body. Similar reasoning to that which proves that the whole weight of a body acts as if lodged in the point called its centre of gravity, proves that the whole buoyancy of a body, or the upward push of the fluid in which a body is immersed, acts as if lodged in the point which was the centre of gravity of the fluid displaced. This point consequently is called the " centre of buoyancy." A floating body, to be stable in its position, either must have its centre of gravity below the centre of buoyancy—in which case it resembles a pendu- lum ; or it must have a very broad bearing on the water, so that any inclina- tion may cause the centre of gravity to ascend,—in which case it resembles a cradle or rocking-horse. Hence arises, in the stowing of a ship's cargo, the necessity of putting the heavy merchandize underneath, and generally of putting iron ballast under all the merchandize. Hence, also, the danger of having a cargo or ballast Avhich is liable to shift its place. A ship loaded entirely with stones, is sometimes lost by a wave making her incline • for a moment so much that the load shifts to one side, which is then kept down. For a similar reason, a cargo of salt or sugar has a peculiar danger attached to it, for if the ship leak, the cargo may be dissolved, and then pump out with the bilge water, leaving her with altered trim. In a fleet coming home from India, in 1809, four fine ships disappeared during a hurricane off the Isle of France/and from what happened to the other ships that were saved, the cause of the destruc- tion was supposed to be, that the saltpetre of the cargoes had been dissolved and pumped out, and that the ships in consequence became unmanageable. Bladders used by beginners in swimming are dangerous, unless secured so as not to shift towards the lower part of the body. A great inventor (in his own estimation) published to the world, that he had solved the important problem of walking safely upon the water : and he invited a crowd to witness his first essay. He stepped boldly upon the Avave, equipped in bulky cork boots, which he had previously tried in a butt of water at home ; but it soon appeared that he had not pondered sufficiently on i FLUID SUPPORT AMONG FLUIDS. 153 the centres of gravity and of floatation, for in the next instant all that was to be seen of him was a pair of legs sticking out of the water, the movements of which showed that he was by no means at his ease. He was picked up by help at hand, and, with his genius cooled and schooled by the event, was conducted home.—Some soldiers once finding a few cork jackets among old military stores, determined to- try them; but mistaking the shoulder straps for lower fastenings, they put them on as drawers, and on then plunging in, with the hope of being able to sit pleasantly on the water, their heavy heads went down, and they Avere nearly drowned. When, on the return of summer, the ice breaks up in the polar regions, immense islands of it are set afloat, rising high into the air and sinking deep into the sea. The melting process, in most cases, does not go on equally in the Avater and in the air, and from the mass, consequently, changing form, its stability is often lost, and one of the grandest phenomena in nature follows— the overturning of a mountain—the sudden subversion of an island—produ- cing a tumult in the ocean around, felt often at the distance of many leagues. The phenomena of pressure, floating, &c, in fluids, vary in proportion to the weight or specific gravity of the fluid. A ship draAvs less water, or swims lighter, by one thirty-fifth, in the heavy salt Avater of the sea than in the fresh water of a river: and for the same reason,a man swimming supports himself more easily in the sea than in a river. Many kinds of wood that float in water will sink in oil. A man floats on mercury as the lightest cork floats on Avater, and with practice he might be able to walk upon mercury. Had the water of our ocean been but a little heavier than it is, men after ship- wreck might have died of famine and cold, but would not have been droAvned. Oil floats on water, but sinks in alcohol or aether. The term proof spirit means spirit light enough for oil to sink in it. The strength of spirit is pro- portioned to its lightness. Cream rises in milk, and forms a covering to it. Blood, allowed to rest after flowing from the living body, separates into parts or layers, which arrange themselves according to their specific gravities. The buffy coat of inflammation (Avhere this exists) is uppermost, forming the surface of the general coagulum: towards the lower part of the coagulum there is an accumulation of red globules: and the whole of the solid part floats in the serum, Avhich is therefore loAvest of all. When the red glo- bules escape from the coagulum, they fall to the bottom even of the serum. Wine, if sloAvly and carefully poured on water, will float upon it. In a vessel shaped like a common sand-glass, only Avith a larger opening between the chambers at c, if wine be put into the Fig. 83. under chamber, and Avater into the upper, the two liquids will gradually change places : and if the lower half of the glass be covered, so as to leave the upper half Avith the ap- pearance of a simple goblet, the water will seem to have been changed into Avine. The liquids are less mixed, and change places sooner, Avhen there is a tube b to carry the water down to the bottom Avithout touching the AA-ine, and a tube a to carry the Avine directly to the top. Mercury, water, oil, air, and some other fluids may all be shaken together in the shme vessel, and on standing will separate again and arrange themselves in the order of their specific gravities. 154 HYDROSTATICS. When, in a mass of Avater, part of it is heated more than the rest, that part, by its expansion, becomes specifically lighter than the rest, and rises to the surface. Hence, when heat is applied to the bottom of a vessel con- taining water, a circulation is established, which goes on from the first moment until the operation of heating finishes:—water is always rising from the hotter parts of the vessel, and descending over the colder parts. In like manner, Avhen a tall glass containing hot water is dipped into cold Avater, a downward current takes place within the glass near the sides all round, and there is an upward current in the middle. This motion may be rendered very obvious by small portions of amber thrown into the water, for these being nearly of the specific gravity of water, rise and descend with it. On account of the current established in such cases, heat applied to the bot- tom of a vessel of liquid is soon equally diffused over it; but heat applied at the top is there confined, because the heated and lighter fluid does not descend. Water may be made to boil at its surface, while a piece of ice lies at the bottom. The converse is impossible. The current in a fluid, produced by local change of temperature, is an important part of the folloAving process, which the author deems applicable to various useful purposes.—Heat may be transferred from one liquid to another, without mixing them, by making the hot liquid descend in a very thin metallic tube, through the cold liquid rising around it in a larger tube. Boiling water from the vessel e, for instance, may descend slowly by the small tube e a b f, which is sur- Fig- 84. rounded from a to b by cold water ascending through the tube c g. Then, as the tem- perature of two liquids, brought so nearly into contact with each other, will not, after a very short time, differ, in any one place, more than a feAv degrees, it fol- Ioavs that the Avater lately cold, will, on leaving the part of the tube g, which is in contact with the boiling Avater descending di- rectly from e, be nearly boiling, Avhile the water lately hot will, jL6 on leaving the tube at b,.which "IN is in contact with cold water pressure, and abstraction of the heat which is combined with them in the aeriform state. Carbonic acid, the common coal gas, &c, have been treated in this way. Now it becomes an interesting question whether many of the substances known as liquids on the face of the earth, A-yhere they are bearing the pressure of the atmosphere, would not appear as airs if that pres- sure did not exist. On investigating this subject by experiment, we accordingly find, that sether, alcohol or ardent spirits, volatile oils, fyc, and even water itself, are known to us here as liquids, only because their particles are kept together by the weight and pressure of a superincumbent atmosphere. Any of these substances, relieved by art from such pressure, quickly becomes an air or gas, just as a common gas, which has been kept in the state of liquid by any great pressure, becomes air again on being relieved. In our first chapter Ave explained the dependence of the three forms which any body may assume, viz., of solid, liquid, or air, on the quantity of heat diffused among the particles; we now see, hoAvever, that to understand the subject completely, Ave must consider also the effect of accidental pressure; for, while heat is the poAver separating the atoms in the changes mentioned, it has to overcome both the mutual attraction of the atoms and the additional force of the atmosphere pressing them together. The combined influence of these forces is fully displayed in the two phenomena called boiling and evaporation, Avhich exhibit the progress of the change of a liquid into an aeriform fluid. We noAV proceed to examine these phenomena. Boiling.—If Avater be placed in a suitable vessel over a common fire, or over the flame of a lamp, it is gradually heated to a certain degree; and then small bubbles of aeriform matter, viz., water, in the state called steam, are seen forming at the bottom of the vessel: and successively rising to the sur- face, where they disappear by mixing Avith the atmosphere; and the opera- tion being continued, the quantity of water diminishes with every bubble, until the whole vanishes under the neAv form of air. This change takes place in water, under common circumstances, at the degree of heat marked 212° on Fahrenheit's thermometer, and called, on that account, the boiling point of Avater ; at which, therefore, the repulsive power among the particles is just sufficient to overcome both their natural attraction, and the compressing force of the atmosphere of fifteen pounds on the inch. But a less degree of heat suffices if the pressure, of the atmosphere be lessened or removed ; and a greater degree is required if pressure be increased. Water on the top, of Mont Blanc boils at 180°, because relieved from the pressure of the air that is beloAV the level of the mountain's summit; and at all inter- mediate heights in descending to the level of the sea, and beyond that into mines, there is a corresponding increase of the boiling temperature. So exactly is this the case, that we noAV find it to be a good method of ascertain- ing the heights of places, merely to observe the heat- of boiling water at them. To many persons the information here given that boiling water is not equally hot in all places, will appear extraordinary: and they will not under- stand, that even in the same place, at different times, when the barometer is high or Ioav, there will be corresponding differences.—Again, near the bottom of a boiler, the water is hotter than above, because it is bearing an additional ATMOSPHERIC PRESSURE—BOILING. 183 pressure proportioned to the depth, and does not, therefore, give out the steam which it would part with if a little higher up. In very large and deep boilers, therefore, such as are used in great porter breAveries, the liquor is much more heated than it can be in smaller vessels ;—a circumstance which proba- bly has an influence on its ultimate quality. While water, under common atmospheric pressure, or when the barometer stands at thirty inches, boils at 212°, other substances, with other relations to heat, have their boiling points higher or lower:—aether, for instance, at 98°; spirit or alcohol at 174°; fish-oil and tallow at about 600°; mercury at 650°. It is in consequence of the different temperatures at which the particles of different substances acquire repulsion enough to rise against the atmospheric resistance, that we are enabled to perform the operation called distilling. If a mixture of spirits and water, for instance, be heated up to 180 deg., the spirit will pass off in the aeriform state, leaving the AA*ater behind, and may be caught apart and cooled to condensation in any fit receiver. Distil- lation is the best means we possess of separating many substances from each other, as spirit from wine or other fermented liquor; various acids from water; water itself from its common impurities ;—and e\ren the separation of mercury from silver or gold Avhich it has been used to dissolve from among the rubbish of a mine or river-bottom, is merely a distillation. We must call to mind here Avhat Avas mentioned in a former part of the Avork,that a large quantity of heat combines with every substance" during the change of form from solid to liquid, or from liquid to air ; a quantity Avhich, from not remaining sensible to the thermometer, has received the name of latent or concealed heat. The Avhole of this is given out again in the contrary change. In the conversion of water into steam, the heat Avhich thus disap- pears is about 1,000 degrees, or six times as much as is required to raise the cold Avater to the boiling point: this is proved by the time and fuel expended in boiling any quantity to dryness, and by the fact that a pint of water in the form of steam will combine instantly with six pints of cold water, raising the whole to boiling heat. But for the fact of latent heat, the conversion of a liquid into air would not be the gradual process of boiling which we now see, but a sudden and terri- ble explosion: for when any quantity of water were raised to the boiling heat, one degree more Avould be sufficient to convert the whole into steam. And but for the same reason, the thaAving of Avinter snoAV would always be a sudden and frightful inundation ; the Avhole load of a mountain or plain becoming at once as a lake bursting from its enclosing barriers. On the other hand, if Avater in freezing had not to give out again its latent heat, after any quantity Avere once cooled doAvn to the freezing point, the abstraction of one degree more AA-ould instantly conA*ert the whole into a solid mass. Thus, then, by an arrangement effecting most important purposes in nature and art, all changes from solid to liquid and from liquid to air, and the converse changes, are very gradual. If a little heat be abstracted from steam, a part of the steam proportioned to the abstraction is immediately condensed into water. What is called steam, in common language—as the vapour Avhich becomes visible at a little distance from the spout of a boiling kettle or the chimney of a tea-urn—is not truly steam, but small globules of AArater already condensed by the cold air and mixed Avith it. Steam is as dry and invisible as air itself; but the instant that it comes in contact with air or other bodies colder than itself, it becomes Avater. 184 PNEUMATICS. By means of the exhausting air-pump on one hand, and of the condensing syringe on the other, all the above-mentioned phenomena, depending on the atmospheric pressure, and its increase or diminution, may be strikingly shown. Thus, to exhibit the effect of diminished pressure, water not heated by several degrees to the boiling point of ordinary low situations, but which would be boiling at the top of Mont Blanc, is caused to boil instantly by placing it under the receiver of an air-pump, and making a few strokes of the piston; if the exhaustion be rendered nearly complete, the water will boil, even when colder by 20 degrees than the blood of animals ; and at degrees of temperature still much loAver,it will rapidly assume the form of air, although not Avith force sufficient to produce the violent agitation of boiling. Other liquids, as spirits, aether, &c.,from requiring inferior degrees of heat to sepa- rate their particles to aeriform distances, boil under the receiver of an air- pump at very low temperatures ; aether, for instance, when as cold as freez- ing water. On the other hand, to exhibit the effect of increased pressure, if we con- fine the particles of a liquid still more than by a common atmospheric or equivalent pressure, degrees of heat higher than the common boiling point will be required to separate them. In a diving-bell, the boiling point of water is higher than 212 deg. in proportion to the depth which the bell has reached: and if, at the surface of the earth, we heat water in a close vessel into which air is forced so as to press thirty pounds on the inch instead of fifteen, as the atmosphere does; or from which we prevent the steam's escaping until it has acquired the force of a double atmosphere,.—before making the liquid boil, we shall have to raise the heat, in a corresponding proportion, beyond 212 deg. Under a very strong pressure, water may be rendered almost red- hot, but the force with which its particles are then tending to separate is almost that of inflamed gunpowder. Even then, however, if a gradual issue were allowed, only a certain quantity of the water would absorb and render latent the existing excess of heat above 212 deg., and would become common steam, leaving behind a considerable portion as boiling water of the ordinary temperature. The fact that liquids are driven off, or made to boil at loAver degrees of heat when the atmospheric pressure is lessened or removed, has recently been applied to some very useful purposes. The process for refining sugar is to dissolve impure sugar in water, and after clarifying the solution, to boil off or evaporate the Avater again, that the dry crystallized mass may remain. Formerly this evaporation was performed under the atmospheric pressure, and a heat of 218° or 220° was required to make the syrup boil; by which degree of heat, however, a portion of the sugar was discoloured and spoiled, and the whole product was deteriorated. The valuable thought occurred to Mr. HoAvard, that the water might be dissipated by boiling the syrup in a vacuum, or at least a place from which air was nearly excluded, and therefore at a low temperature. This was done accordingly ; and the saving of sugar and,the improvement of quality were such, as to make the patent-right, which secured the emoluments of the process to him and other parties, worth many thousand pounds a-year. The syrup, during this process, is not more heated than if in a vessel merely exposed to a summer sun. In the preparation of many medicinal substances, the process of boiling in ATMOSPHERIC PRESSURE —BOILING. 185 vacuo is equally important. Many extracts from vegetables have their' vir- tues impaired, or even destroyed, by a heat of 212° ; but when the water U m m.ak»ng the extract is driven off in vacuo, the temperature need never be higher than blood-heat, and all the activity of the fresh plant remains in the extract. • In the same manner, in the process of distillation,—Avhich is merely the receiving and condensing again in appropriate vessels the aeriform matter raised by heat from any mass,—substances which are changed and injured by an elevated temperature, may be obtained of admirable quality by carry- ing on- the operation in a vacuum. The essential oils of lavender, pepper- mint, «fec, never had the natural flavour and virtues of the plants until within the last few years, since this plan has been adopted. The influence on the human system of vegetable medicines obtained in the old or in the neAv way, is so different, that the prescriber should carefully advert to the circumstance. The apparatus for evaporating and distilling in vacuo consists of vessels strong enough to bear, when quite empty, the external atmospheric pressure, and which are therefore generally of arched form. The vacuum is produced and maintained by air-pumps driven by a steam-engine or otherwise ; or by first admitting steam to expel the air, and then condensing the steam into water. The author has suggested a very simple contrivance to answer, in certain cases, the purpose of such air-pumps and steam-engines or apparatus. It is merely to establish a communication between a close boiler, as a, and the vacuum at the top of a water barometer, as b. To produce that vacuum, the strong vessel b forming the top of the barometer, and thirty-six feet of tube below, reaching to d, are first filled with Avater through a cock c at the top ; this cock being then shut, and another cock d at the bottom, which was shut, being opened, the Avater will sink down out of the bessel b, until the column in the tube be only thirty-four feet high, as at/, that being the height Avhich the atmosphere will support. On then opening a communication between the boiler a and the vacuum in b, the operation will go on as desired, and the steam rising from a may be condensed in b by a little stream of cold Avater allowed constantly to run through from above. This water, it is evident, would always pass downwards to form part of the column below, Avithout filling up or impairing the vacuum. If air should find admittance in any way, the original degree of vacuum could easily be reproduced as at first; and to prevent inter- ruptions, it might be convenient to have two vessels like b, of Avhich one could always be in action while the other was being emptied of air. The author planned this as a simple apparatus for the preparation of medicinal extracts; and it appears Avell suited also for the manufacture of sugar in the colonies, where air-pumps and nice ma- chinery can Avith difficulty be either obtained or managed. On many sugar estates there is a fall of Avater, Avhich would supply the barometer Avithout the trouble of pumping. The tube d c need not be perpendicular, provided it be longer in proportion to its obliquity; and it may be very small: some yards of common lead-pipe Avould ansAA-er. When it was understood that, at common temperatures, water and many 186 PNEUMATICS. other liquids would be existing in the form of air, but for an atmospheric pressure opposing the separation of the particles, it became of great import- ance in many of the arts, and for comprehending certain phenomena of nature, to ascertain, very exactly, with respect to some of these liquids, the deo-rees of txpansive force belonging to them at different degrees of tempera- ture. The subject, as water is concerned, has been investigated with great care, and the folloAving table shows part of the results. The left-hand column marks temperatures from 32 deg. of Fahrenheit's thermometer, or the freez- ing point of water, to 290 deg.; and the right-hand column marks the cor- responding degrees of force with which the water tends to expand into the state of steam, and therefore also the force and density of the steam existing in any vessel above the water which it contains. One ounce and a half per square inch, is the force exerted on the sides of any containing vessel by steam rising from freezing water, that is to say, the force with which freez- ing water seeks to dilate into steam or air ; and sixty pounds per inch is the force of Avater heated to 290 deg. To many readers the idea will be quite new and surprising, that if some freezing water, or even ice, be placed in a bladder containing nothing else, and the bladder be then placed in the ex- hausted receiver of an air-pump or other vacuum, the bladder will quickly be distended with steam strong enough to support one ounce and a half on every square inch of its upper surface. At 32° force of steam is - - - - Is oz. per inch. 50 - - - - - 2| oz. 100 - . - - - 13 oz. 150 . ' . . - - 4 lbs. 180 . . - - - 7£ lbs. 212 - . - - - 15 lbs. 250 . . . . - 30 lbs. 272 - . - . - 45 lbs. 290 . . - - - 60 lbs. In this table Ave have to remark how much more rapidly the tendency to become steam increases than the temperature of the water: for a rise of eighteen degrees, viz., from 32° to 50°, at the beginning of the scale, only increases the dilating force one ounce and a quarter on the inch, while an equal rise at the top of the scale, viz., from 272 deg. to 290 deg., increases it fifteen pounds. It is most important to distinguish, however, betAveen the tendency to form steam at any temperature, and the bulk or quantity of steam formed by a given quantity of heat; for the matter imperfectly under- stood has led to many vain schemes for improving the steam-engine. The truth is, that high-pressure steam is nearly condensed steam, as high-pres- sure air is condensed air ; in other Avords, the density of steam is greater, or there must be more of it, exactly as its force is greater according to the rule explained at page 160 ; and the heat absorbed in its formation being pro- portioned to the quantity of steam in a given space, or the density, the force and the cost in fuel have ahvays nearly the same relation to each other. In one pint of steam, at 290 deg., having an elastic force of sixty pounds on the inch, there are very nearly four times as much water and four times as much latent heat as in one pint of steam at 212 deg., which has a force of fifteen pounds on the inch ;—indeed, the one pint, at 290 deg., may be changed into the four pints at 212 deg., or the contrary, by merely changing the degrees of pressure. It does not accord Avith the plan of the present work to enter farther into the details of this subject, but they may be found in various modern treatises. STEAM ENGINE. 187 Seeing the rapid increase of the expansive force in the preceding table, we have the explanation of the terrible effects occasionally produced by confined water Avhen over-heated. A boiler of any kind completely closed, and hav- ing no safety-valve, if heated to a certain degree, will explode as if charged with gunpoAvder. Unhappily the instances are too numerous where the in- cautious or ignorant use of steam has produced explosions, which have shat- tered buildings and destroyed whole neighbourhoods. The prodigious force generated by heating water Avould at first only sur- prise and terrify men, but in the course of time would lead inventive minds to inquire whether it might not be turned to use; in other words, whether some mechanism, to be called a steam-engine, might not be contrived to en- able men to make it aid them in their various labours. To this inquiry, after numerous less successful attempts, a glorious ansAver has been given in our own day by the illustrious Watt ;—and to this part of our work it belongs to consider what he has accomplished, viz., to describe The Steam-Engine, which, in the few years since the genius of Watt carried it to its present state of perfection, has changed the direction of human industry, and may almost be said to have elevated man in the scale of existence. The name of steam-engine, to most persons, brings the idea of a machine of the most complex nature, and hence to Fig. 104. be understood only by those who will devote much time to £==5) the study of it ; but he who can understand a common pump, iT may understand a steam-engine. It is in fact -only a pump in which the fluid passing through it is made to impel the r * piston instead of being impelled by it, that is to say, in which the fluid acts as the power instead of being the resistance. It may be described simply as a strong barrel or cylinder c d, with a closely fitting piston in it, here shown at b, which is driven up and doAvn by steam admitted alternately above and beloAV it from a suitable boiler ; while to the end of the pis- ton-rod a, at Avhich the whole force may be considered as concentrated, there- is attached in any convenient way the Avork Avhich is to be performed. The poAver of the engine is of course pro- portioned to the size or area of the piston, on Avhich the steam acts with a force, according to its density, of from 15 to 100 or more pounds to each square inch. In some of the Cornish mines there are cylinders and pistons of more than ninety inches in diameter, on Avhich the pressure of the steam equals the efforts of six hundred horses. In one place this Avonderful piston-rod may be seen acting upon the end of a great vibrating beam, to the other end of which capacious Avater-pumps are attached, Avhose motion causes almost a river to gush up from the boAvels of the earth, hi another place, it is seen Avorking a crank, and urging com- plicated machinery. One steam-engine four miles from London is at the same instant filling all the water reservoirs, and baths, and fountains of the finest quarter of the tOAvn. One engine stretching long arms over a great barrack or manufactory, keeps in one quarter, thousands of spinning-wheels in motion, while in another it is carding the material of the thread, and in • another weaving the cloth. In like manner, one steam-engine, in a great metropolitan brewery, may be seen at the same time grinding the malt, pull- ing up supplies of all kinds from wagons around the building, pumping cold water into some of the coppers, sending the boiling wort from others up to lofty cooling-pans, over which it is turning the fans, perhaps also working v 188 PNEUMATICS. the mash-tub, drawing Avater from the deep wells under ground, and loading the drays—in a word, performing the offices of a hundred hands. Again there are manufactories where this resistless power is seen with its mechanic claws seizing masses of iron, and in a few minutes delivering them out again pressed into thin sheets, or cut into bars and ribbons, as if the iron had be- come to it like soft clay in the hands of the potter. And now for some years over nearly the whole world, has this wonderful piston-rod, working at its crank, been turning the paddle-wheels of innumerable steam-boats, thereby setting at defiance the violence of the winds and waves, and the currents of the fleetest rivers, while it carries men and civilization into the remote recesses of all the great continents. To wherever a river leads, the region although concealed perhaps since the beginning of the world, is now by the steam-engine called as it were from its solitude, to form a part of the great garden which civilized man is beautifying.—Such are a few of the prodigies which this machine is already performing, and every day is witnessing new applications of its utility. The following account of the parts of the steam-engine is intended, with- out entering into minute practical details, still fully to explain the principle or general nature of the machine. It should serve to render very interesting to an attentive reader, a visit to any place where a steam-engine is in use: and it should make'evident the folly of many of the modern schemes for improving the engine. To avoid complexity in the figure, the parts Avhich the reader can easily conceive are not here sketched. Fig. 105. I'^'^in 1st. The part Avhich first claims attention is the great barrel c d, already spoken of as the centre or main portion of the machine, in which the piston !f ™°ved UP and down by the action of steam entering alternately above and below it, through the pipes e c and e d. The barrel or cylinder is bored with extreme accuracy, and the piston is padded round its edge with hemp or other soft material so as to be perfectly air or steam-tiaht. Lately pistons have been made altogether of metal, and, in some cases, from work- ing with Jess friction, these ansAver even better than the others.—2d. The next part to be mentioned is the boiler B, which is made of suitable size and strength.—3d. 1 he steam passes from the boiler along the pipe to e, and there by any suitable cock or valves, worked by the engine itself, is directed alter- nately to the upper and under part of the barrel; and while it is entering to STEAM-ENGINE. 189 press on one side of the piston, the waste steam is allowed to escape from the other side, either to the atmosphere, for high-pressure engines, or into— 4th, the condenser at C, for those of low-pressure ; the condenser being always kept at a low temperature by cold water running into it and pumped out again by the piston k.—5th. The supply of steam from the boiler to the cylinder is regulated by a valve placed somewhere in the pipe B e, and made obedient to Avhat is called—6th, the governor, a contrivance not represented here, but already described at page 52, to illustrate centrifugal force. We may recall it by saying, that it consists of two balls hanging by jointed rods like the legs of a tongs, from opposite sides of an upright spindle, which is made to revolve by connection with some turning part of the machinery:— when the spindle turns at all faster than with the desired speed, the balls fly more apart and are made to affect the steam valve so as to narrow the passage ; and, on the contrary, when it turns more slowly than is desired, they collapse, and by so doing open the valve wider.—7th. The supply of water to the boiler is regulated by afloat on the surface of the water in the boiler; Avhich float, on descending to a certain point, by reason of the consumption of wa- ter, opens the valve to' admit more.—8th. There is a safety-valve in the boiler, viz., a well fitted flap or stopper, held against an opening by a Aveight, but loaded so as to open before danger can arise from the over-heating of the water.—9th. The rapidity of the combustion, or force of the fire, is exactly regulated by the state of the boiler and the wants of the machine, thus:— there is a large open tube (not represented here) rising from near the bottom of the boiler, through its top, to the height of several feet, and when the water in the boiler is too hot, and the steam therefore too strong, part of the Avater is pressed up into this tube, and by the agency of a float Avhich rests on its surface, it shuts the chimney valve or damper: the draught is then diminished and the fuel saved, until a brisker fire is again required.—10th. In this figure a i g marks the place of the great beam, turning on an axis at i, and transmitting the force of the piston to the remote machinery. When the object is to raise water, the pump rods are simply connected with the end g of the beam; but when any rotatory motion is wanted, the end g is made to turn—11th, a crank In by the rod g I; and uniformity of mo- tion is obtained by the influence of—12th, the great fly wheel m, fixed to the axis of the crank. The smallest and simplest steam-engine, and therefore the cheapest, is that called the high-pressure engine. In it steam is used of great density, and consequently of great force, as of 50 lbs. or more to the inch ; andAvhile the fresh steam is admitted to press on one side of the piston, the steam which has already worked, is allowed to escape, or is driven out to the air, from the other side. The atmospheric resistance to the issue of the steam diminishes the working force of the piston just 15 lbs. per inch. The sim- plicity of this form of engine recommends it, but the danger of a large boiler of over-heated Avater,"! always, like inflamed gunpowder, seeking to escape, has, by numberless fatal accidents, been proved to be so great, that the use of such an engine is limited to certain situations. Notwithstanding all the ingenious securities recently contrived against the danger, and which will suffice for small engines, such as are required for steam carriages, the high-pressure engine is not employed in a single English passage-vesselA * In this country, also, what is called the low-pressure engine, is at present employed in all the steam-boats on our eastern waters, but we have reason to believe that few if any of them are worked wth a less pressure than 25 lbs. on the square inch, and we have seen many of them worked with a much higher pressure. It is stated, that the steam gauge on board the Pulaski, just before the fatal explosion, indicated a pressure of 26 lbs., which was 190 PNEUMATICS. In the low-pressure engine, the steam is used generally of force not ex. ceeding 20 lbs. on the inch, which force is only 5 lbs. more than the atmo- spheric pressure, and is insufficient to burst a common boiler, or to do serious mischief:* but as the interior of the low-pressure engine is kept in a state of considered by the engineer a safe working force. The British Ocean Steamers work with a pressure of only 3^ to 1% lbs. to the square inch. On our western waters, the low-pressure „ engine has been discarded in favour of the high-pressure.—Am. Ed. * Our author must be understood as saying, only, that explosions do not take place in low- pressure engines whilst working under a pressure of only 20 lbs. to the square inch. But from various circumstances the elastic force of the steam in a low-pressure engine may be greatly increased, and instead of its ordinary power of 20 lbs., it may acquire one of 100 or 200 lbs., and if the boiler, as is often the case, is unable to bear this pressure, it will burst. In this way explosions have repeatedly taken place in low-pressure engines. Several of these will be found related in an interesting memoir by M. Arago, originally published in the " Jlnnuaire du Bureau des Longitudes," and which has been translated and published in that useful periodical, " The Journal of the Franklin Institute of Pennsylvania," M. Arago, in this memoir, remarks, " I ought not to conclude so long a paper on the subject of the explosions of steam-boilers, without explaining why I have not separated the examples of the explosions of high-pressure boilers from those of the low-pressure; it is because! think there is no reason to make such distinction. Every man must in fact admit, that at the time of an explosion, all boilers contain high-pressure steam. The belief that low-pressure boilers are not liable to burst, or do mischief, has led, as has been already observed, to their exclusive use in passage vessels; this belief, however,is founded in error. M. Arago, in the memoir already quoted, observes, " it does not appear established by any means, that explosions take place more frequently in high than in low- pressure boilers; the contrary has been maintained by different engineers, among whom may be classed Messrs. Perkins, Oliver Evans, &c." Indeed, a little reflection will show that high-pressure boilers ought not to be more liable to explosions than the low. Boilers may be made of either iron or copper of sufficient strength to resist a much greater force than that of the steam ever employed in high-pressure engines. Now boilers are always constructed of a strength proportionate to the pressure they are to sustain. Thus, in a low- pressure engine working with a force of 20 lbs., the boiler is made of a strength calculated to support from 3 to 5 times that pressure; in a high-pressure engine destined to work with a pressure of 150 lbs., the boiler is constructed so as to resist from 3 to 5 times that pres- sure. It will immediately be asked, why cannot the boiler of a low-pressure engine be made of the same strength as if it were for a high-pressure engine 7 In answer to this, it may be remarked, that independent of many difficulties to be overcome before we can exceed cer- tain limits in the thickness of boilers, the weight and cost of the low-pressure engine are already so great that it would be impossible to persuade owners of steam-boats to incur any addition in these particulars—and even would they do so, perfect safety would still not thus be obtained. We have already observed that at the time of an explosion, all boilers contain high-pressure steam, and as we know no limits to the force of this steam, however strong the boiler may be, it may burst, unless this be prevented by other means. It was long ago known that if a vessel, however strong it might be, containing water, be placed over a fire, it will burst, unless an opening/is provided for the escape of the steam as fast as produced. The temperature which will cause the rending of a vessel must de- pend upon its form and dimensions, and upon the tenacity and thickness of the material of which it is made. If we could keep the heat of our furnaces below a certain limit, no other caution would be required to prevent explosions. But it is evident that this cannot be done ; we must therefore resort to some other expedient, and the safety-valve invented by Papin would seem to answer this purpose. We must be allowed to anticipate the subject a little in order to explain the nature of this valve. The safety-valve consists of a hole, say of an inch square, made in the upper part of the boiler, upon which is placed a metal plate loaded with a certain weight. It is evident that the hole will remain closed as long as the pressure of the steam within the boiler is less than the weight of the valve, together with that of the atmosphere, upon the square inch, and that as soon as the pressure within shall exceed this, the valve will be raised and give a free vent to the steam. It would lead us too far to explain how it has happened that so simple and apparently efficient means,has not always proved efficacious; since these causes are various and many of them as yet not perfectly understood. STEAM-ENGINE. 191 vacuum, except where the steam is acting, the whole pressure of 20 lbs. is made available, and the engine has the same power, if of equal size, as a high-pressure engine Avorking Avith steam of 25 lbs. on the inch. The re- quired vacuum is preserved by means of a separate vessel or box, represented at C, called the condenser, into which cold water is constantly running to condense the steam, and is afterwards pumped out with the condensed steam, and with any little air that may have entered: the pump is repre- sented at k in the figure. Steam, on coming into contact with a cold body, is condensed almost with the rapidity of an explosion ; and therefore the instant that the opened valves make a communication betAveen the cold condenser and any part of the engine containing steam, this rushes to the condenser, and becomes water, leaving a vacuum behind. The great merit of Mr. Watt was in the contrivance of this separate condenser, for, until his time, cold Avater had always been thrown directly into the working cylinder, cooling it so much, that tAvice or thrice its fill of steam was destroyed at each stroke to warm it again before it could work. This single change saved three-fourths of the quantity of fuel formerly expended. Before Watt's day, the only steam-engine in use was a rude single-stroke engine, as it Avas called, in which steam, admitted under the piston, allowed the weight of the pump-rods at the far end of the beam to lift the piston, and the steam being then condensed so as to leave a vacuum in the cylinder, the pressure of the atmosphere pushed the piston down to do ks work : on this last account the engine was also called an atmospheric engine. It was used almost solely for pumping water ; but it Avasted so much fuel, from causes of which the chief is mentioned in the last paragraph, that the expense was not much less than that of employing horses. In the atmospheric engine, the steam which lifted the piston against the atmospheric pressure, required to be at least as strong as that pressure, to the very end of the stroke. Another of Watt's great improvements Avas, his ex- Those who wish to investigate the subject, we refer to the memoir of M. Arago, and to the report of a committee of the Franklin Institute, who have collected an account of all the explosions in this country, and who have instituted a very interesting series of experi- ments, in order to examine into the causes of the explosion of steam-boilers, and devise means, for its prevention. This report has been published in the Journal of the Institute. We must not omit, however, to mention that when a low-pressure boiler does explode, it has been found to produce greater destruction than a high-pressure one, in consequence of the greater size, and, therefore, larger quantity of water contained in the former. It may, perhaps, be supposed that the steam from a high-pressure engine would scald more severely than that from a low-pressure one. This, however, is not the fact: on the con- trary, whilst the steam issuing from a low-pressure engine scalds at all moderate distances from the boiler, that from a high-pressure one scalds only at certain distances. Thus the hand may be placed an inch from an aperture in a high-pressure engine without any incon- venience being felt; at greater distances, however, it will scald most severely. A friend has infe>rmed us that he has placed his hand within an inch of the aperture in a boiler from which the steam was issuing at a time when the force of the steam within the boiler was equal to 300 lbs. on the square inch, without feeling any inconvenience. Some interesting experiments on this subject have been instituted by Peter Ewart Esq., and an account of which will be found in the fifth volume of the Journal of the Franklin Institute. It must not be supposed from any thing that we have said in this note, that explosions of steam-boilers cannot be prevented. But we may be allowed to quote on this subject the following remarks of M. Arago. " No cause of explosion exists which cannot be avoided, by means at once simple and within the reach of every one. As we should not trust fire- arms in the hands of children, so, I think, we should not trust the direction of a steam- engine to a man either unskilful, without experience, or wanting in intelligence. It is a mistaken idea, that because steam-engines usually move without attention to them, such attention is not required; Watt contended strongly against this error."—A.n. Ed. 192 PNEUMATICS. eluding altogether the air from his machine, by doing which he not only avoided the cooling effect of the air, but Avas at liberty to shut off the steam, as it is expressed, or to stop the supply for each stroke, before the cylinder was full, and then to make the farther expansion of the quantity admitted impel the piston to the end of the stroke. This principle of causing the mere expansion of steam to do work Avas afterwards carried to a great extent by Messrs. HornbloAver, Woolfe, and others, who constructed engines with two • barrels, in the first and smaller of which, the steam Avas made to act in its dense or strong state, as it issued from the boiler, and when it has finished a stroke there, instead of being at once sent useless to the condenser, it was admitted to a larger piston, which it moved by its continued expansion alone: —the same steam thus doing double Avork or more. All the advantages of the two cylinders, however, are obtainable from the single cylinder Avith its condenser, as now used in most of the Cornish mines. Steam of about 60lbs. pressure on the inch is admitted to the cylinder, until the piston is driven nearly one-third of its way, and the valve being then shut, the same steam is left to finish the stroke by its expansion. The pressure of the expanding Steam gradually diminishes, it is true, in proportion as the volume increases; but in pumping water there is a great saving of time, from having the power more intense at the beginning of the stroke, Avhen the vast mass of Avater and machinery has first to be put into motion. Steam, while doubling its volume by mere expansion, will do about two-thirds as much work as Avhile origin- ally rising from the boiler, and by every subsequent doubling it might do as much as by the first: the increasing size of the cylinder, however, and in- creased friction, confine this mode of using it to narrow limits. It might be supposed that high-pressure engines Avithout condensers avouU be comparatively wasteful, because in them the steam which has acted must be driven out of the cylinder against the powerful resistance of the atmosphere, while in the low-pressure engine it has instant access to the condenser, and leaves effective the Avhole pressure of the fresh steam on the opposite side of the piston. But as in the low-pressure engine, nearly half the power of the steam is expended in overcoming the friction, and other impediments of the numerous parts, while in that of high-pressure, the parts are so much fewer, and the piston is so much smaller in proportion to the force acting upon it, that the loss from friction is often less than a fourth or even a sixth of the steam-power, although the resistance of the air is to be overcome by the high-pressure engine, still there is often a saving on the whole. The saving becomes very considerable if the steam be allowed to act by its expansion also, as described in the last paragraph. From misapprehension of the law of increase of force by increase of heat in water, explained by the table at page 180, some exceedingly false conclu- sions have been draAvn, and acted upon at great expense (as lately by Mr. Perkins,) in attempts to make engines work with an excessively high pres- sure. Besides making the error noAV alluded to and others, Mr. Perkins over- looked the fact, that Ave possess no material for cylinders and pistons, strong enough to bear the contemplated pressure and friction even for a moderate time. Perhaps more striking examples could not be adduced of the absurdi- ties into which even highly ingenious men may fall, Avhen not sufficiently acquainted Avith the general truths of nature on Avhich the arts Avhich occupy them are founded, than in the history of supposed inventions and improve- ments connected with the steam-engine. The fertile, genius of James Watt did not stop at the accomplishment of the two or three important particulars described above, but throughout the whole EXPLOSION. 193 detail of the component parts, and of the various applications of the engine, he contrived miracles of simplicity and usefulness. We should exceed the prescribed bounds of this work by entering more minutely into the subject; but we may remark that, in the present perfect state of the engine, it appears a thing almost endowed Avith intelligence. It regulates Avith perfect accuracy and uniformity the number of its strokes in a given time, counting or record- ing them, moreover, to tell how much work it has done, as a clock records the beats of its pendulum;—it regulates the quantity of steam admitted to work;—the briskness of the fire;—the supply of water to the boiler;—the supply of coals to the fire;—it opens and shuts its valves Avith absolute pre- cision as to time and manner;—it oils its joints ;—it takes out any air which may accidentally enter into parts which should be vacuous;—and when any thing goes wrong which it cannot of itself rectify, it warns its attendants by ringing a bell:—yet with all these talents and qualities,and even when exert- ing the force of hundreds of horses, it is obedient to the hand of a child;—its aliment is coal, Avood, charcoal, or other combustible;—it consumes none while idle;—it never tires, and Avants no sleep ;—it is nof. subject to malady Avhen originally Avell made;—and only refuses to work when Avorn out with age ;—it is equally actiA*e in all climates, and will do work of any kind;—it is a Avater-pumper, a miner, a sailor, a cotton-spinner, a weaver, a blacksmith, a miller, &c. &c.; and a small engine in the character of a steam pony, may be seen dragging after it on a rail-road a hundred tons of merchandize, or a regiment of soldiers, Avith thrice the speed of our fleetest horse coaches. It is the king of machines, and a permanent realization of the Genii of Eastern fable, submitting supernatural powers to the command of man. We need not Avonder that the inventor of an engine having such qualities, should be deemed deserving of the highest honours from his fellow-men. In November, 1825, a public meeting Avas called, to vote a monument to Watt, then not long deceased; and the most distinguished men of the empire, of all parties, philosophers and statesmen, met to vie with each other in speaking his praise. Perhaps a series of such eloquent discourses has rarely been pronounced at one time; but perhaps in the progress of the arts of civiliza- tion there can rarely be offered such motive and occasion. The common voice of that assembly scarcely exaggerated, Avhen attributing to Watt's genius and perseverance that increase of our national commerce and riches, which had enabled free Britain, single-handed, at an extraordinary crisis of human affairs, to contend with Europe combined against her, and at last to triumph, so as to secure her OAvn happy destinies, and probably much to in- fluence those of the human race. As science and the twin sister art are making constant advances, who shall say that even the steam-engine, perfect as AA*e have described it, forms the limit to human discovery of mighty yet obedient force? It is true that the nature of steam, and the laAvs of its formation and action, are now so well understood, that the intelligent engineer no more hopes for great improvement in steam-engines, than he hopes for it in the mode of using a water-fall to turn a mill; but still there are kindred regions of nature left almost unexplored. We shall have occasion to make a remark on this subject in our chapter on the nature of heat. The explosion of gunpowder and of all fulminating mixtureshears so strong an analogy to the phenomenon of the formation of steam, that the mind may advantageously contemplate the subject in this place. The ingredients of which gunpowder is formed are chiefly substances 194 PNEUMATICS. which, Avhen separate, exist, at any common temperature, in the form of air; and the combustion sets them loose, with a production of intense heat, caus- ing an increase of volume which is instantaneous, and almost irresistible. By experiment and mathematical deduction, it appears that the exploding particles begin to separate from each other with a velocity as if ten thousand volumes of air had been condensed into one: and this explains the corresponding force and swiftness with Avhich a bullet is propelled. All the fulminating metals are chiefly combinations of the like substances with the metals; and the ingredients are held together by so slight a tie, that a little friction or elevation of temperature disunites them so as to produce the explosion. The escape of condensed air from the chamber of an air-gun, is a species of explosion; but is very gentle compared with the shock of discharged gun- powder. It has lately been shown that a gun-barrel may be connected Avith a high- pressure steam-boiler, in the same manner as with a chamber of condensed air; and as the steam may be supplied as long as water remains in the boiler, if bullets be allowed to fall into the barrel fast enough, a hundred or more may be throAvn out every minute, with the same force and precision as if each issued from a common fire-arm. The rapid succession resembles the issue of water from a jet pipe; and if such an engine were used in a field of battle, its barrel of death, made, to point gradually along a line of men, would mow them down like corn-stalks before the scythe—none could escape. The horrible idea and proposal haAre been excused by saying, that to prove the possibility of such carnage must have the effect of putting an end to war • altogether. The invention of gunpoAvder, Avith the consequent change of military tactics, because it gave to a handful of men possessing it the mastery over thousands who had it not, Avas hailed by the philosophers of the day as a certain secu- rity against the relapse of civilized mankind into such a state of barbarism as followed the irruption into Europe of the Goths and Vandals:—none but well- instructed and disciplined armies could then enter a European kingdom. This consideration, hoAvever, has lost its interest, since the invention of printing, and other changes in society, have afforded still better and more humane securities. Besides the interesting instances above cited of the pressure of the atmosphere determining whether certain substances shall or shall not have the form of air, there are others that deserve mention, where the effect is modified by the mutual attraction of substances. The pressure of the atmosphere at the surface of the earth keeps a certain quantity of air in combination Avith A\*ater, so as to form part of the liquid mass. This air re-appears at once on taking off the pressure. If Ave place a glass of water under the receiver of an air-pump and then exhaust this, the water is soon crowded with bubbles of air, seen adhering to the glass all round, or rising through the water. This admixture of air in Avater is necessary to the life of fishes. It is driven off by boiling, and hence the vapid taste of water that has recently been boiled. In the making of beer, Avine, and other fermented liquors, there is formed, during the fermentation, a large quantity of the substance called carbonic acid. Much of it flies off in its usual form of gas, but, because of the pressure of the atmosphere, much still remains in union Avith the liquid. On removing PRESSURE AFFECTING TEMPERATURE. 195 this pressure suddenly, the liquid appears almost to boil, as when a glass of warm beer is placed in the air-pump vacuum. A degree of pressure still greater than that of the atmosphere keeps a pro- portionally larger quantity of this carbonic acid in liquid combination ; as in bottled porter or sparkling champagne before the cork is drawn ; but as soon as the compression maintained by the cork is removed, the gas escapes, caus- ing the thin champagne to sparkle, and the more viscid beer, which retains the little bubbles as they rise, to be covered with froth. After the sparkling or frothing has ceased under the atmospheric pressure, the phenomenon may be renewed by placing the glass in the air-pump receiver. Carbonic acid so readily becomes liquid when its attraction for water assists the compression, that enough of it may be united Avith water to make a pint become a pint and a half. The soda-water, or aerated Avater, noAV so gene- rally used as drink in warm weather, is water with several times its bulk of carbonic acid forced into it by pressure ; and a part of this is seen escaping always at the instant of the confining cork being drawn. Carbonic acid forms nearly half of the substance of marble or lime-stone. When an acid with stronger attraction, as vinegar or sulphuric acid, is poured upon marble, it dispossesses the carbonic acid, and unites itself Avith the pure lime. The carbonic acid in rising, constitutes the effervescence which then appears. Carbonic acid, for the manufacture of the common soda-water and other aerated drinks, is obtained in this way. Many mineral waters contain carbonic acid, which remains in tranquil combination while the water is bearing a certain pressure under ground, but which in part escapes as soon as the water issues to the air and only the atmospheric pressure remains: such waters are called sparkling waters. The reason that champagne and the aerated waters are so cool when first decanted is, that the carbonic acid, in assuming its gaseous form, absorbs as latent heat, a large proportion of the heat which Avas previously existingin the liquid. The atmospheric pressure, by making the density of the air in any place dependent upon the height of the place above the level of the sea, causes corresponding differences of temperature. The explanation of this is simple. If a gallon of air, at the surface of the earth, contain a certain quantity of heat, this must be diffused equally through the space of a gallon; but if the air be then compressed into one-tenth of the bulk, there will be ten times as much heat in that tenth as there was be- fore ; the increase affecting the thermometer to an extent modified by circum- stances explained in a future part of this Avork. In like manner, if by taking off pressure, the gallon be made to dilate to ten gallons, the heat Avill be in the same degree diffused, and any one part will be colder than before. It is knoAvn that air may be so much compressed under the piston of a syringe, that the beat in it, similarly concentrated, becomes intense enough to inflame tinder attached to the bottom of the piston :—this means, under the name of the mat eh-syringe, being in common use for obtaining an instantaneous light. Now, for the reason here explained, the air near the surface of the earth, forming the bottom of the atmosphere, because condensed by the weight of the air above it, is much Avarmer than if it Avere suddenly carried higher up, to Avhere, from the pressure being less, it Avould be more expanded or thin. In many cases the height of mountains maybe estimated by the difference of temperature observed at the bottom and at the top. While a thermometer 196 PNEUMATICS. stands at 00° at the bottom of St. Paul's Cathedral, in London, another marks only 58° at the top of the dome ; and in the lofty ascent of a balloon, the thermometer soon falls to the freezing point and below it, the cold to the aeronaut becoming almost insupportable. In every part of the earth, at a certain elevation in the atmosphere, differ- ent according to the latitude or proximity to the equator, the thermometer never rises above the freezing point,—and this limit in the atmosphere is called the line or leA*el of perpetual congelation. In Nonyay it is at five thousand feet above the level of the sea ; in Switzerland at six thousand five hundred; in Spain and Italy at seven thousand, farther south, at Teneriffe, at nine thousand ; directly under the sun, as in central Africa, and among the Andes in America, it is about fourteen thousand. We see therefore why the snow-capt mountains are not the tenants only of high northern and southern latitudes. It is this effect of elevation Avhich renders many of the tropical regions of the earth not only tolerable abodes for man, but as suitable as any others, contrary to the opinion of the ancient philosophers of Europe, who accounted them, by reason of the great heat, an everlasting barrier, as regard- ed man, between the northern and southern hemispheres. Much of the tropical land of America is so raised, that it rivals, as to agreeable tempera- ture, even a European climate ; while the lightness and purity of the air,and the brightness of the sun, add delightfully to its charms. The vast expanse of table-land forming the empire of Mexico is of this kind, enjoying the im- mediate proximity of the sun, and yet by its elevation of seven thousand feet above the level of the ocean, possessing the most healthful freshness. The land in many parts has the fertility of a cultivated garden, and can produce naturally most of the riches Avhich vegetation offers over the diversi- fied face of the globe. The plains of Colombia, in South America, and indeed all along the ridge of the Andes, are similarly circumstanced. The contrast is very striking, after sailing a thousand miles up the level river Magdalena, in a heat scarcely equaled on the plains of India, at once to climb to the table-land above, where Sante Fe de Bogota, the capital of the republic, is seen smiling over interminable plains, that bear the livery of the fairest fields of Europe ! Persons not understanding the law which we are now illustrating, wif. express surprise that Avind or air blowing doAvn upon them from a snow- clad mountain, should still be warm and temperate. The truth is, that there is just as much heat combined Avith an ounce of the air, on the mountain top as in the valley: but above, the heat is diffused through a space perhaps twice as great as when beloAV, and, therefore, is less sensible. It may be the same air Avhich sweeps along as a warm gale on a plain at the foot of a moun- tain,—which then rises and freezes water on the summit—and Avhich in an hour after, or less, is playing among the floAvers of another valley, as warm and genial as before, y As the temperature in different parts of the atmosphere depends thus upon the rarity of the air, and therefore upon the height, the vegetable productions of each distinct region or elevation are of a distinct character; and many other peculiarities of place and climate acknoAvledge the same cause. Because the atmospheric pressure determines the temperature of the air in different situations, as noAV explained, it has also a corresponding influence upon the state of aerial humidity, which is modified by the temperature. It was explained at page 184, that water and other liquids under a vacuum, PRESSURE AFFECTING TEMPERATURE. 197 rise in the form of air or vapour with force, and in quantity having a strict relation to the temperature—heat being in fact the cause of their rising; and the table at page 186 exhibits the force, and therefore the density of Avatery vapour corresponding to some certain temperature. Now it is a remarkable circumstance, that vapour in the same quantity and of equal tension rises from any liquid, whether placed under the pressure of air, or under a Aracuum; only through a space containing air it diffuses itself more slowly than if the air Avere not present. As regards the former case, it Avas for a long time supposed that the air dissolved the liquid as a liquid dissolves a salt: but it now appears that there is merely a mechanical mixture of the two. If the vapour, while rising from a liquid, has not a tension or elastic force equal to the pressure of the atmosphere the process is tranquil, and is called evapora- tion, and it goes on only as the vapour can diffuse itself among the particles of the air, and therefore slowly in air perfectly quiescent, but quicker as the air is moving more, or as the density of the air is less. But when the vapour, owing to greater heat, is strong enough to overcome the atmospheric pressure of fifteen pounds per inch, and the weight of a certain quantity of liquid over it, the phenomena of boiling arises as already described. For the reason now explained, the air of our atmosphere contains diffused through it a large quantity of invisible aeriform water ; and if there Avere no intestine motions, and no changes of temperature in the atmosphere, the quantity of water Avould soon everyAvhere reach a maximum, or would be the greatest that the temperature of the place could support: instead of this, hoAvever, from a variety of causes to be explained beloAV, the air is moving about constantly as winds, and the local temperatures are ever fluctuating, and when the temperature is lowered, in situations where a maximum of A\ratery vapour is present, part of this is instantly reduced to the state of water again. and appears, according to circumstances, in the form of mist, rain, snow, or hail; Avhile to supply material for these phenomena, evaporation is going on wherever, over Avater, there is not a maximum of vapour in the air. These opposing operations of evaporation and condensation keep up that constant circulation of moisture which is the life of nature. When a given quantity of water assumes the aeriform state, it contains the same quantity of latent heat, in all cases, Avhether rising, for instance, from a boiling caldron, or from the surface of a Jake. Hence we see Avhy evap- oration is so cooling a process to any liquid or moistened solid from Avhich it is arising: and as we have already shoAvn that a rapid passing of dry air, or the substance being placed in a vacuum, quickens evaporation, we now see why both of these conditions accelerate the cooling. Wet linen placed in a strong Avind, Avhich does not contain a maximum of moisture, becomes dry almost immediately ; a bottle of Avine covered with aAA'et cloth and suspended in a current of air, as is practised in Avarm climates to prepare Avine for the table, is quickly cooled; mats hung around the walls of houses in India, and frequently Avetted through the day, preserve a delightful freshness in the apartments. Sprinkling Avater or vinegar over a hot sick-room cools and refreshes it; and Avatering the streets of a city moderates in them the inten- sity of summer heat. In warm climates Avater is cooled for drinking by being put into vessels so porous that the external surface is always moist, the vessels being then suspended in a current of air, or during a calm being made to vibrate in the manner of a pendulum. Again, the rapidity of eAraporation from Avater under the exhausted receiver of an air-pump, and particularly when some other substance which poAverfully absorbs watery vapour is in- cluded in the receiver, is so rapid, and carries off the heat so quickly, that 14 • 198 PNEUMATICS. the mass of water freezes before much of it has been carried away. This process is used for making ice in India. It is partly because air saturated with moisture, that is to say, having as much Avater diffused in it as can be supported in the invisible or aeriform state of the existing temperature,—lets falli a part on any reduction of the temperature, that air Avhich, as a portion of the atmosphere, has been heated by the sun during the day, and has received much moisture, lets it fall again during the night, and exhibits the night fogs of certain seasons, which float upon the surface of the earth, until again acted upon by the beams of the next morning's sun. Fog, Avhen farther condensed, by groups of the minute particles uniting, forms rain ; and rain When cooled becomes shoav or hail. The quantity of deAV Avhich falls at night is influenced by the quantity of moisture taken up by the atmosphere during the heat of the day; and the immediate cause of the dew is, as was ingeniously proved by Dr. Wells, some years ago, that the temperature of the objects on which it settles has become lower during the night than that of the air around, »and than is required to maintain in the invisible state, the moisture in the surrounding atmosphere. There is a tendency in heat to diffuse itself uniformly among bodies, by a constant radiation from one to another, rapid in proportion to the differences of temperature, and Avhich, if continued, would reduce all to the same degree. The earth, therefore, during the day, receives radiated heat from the sun, and becomes comparatively hot, and during the night it gives out heat again by radiation towards the sky, from which there is little or no return. When there are clouds in the atmosphere at night, they receive the heat darted upAvards from the bodies on the earth's surface, and they radiate heat back, becoming thus, as it were, a clothing to maintain the warmth of the earth beneath them,—and on cloudy nights there is no dew,— but with a clear sky, the heat, radiated upwards, darts into boundless space," and is lost altogether to the objects Avhich emitted it. These objects, there- fore, AArhich during the day had the same, or even a higher temperature than the atmosphere around, now become colder, and the aeriform Avater which comes in contact with them is condensed, and forms what we call dew. This beautiful provision of nature supplies the necessary moisture to vegetables during seasons when rain is deficient. DeAV on very cold objects freezes as it settles, and is then called hoar frost. A phenomenon which may be classed with dew, is the perspiration, as it is vulgarly called, of massive walls and furniture, occurring on the sudden setting in of warm weather, or onrthe*occasion of a warm moist air of higher temperature than the Avails being suddenly introduced, as when a crowd assembles in a cold church :— the Avail or other object then, from not having yet acquired the temperature of the surrounding air, condenses upon itself a copious deposition of the atmospheric moisture. For a similar reason a bottle of Avine brought from a cold cellar or from an ice-pail, into a room with company, is soon covered with thick moisture or dew ; as are the glasses also into which the wine is poured. It is another phenomenon of the same kind.when we see the moisture of warm breath condensed on any cold polished surface, as on a mirror's face, or on the glasses of a carriage shut up, or on the windows of a room in winter, Avhen the surface is very cold, the moisture being frozen with the appearance of beautiful arborescence. Many instruments have been contrived, with the name of hygrometers, for indicating the quantity of water in the atmosphere. A prepared human hair is the essential part of one of the best of those formerly used; the lengthening or shortening of the hair, according to the quantity of moisture PRESSURE AFFECTING MOISTURE. 199 around it, being caused to move an index like that of a wheel-barometer, to mark the degrees. This, however, and other common hygrometers, are only philosophical toys; but Mr. Daniel (see his excellent work, entitled Meteoro- logical Essays) has lately given to the philosophical Avorld a correct and simple instrument for the purpose, depending on the principle explained above,—that wheneA'er the temperature of a body in the atmosphere is reduced below that at which the quantity of Avatery vapour in the air around it can be maintained in the aeriform or invisible state, dew forms on the body. His apparatus consists of a bulb of glass, which can be cooled to any desired degree from being connected with another bulb enveloped in an evaporating liquid; and when moisture begins visibly to settle upon the first, its tempera- ture is exhibited on a thermometer enclosed within it; and the proportion of water mixed with the air around is then, as indicated by the table, partially copied here, at page 186. A great fall of the barometer marks a diminished pressure in the atmo- sphere around, with a consequent dilatation of the air and fall of temperature, as explained a feAV pages back: and if the air at such a time holds a maxi- mum of moisture, a part of this must become visible as fog or rain. Thus a fall of the barometer, a fall of temperature, and a fall of rain, often occur as associated phenomena. Illustrating this by experiment, we find, that on the extraction of air from the receiver of an air-pump, a cloud or mist generally appears in it with the first strokes of the piston :—the reason being that the still remaining air, because cooled by the rarefaction, absorbs heat from the vapour in combination Avith it, and renders the \Arater visible. The mist is then removed by the subse- quent action of the machine, or is re-dissolved when the usual quantity of air is re-admitted. We understand from this why rain happens so much more frequently among mountains than on extended plains. When air saturated with mois- ture approaches a mountain ridge to rise over it, for every foot that it rises, it escapes from a degree of the pressure Avhich it bore while lower down, and in then dilating, it becomes colder, and lets fall part of its moisture. It is the rain copiously thus produced in mountainous regions which constitutes the chief supply of their many rivers, and which, with periodical changes of Avind bringing more moisture, causes the extraordinary annual overflowing of such rivers as the Nile, the Ganges, &c. Those Avho have visited the Cape of Good Hope, will recollect a striking phenomenon illustrative of our present subject, observed there when the Avind blows from the south-east. Beyond the city, as viewed from the bay, there is a mountain of great elevation, called, from its extended flat summit, the Table Mountain. In general its rugged steeps are seen rising in a clear sky; but Avhen the south-east wind bloAvs, the Avhole summit becomes enveloped in a cloud of singular density and beauty. The inhabitants call the pheno- menon the spreading of the table-cloth. The cloud does not appear to be at rest on the hill, but to be constantly rolling omvard: yet, to the surprise of the beholder, it never descends, for the snowy Avreaths seen falling over the precipice tOAvards the tOAvn below, A*anish completely before they reach it, while others are formed on the other side to replace them. The reason of the phenomenon is this. The air constituting the Avind from the south-east having passed over the vast southern ocean, comes charged Avith as much invisible moisture as its temperature can sustain. In rising up the side of the mountain it is rising in the atmosphere, and is therefore gradually escap- ing from a part of the pressure lately borne; and on attaining the summit it 200 PNEUMATICS. has dilated so much, and has consequently become so much colder, that it lets go part of its moisture. This then appears as the cloud just described; but it no sooner falls over the edge of the mountain, and again descends in the atmosphere to Avhere it is pressed, and condensed, and heated as before, that it is re-dissolved and disappears :—the magnificent apparition dwelling only on the mountain top. When the elevation to which moisture is suddenly carried is very great, the fall of temperature is proportioned, and the separating water becomes snow instead of rain. This phenomenon is remarkably illustrated by a great Hiero's fountain, used in one of the mines of Hungary ; during the play of which, the air in one place is so compressed, that on being suddenly released, it expands and cools enough to cause the moisture driven out with it to appear, even in summer, as a shower of snoAV. The foregoing reasoning explains why, along the sides of mountain ridges, clouds are generally seen floating at a certain height only, and therefore in horizontal strata. The Avater is separated from the air at a certain tempera- ture, Avhich is dependent on the height, and above that height the air.is at the time too dry and rare to have clouds. Very lofty summits are always seen much above the clouds, and the admirer of nature who climbs towards them, may often contemplate the grand phenomena of the thunder-storm far beneath his feet. Teneriffe soars so sublimely, that the distant sailor not unfrequentiy mistakes the line of clouds hanging around its sides for the Avhite streak which elsewhere indicates the cliffs and waves of the sea- shore. Fluid support or floating, in air. . (Read the Analysis, page 156.) When it was explained under" Hydrostatics," that any body immersed in a fluid has its downward tendency or weight resisted with exactly the force AA'hich supported the quantity of the fluid previously occupying the same space, and therefore that the body will sink or swim, according as it is heavier or lighter than its bulk of the fluid, the reasoning was as applicable to the case of a body immersed in an air or gas as in a liquid. We hence see Avhy a body weighed in air appears lighter, by the exact weight of its bulk of the air, than when Aveighed in an empty space or vacuum;—and why, for the same reason, the jocular question, Avhether a pound of lead or a pound of cork be the heavier, is not truly answered by saying that they are of equal weight; the cork being really the heavier, for Avhen balanced in air, bulky cork is more supported than dense lead. A small weighing beam having attached to its opposite ends pieces of cork and lead which equipoise in the air, if placed under the exhausted receiver of an air-pump, quickly exhibits the cork preponderating. As any liquid lighter than water, such as oil or spirits, on being set at liberty under the surface of water, will rise, Avhile any heavier liquid, such as brine, syrup, or sulphuric acid, will sink; and in both cases Avith force proportioned to the difference of specific gravities:—so we find, that in com- mon air, a mass of hydrogen, or hotter air i&scends, because specifically lighter; while oxygen, carbonic acid gas, a? colder air, descends, because specifically heavier. This truth is well exemplified in The Balloon, which is a thin light bag of varnished silk, generally shaped like a globe or egg, and filled with a fluid lighter than common air. It is made sufficiently FLOATING—BALLOONS. 201 large that the difference between its weight when filled and that of an equal bulk of common air, may enable it to carry aloft the material of which it is constructed, with the aeronauts, and their apparatus. It is in principle like a bladder of oil immersed in water. A globe of thirty-five feet diameter has a capacity of nearly twenty-two thousand cubic feet. This quantity of com- mon air weighs about sixteen hundred pounds, and the same quantity of hydrogen gas, of easily obtained purity, Aveighs only one-eighth as much, or two hundred pounds. Such a globe, therefore, being buoyed up, or sup- ported in common air, with a force of sixteen hundred pounds, while, if filled with hydrogen, it only weighs two hundred, will carry up into the sky four- teen hundred pounds of material and load. The first balloon was exhibited by a man ignorant of what he was really effecting. Seeing the clouds float high in the atmosphere, he thought that if he could make a cloud and enclose it in a bag, it might rise and carry him with it. Then, erroneously deeming smoke and a cloud the same, he made a fire of green wood, wool, &c, and placed a great bag over Avith the mouth downwards to receive the smoke. He soon had the joy to see the bag full, and, when set free, ascending ; but he understood not that the cause Avas the hot and dilated air within, which, being lighter than the surrounding air, was buoyed up; while the visible part of the smoke, which chiefly engaged his attention, Avas really heavier than the air, and was an impediment to his wishes. This modification, called the hot air or fire balloon, was afterwards better understood, and was used by aeronauts, until the more commodious and less dangerous modification, called the inflammable air balloon, or balloon of hydrogen gas, was substituted. Since the modern introduction of gas lights, the carburetted hydrogen prepared for them is generally employed for filling balloons. It is consi- derably heavier than pure hydrogen, but is so much more readily obtained, that aeronauts like better to make a larger balloon to suit it, than a smaller one which obliges them to prepare the other.—A thin paper bag, filled with the hot air rising from a large lamp, is a miniature hot air or afire balloon ; and a common soap bubble, filled Avith hydrogen, is a little inflammable air balloon, which mounts with great rapidity. There are, perhaps, feAv occasions on Avhich a youth is more surprised and delighted than when he first beholds a balloon sailing high in the bosom of the air and bearing a human being to regions far beyond AA'hat the soaring eagle has eyer reached: while to the intrepid aeronaut himself, the scene of a Avorld displayed beneath him is unquestionably the grandest, except that of the starry heavens, Avhich mortal eye has ever compassed. To him eA*en wide-spread London, the queen of the cities of the earth, and a little Avorld Avithin itself, Avhen vieAved from a great elevation in the sky, appears but as a dusky patch upon a map, with the far-famed Thames winding there as a silvery line, and the magnificent temples and palaces scattered around, ap- pearing but as darker points rising out of the general mist of buildings, in which a million and a half of human beings reside. The first aeronautic expeditions astonished the world, and endless reveries passed through men's minds of important uses to Avhich the new discovery , might be applied : but more mature reflection, and noAV frequent trials have shown that the balloon, while furnishing philosophers with the opportunity of making some observations in elevated regions of the atmosphere, is still interesting chiefly as a philosophical toy. The French, under the Directory in 1796, attempted to use it as a military station, from Avhich the position 202 PNEUMATICS. and motions of an enemy might be descried : but the plan was eventually abandoned. It has since been thought of as a means by which travellers might obtain information Avhile penetrating into unknoAvn countries, like the almost interminable plains of Australasia. Although aeronauts, while aloft, have the power of making the balloon rise farther by throwing out part of the sand-ballast which they carry with them, or of making it descend by opening a valve at the top through Avhich the hydrogen may escape, still they have no power of producing a lateral motion. The idea which yet strongly excites the minds of some projectors, that by wings or other means, a balloon may be directed in the sky nearly as a ship is directed on the sea, is not much more reasonable than to suppose that an insect; suspended to a huge block of Avood, driven along at the rate of eight or ten miles an hour by river torrent, should have power to stop or sail against the stream. A man in a balloon would generally have to resist or change a motion exceed- ing fifty miles in an hour. A balloon which is only half full at the surface of the earth, becomes quite full when it has risen three miles and a half, because, at that altitude, air from below doubles its volume on account of the diminished pressure. A balloon, therefore, if quite distended on first rising, must let air escape as it ascends, or it will burst: this is true also of the drum of the human ear under the same circumstances, and in a contrary way under the opposite circumstances of a person descending in a diving-bell. The downy seeds of plants seen floating about upon the winds of autumn are not lighter than air, but have so much bulk and surface, in proportion to their weight, that the friction upon them of the moving air is greater than their weight, and carries them along. A sheet of paper, made in some degree to resemble a balloon, by its having a little weight, representing the hanging car, attached by threads from its angles, is often seen rising at a street corner, to the delight of the boy who watches it. Its rise depends upon eddy winds or currents which the corner produces. The ascent of flame and smoke in the atmosphere, affords other examples of a lighter fluid rising in a heavier; for both these are merely hotter air rising in the midst of colder. The phenomenon of flame is produced when a burning substance contains some ingredient capable, on being heated, of assuming the form of air or gas, Avhich ingredient, on ascending, burns or combines with the oxygen of the atmosphere, with intensity of action sufficient to produce a white heat. It is because charcoal and coke have nothing in them thus volatile, that they burn without flame, appearing like red-hot stones. The flame of a lamp or candle is merely the oil, wax, or tallow converted into gas, and allowed to burn as it is disengaged and rises. The same gas obtained by heating the oil, &c, in vessels which exclude the atmosphere, so as to prevent imme- diate combustion, and from which tubes lead to suitable receptacles, is the pommon oil-gas used for illumination. Smoke consists of all the dust and visible particles which are separated from the fuel without being burned, and are, moreover, light or minute enough to be carried aloft by the rising current of heated air; but all that is visible of smoke is really heavier than air, and soon falls again as powdered chalk falls in water. In the receiver of an air-pump, where a candle has been extinguished by exhausting the air, the stream of smoke that continues FLOATING —FLAME AND SMOKE. 203 to pour from the wick after the exhaustion, is seen to fall on the pump-plate, because there is no air to support it. Chimneys quicken the ascent of hot air by keeping a long column of it together. A column of two feet high rises, or is pressed up with twice as much force as a column of one foot, and so in proportion for all other lengths ; just as two or more corks strung together and immersed in water, tend up- wards Avith proportionally more force than a single cork ; or as a long spear of light wood, allowed to ascend perpendicularly from a great depth in water acquires a velocity Avhich makes it dart above the surface, while a short piece under the same circumstances rises very slowly. In a chimney Avhere one foot in height of the column of hot air is one ounce lighter than the same bulk of the external cold air, if the chimney be one hundred feet high, the air or smoke in it is propelled upwards with a force of one hundred ounces. In all cases, therefore, the draught, as it is called, of a chimney, is proportioned to its length. The folloAving facts are consequences of this truth. In low cottages, and in the upper floors of houses, the annoyance of smoky rooms is much more frequent than where chimneys are longer. If there are two fires in the same room, or in any rooms open to each other, which have chimneys of different lengths, and of which the doors and win- dows are very close, sd that air to supply the draughts cannot enter by them, the taller chimney will overpower the shorter, and cause it to smoke into the room ; just as the long leg of a syphon overcomes the short one, or as a long log of Avood, held down in water by a cord passing from it round a pulley at the bottom to a shorter log also floating, will rise, and pull down the shorter log. A long chimney, for the reasons above explained, causes a current of air to pass through the fire very rapidly, and it has the advantage also of acting more uniformly than any bellows or blowing machine. On these accounts, for fires of steam-engines, and many others, it is the means of blowing gene- rally preferred. The importance of length in a chimney explains the remarka- ble appearance of some mining districts and modern English tOAvns, where steam-engines abound. WThen we heap dying embers together, so that the hot air rising among them may become a mass or column of considerable altitude, this column has the effect of blowing them gently, and helps to light them up again. A piece of burning paper throAvn upon the top of a half-extinguished fire, often makes it blaze afresh, by causing a more rapid current of air to pass through it from beloAV. The action or draught of a chimney, influenced as we have seen, by its length, depends also on the degree in Avhich the air in it is heated, because this de- termines the dilatation, or comparative lightness, which makes theairascend. In Avhat are called open fire-places, such as those in the sitting-rooms of Britain, a large quantity of air directly from the apartment enters the chimney above the fire, and mixes with the hot air from the fire itself. This mixture ascends more sloAvly than if hot air alone entered, and in a proportion de- pendent on the degree of mixture. The effect of excluding a part of this colder air, is seen when a board or plate of metal is suspended across the opening of the chimney, so as to narroAv the entrance :—almost instantly a quicker action is produced, and the fire begins to roar as if blown by a bel- Ioavs. This means is often used to Uoav the fire instead of bellows, or to cure a smoky chimney, by increasing the draught. What is called a register ■ 204 PNEUMATICS. stove is a kindred contrivance. It has a flap placed m the throat of the chim- ney, which serves to Aviden or contract the passage at pleasure. Because the flap is generally opened only enough to allow that air to pass which rises directly from the fire, the chimney receives only very hot air, and therefore acts well. The register stoA-e often cures smoky chimneys : and by prevent- ing the too ready escape of the moderately Avarmed air of the room, of which so much is Avasted by a common fire-place, it also saves fuel. In what are called close fire-places, as those of steam-engines, or brewers' coppers, when the furnace door is shut, no air can enter the chimney but directly through the fire ; hence the action of such chimneys is very powerful. In a room Avith two fires, or in drawing-rooms communicating with each other, although the chimneys be of equal length, that one over the best fire will act the most strongly ; and if the doors and Avindows of the apartment be so close as to prevent a sufficiency of air from entering by them to supply both fires, cold air will enter by that chimney which has the weakest fire, and the smoke from it will spread into the room. Hoav often is an assembling dinner party annoyed by the smoke of a second drawing-room fire just lighted before their arrival, and Avhich had therefore to contend with the antagonist fire already in poAverful action all the day. W^bile only one fire was lighted, the cold chimney was admitting the air to feed it, jusf as an open pane in the Avindow would have done. A room may be so close, that no air can find entrance, and in such a case the smoke of its fire must all spread into the room. When all the windows and doors of a house fit so closely as not to admit air for the acting chimneys, the supply comes down the chimneys that are not in use. Inattention to this fact causes many a good chimney to incur the imputation of being smoky, because on the attempt being made to light a fire at it, the smoke at first is always thrown back. The truth is, that at the time when the servant begins to light the fire, there is a dowmvard current in the chimney, repelling, of course, any heated air and smoke that approaches it, and spreading them over the whole house ; but were the room door to be shut for a few minutes, so as to cut off communication with* the other drawing chimneys in the house, while at the same time the windows Avere opened, the chimney would act at once : and Avhen sufficiently heated, would continue to act in spite of the others, and as well as they. There are some cases of smoky rooms not to be so easily corrected as Avhat we have now mentioned. When a low house adjoins a lofty house, the wind, blow- ing towards the latter, is obstructed and becomes a gathering or condensation of air against the Avail; and if the top of a Ioav chimney be there, the compressed air enters it, and pours dowmvards. The same happens occasionally from the proximity of trees or rocks. In such cases, to avoid the influence, the chimneys of the low house are often made very lofty. Again, whenever, from the nature of buildings, eddies of wind occur, or unequal pressures, as at street corners, &c, the chimneys around do not act regularly. It is proverbial, the corner houses, or those at the ends of a row, are smoky houses, and Ave see the uniformity of architecture in a street often destroyed by the necessity of lengthening the chimneys of the houses at the extremities. When smoke is found descending into a room Avhere there is no fire, the empty chimney is serving as an inlet for air to the house, while the smoke of a neighbouring chimney is passing closely over the top of it. In summer, when fires are not in use, there is often a strong smell of soot perceived in the apartments during the whole of the day, but Avhich ceases at night. The reason is, that during the day the chimney is colder than the external air, and by condensing the air which enters it, causes a doAvnward FLOATING —FLAME AND SMOKE. 205 current through the soot. During the night, again, when the external air becomes colder, OAving to the absence of the sun, the chimney, by retaining the heat absorbed during the day, is hot enough to warm the air in it, and to cause an upward current. These currents, in chimneys left open during the days and nights of summer, are almost as regular as the land and sea breezes of tropical countries. All these remarks prove how important it is to be able to conceive clearly of the motions going on, according to the simple laAvs of matter, in the in- visible air around us. Were such subjects better and more generally under- stood, many prevalent errors in the arts of life, influencing much the comforts and health of the community, would soon be corrected. If we are filled with admiration on discovering hoAv perfectly the simple law of a lighter fluid rising in a heavier, provides a constantly reneAved sup- ply of fresh air to our fires, which supply we should else have to furnish by the unremitted action of some expensive blowing apparatus, still more must we admire that the operation of this law should effect the more important purpose of furnishing the ever-renewed supply of the same vital fluid to breathing creatures. The air which a man has once respired becomes poison to him ; but because the temperature of his body is generally higher than that of the atmosphere around him, as soon as he has discharged any air from the lungs, it ascends completely away from him into the great purify- ing laboratory of the atmosphere, and new air takes its place. No art or labour of his, as by the use of fans or punkas, could have done half so well what this simple law unceasingly and invisibly accomplishes, and accom- plishes without effort or even attention on his part, and in his sleeping as in his waking hours. Truly in this, may he be said to be watched over by a kind Providence. TJie warming and ventilating of houses is an important art, founded chiefly on the foregoing considerations, and at present too little understood, not only by the public at large, but even by medical practitioners, Avhose management of disease, though judicious in other respects, is often rendered vain by error or omission in this. Excellent fuel is so cheap in Britain, owing to the profusion with Avhich beds of rich coal are scattered in it, that a careless domestic expenditure has arisen; Avhich, however, instead of securing the comfort and health that might be expected, has led to plans of Avarming Avhich often prove destruc- tive to both. The mischief lies chiefly in the unsteadiness or fluctuations of our domestic temperature ; for in still colder countries, and Avhere fuel is more expensive, as in the north of continental Europe, the necessity for eco- nomy has led to contrivances which give steady temperature and impunity. In cold countries, to retain and preserve the heat once obtained, the houses are made Avith thick AA'alls, double windows, and nice fittings; and more- over Avith close stoves or fire-places, which draAv their supply of air, not from the apartments Avhere they are placed, Avasting the temperate air of these, but directly from without. Thus fuel is saved to a great extent, and a uni- formity of temperature is produced, both as regards the different parts of the room, so that the occupiers may sit Avith comfort where they please, and as regards the different times of the day, for the stove being once heated in the morninor, often suffices to maintain a steady warmth until night. The tem- perature can be carried to any required degree, and sufficient ventilation is easily effected. In England, again, the apartments, Avith their open chimneys, may be 206 PNEUMATICS. compared to great air-funnels, constantly pouring out their warm contents through a large opening, and constantly requiring to be replenished. They thus waste fuel exceedingly, because the chimney being large enough to allow a Avhole room-full of air to pass away in two or three minutes, the air of the room has to be warmed, not once in the course of the day, but very many times. The temperature in them is made to fluctuate by the slightest causes, as the opening a door, the omitting to stir the fire, &c. The heat is very unequal in different parts of the room, rendering it necessary m general for the company to sit near the fire ; where they must often submit to be almost scorched on one side, while they are chilled on the other. There is generally a Avarm stratum of air above the level of the chimney-piece, surrounding, therefore, the upper part of the bodies of persons in the room, Avhile a cold stratum below envelops the sensitive feet and legs. As a very rapid current is constantly ascending in the chimney, a corresponding supply must be en- tering somewhere ; and it can only enter by the crevices and defects in the doors, AvindoAVS, floors, &c.:—now there is nothing more dangerous to health than to sit near such inlets, as is proved by the rheumatisms, stiff necks, and catarrhs, not to mention more serious diseases, which so frequently follow the exposure. There is an old Spanish proverb, thus translated, '«* If cold wind reach you through a hole, Go make your will and mind your soul," which is scarcely an exaggeration. Consumption is the disease which carries off a fifth or more of the persons born in Britain ; owing in part, novdoubt, to the changeableness of the exter- nal climate, but much more to the faulty modes of warming and ventilating the houses. To judge of the influence of temperature in producing this dis- ease, we may consider,—that miners who live under ground, and are always, therefore, in the same temperature, are strangers to it, while their brothers and relatives, exposed to the vicissitudes above, fall victims,—that butchers and others, who live almost constantly in the open air, so as to be hardened by the exposure, enjoy nearly equal immunity,—that consumption is scarcely known in Russia, where close stoves and houses preserve a uniform tempera- ture within doors, while fit clothing gives safety on going out,—and that in all countries and situations, whether tropical, temperate, or polar, the fre- quency of the disease bears relation to the degree and manner of change. We may here remark, also, that it is not consumption alone which springs from changes of temperature, but a great proportion of acute diseases, and particularly of rthe common winter diseases of England. There are few cases of these in which the invalid has not to remark, that if he had avoided cold or wet on some certain occasion, he might yet have been well. While temperature is thus so frequently an original cause of disease, it is also a circumstance of the very highest importance in the treatment,—as is proved by every fact bearing upon the question. We may, therefore, at first Avonder that it should be so negligently and unskilfully controlled as Ave often see it; disease and death being thence allowed to lurk, as it were, undisturbed in the sanctuaries of our homes : but Avhen we reflect on the subtile and in- visible nature of air and heat, and that the science which detects their agen- cies has been hitherto so little an object of general study, and is, indeed, of modern discovery, the fact is accounted for. In England, the open fire-place is so generally in use for common dwell- ings, and the cheerful blaze is accounted so essential to the comforts of the winter days and long evenings, that it would be difficult to persuade persons FLOATING —WARMING AND VENTILATING. 207 to abandon it: let us hope, then, that when the subjects Avhich we are now discussing come to be better and more generally understood, the open fire, with close flooring, better for double Avindows, doors that fit well, register stoves, and good general management, may be rendered almost as efficient for warming, and as safe to health, as any other contrivance. The following considerations present themselves in this place.—Small rooms in Avinter are more dangerous to health than large ones, because the cold air, entering towards the fire by the doors or Avindows, reaches the per- sons in the room before it can be tempered by mixing with the Avarmer air already around them.—-Stoves in halls and stair-cases are useful, because they warm the air before it enters the rooms ; and they prevent the hurtful chills often felt on passing through a cold stair-case from one warm room to another.—It is important to admit no more cold air into the house than is just required for the fires and for ventilation ; hence there is a great error in the common practice of leaving all the chimneys that are not in use quite open, eachadmittingair as much as a hole in the wall, or an open pane in the window would do.—Perhaps the best mode of admitting air to feed the fires is through tubes, leading directly from the outer air to the fire-place, and provided Avith what are called throttle-valves, for the regulation of the quantity; the fresh air admitted by them being made to spread in the room either at once, or after having been Avarmed during its passage imvards, by coming near the fire.—In a very close apartment, ventilation must be expressly provided for by an opening near the ceiling, through which the impure air, rising from the respiration of the company, may pass away. With an open fire, the purpose is effected, although less perfectly, by the frequent change of the Avhole air of the room Avhich that construction occasions. With a view to have, in rooms intended for invalids, the most perfect security against cold blasts and fluctuation of temperature, and still to retain the so much valued appearance of the open fire, a glazed frame or windoAv may be placed at the entrance to the chimney or stove, so as completely to prevent the passage of air from the room to the fire. The room Avill then be Avarmed by the fire through the glass, nearly as a green-house is Avarmed by the rays of the sun. It is true, that the heat of combustion does not pass through glass so readily as the heat of the sun; but the difference for the case supposed is not important. The glass of such a windoAv must, of course, be divided into small panes, and supported by a metallic frame-work to resist the heat ; and there must be a flap or door in the frame-work, for the purpose of admitting the fuel and stirring the fire. Air must be supplied to the fire, as described above, by a tube leading directly from the external atmosphere to the ash-pit. The ventilation of the room may be effected by an opening into the chimney near the ceiling ; and the temperature may be regulated Avith great precision by a valve placed in this opening, and made to obey the dilatation and contraction of a piece of Avire affixed to it, the length of Avhich will ahvays depend on the temperature of the room.—The author contrived the arrangements here described, for the winter residence of a person threatened with consumption, and the happy issue of that particular case, and of others treated on similar principles, has led him to doubt, whe- ther many of the patients with incipient consumption who are usually sent to Avarmer climates, and Avho die there after suffering hardships on the jour- ney, and distress from the banishment sufficient to shake even strong health, might not be saved by judicious treatment in properly warmed and ventilated apartments, under their own roofs, and in the midst of affectionate kindred. And if a boy be almost certainly secured from consumption by being made 208 PNEUMATICS. J a miner or a butcher, may Ave not hope that, when all the influencing circum- stances come to be better understood, something of the same immunity may be obtained for persons in all the professions and conditions of civilized society? . It must not be supposed that the remarks made in this section exhaust even nearly the very important subject of temperature as affecting health. The questions of clothing, of hot and cold bathing, of exercise, and others, equally belong to it, but the consideration of them falls under other depart- ments of study. Winds or currents in the atmosphere are also phenomena, in a great measure dependent on the law, that lighter fluids rise in heavier. As oil let loose under water is pressed up to the surface and SAvims, so air near the surface of the earth, Avhen heated by the sun, rises to the top of the atmosphere, and spreads there, forced up by the heavier air around ; this heavier air rushing inAvards, constitutes the wind felt at the surface of the earth. The cross currents in the atmosphere arising as now described, are often rendered evident by the motion of clouds* or balloons. If our globe were at rest, and the sun were always beaming over the same part, the earth and air directly under the sun would become exceedingly heated, and the air there would be constantly rising like oil in water, or like the smoke from a great fire ; while currents or winds below would be pouring towards the central spot, from all directions. But the earth is constantly turning round under the sun, so that the whole middle region or equatorial belt may be called the sun's place : and therefore, according to the principle just laid down, there should be over it a constant rising of air, and constant currents from the two sides of it, or the north and south, to supply the ascent. Noav this phenomenon is really going on, and has been going on ever since the beginning of the world, producing the steady winds of the northern and southern hemispheres, called trade winds, on which in most places within thirty degrees of the equator, mariners reckon almost as con- fidently as on the rising and setting of the sun himself. The trade winds, hoAvever, although thus moving from the poles to the equator, do not appear on the earth to be directly north and south, for the eastward whirling, or diurnal rotation of the earth, causes a wind from the north to appear as if coming from the north-east, and a wind from the south as if coming from the south-east. This fact is illustrated by the case of a man on a galloping horse, to Avhom a calm appears to be a strong wind in his face ; and if he be riding eastward, while the wind is directly north or south, such wind will appear to him to come from the north-east, or south-east:— or again, is illustrated by the case of a small globe made to turn upon a per- pendicular axis, while a ball or some water is allowed to run from the top of it downwards ; the ball or water will not immediately acquire the whirling motion of the globe, but will fall almost directly downwards, in a track which, if marked upon the globe, will appear not as a direct line from the axis to the equator, that is from north to south, but as a line falling obliquely. Thus, then, the whirling of the earth is the cause of the oblique and westward direc- tion of the trade winds, and not, as has often been said, the sun drawing them after him. The reason why the trade winds at their external confines, which are about 30 degrees from the sun's place, appear almost directly east, and become FLOATING —WINDS. 209 more nearly north and south as they approach the central line, is, that at the confine they are like fluid coming from the axis of a turning Avheel, and which has approached the circumference, but has not yet acquired the velocity of the circumference; while, nearer the line, they are like the fluid after it has for a considerable .time been turning on the circumference, and has acquired the rotary motion there, consequently appearing at rest as regards that motion, but still leaving sensible any motion in a cross direction. While, in the lower regions of the atmosphere, air is thus constantly flow- ing towards the equator and forming the steady trade winds between the tropics, in the upper regions there must of course be a counter-cqrrent distri- buting the heated air again over the globe: accordingly, since reasoning led men to expect this, many striking proofs have been detected. At the summit of the Peak of Teneriffe, observations now shoAv that there is always a strong wind bloAving in a direction contrary to that of the trade wind on the face of the ocean beloAV. Again, the trade Avinds among the West India Islands are constant, yet volcanic dust thrown aloft from the Island of St. Vincent, in the year 1812, Avas found, to the astonishment of the inhabitants of Barbadoes, hovering over them in thick clouds, and falling, after coming more than 100 miles directly against the strong trade Avind, which ships must take a circui- tous course to avoid. Persons sailing from the Cape of Good Hope to St. Helena, have often to remark that the sun is hidden for days together, by a stratum of dense clouds passing southward high in the atmosphere; Avhich clouds consist of the moisture raised near the equator with the heated air, and becoming condensed again as it approaches the colder regions of the south. Beyond the tropics, Avhere the heating influence of the sun is less, the Avinds occasionally obey other causes than those Ave have noAV been consi- dering, which causes have not yet been fully investigated. The winds of temperate climates are in consequence much less regular, and are called variable; but still, as a general rule, whenever air is moving towards the equator, from the north or south poles Avhere it Avas at rest, it must have the appearance of an east Avind, or a wind moving in the contrary direction of the earth itself, until it has gradually acquired the whirling motion of that part of the surface of the earth on Avhich it is found; and again, when air is moving from the equator, where it had at last acquired nearly the same motion as that part of the earth, on reaching parts nearer the poles, and which have less eastAvard motion, it continues to run faster than they, and becomes a westerly wind. In many situations beyond the tropics,the Avesterly winds, which are merely the upper equatorial currents of air falling doAvn, are almost as regular as the easterly Avinds within the tropics, and might also be called trade winds : —witness the usual shortness of the voyages from NeAv York to Liverpool, and the length of those made in the contrary direction. North of the equator, then, on earth, true north Avinds appear to be north-east, and true south winds appear to be south-Avest:—Avhich are the tAVOAvinds that Woav in England for three hundred days of every year. In southern climates the converse is true. While the sun is beaming directly over a tropical island, he Avarms very much the surface of the soil, and therefore also the air over it; but the rays which fall upon the ocean around penetrate deep into the mass, and produce little increase of superficial temperature. As a consequence of this, there is a rapid ascent of hot air over the island during the day, and a cooler wind blowing tOAvards its centre from all directions. This Avind constitutes the refreshing sea-breeze of tropical islands and coasts. A person must have been among these, to conceive the delight Avhich the sea-breeze brings after 210 PNEUMATICS. the sultry stagnation Avhich precedes it. The welcome ripple shorewards is first perceived on the surface of the lately smooth or glassy sea ; and soon the whole face of the sea is white with little curling waves, among which the graceful canoe, lately asleep on the water, noAV shoots swiftly along. During the night a phenomenon of opposite nature takes place. The sur- face of the earth, then no longer receiving the sun's rays, is soon cooled by radiation, while the sea Avhich absorbed heat during the day, not on the sur- face only, but through its mass, continues to give out heat all night. The consequence is, that the air over the earth becoming colder than that over the sea, sinks down, and spreads out on all sides, producing the land-breeze of tropical climates. This wind is often charged with unhealthy exhalations from the marshes and forests, while the sea-breeze is all purity and freshness. Many islands and coasts would be absolutely uninhabitable but for the sea- breeze'. The peculiar distribution of land in the Asiatic part of the globe, produces the curious effect there of a sea-breeze of six months, and a land-breeze of six months. The great continent of Asia lies chiefly north of the line, and during its summer, the air over it is so much heated, that there is a constant steady influx from the south—appearing south-west, for the reason given in a preceding page; and during its winter months, while the sun is over the southern ocean, there is a constant land-breeze from the north—appearing, for a like reason, north-east. These winds are called monsoons; and if their utility to commerce were to be a reason for a name, they also deserve the name of trade winds. In early periods of navigation, they served to the mariner the purpose of compass, as well as of moving power; and one voyage outward, and another homeward with the changing monsoons, filled up his year.—On the western shores of Africa and America also, the trade winds are interfered with by the heating of the land; but much less so than in Asia, and always in accordance with the laws now explained. The frightful tornadoes, or Avhirlwinds, Avhich occasionally devastate cer- tain tropical regions, making victims of every ship or bark caught on the Avaters, and the shore gusts or squalls met with everyAvhere, are owing to some sudden chemical changes in the atmosphere, not yet fully under- stood. The Pneumatic Trough and Gasometer of the chemist are contrivances constantly displaying the truth noAV under consideration, "that a lighter fluid is pushed up and floats on a heavier." They are important parts of the apparatus for operating on substances while in the form of air. The trough a may be made of metallic plate, or of wood lined Avith metal, and of any convenient size. It is nearly filled FiS- 106- with water, and has at one end about an inch under the surface of the water, a shelf, on which jars or vessels, as b and c, may rest. Any particular air or gas is preserved separate from the atmosphere, by being placed in one of these jars with the mouth downwards. The gas is passed into the jar by the operator first immers- ing the jar in the trough, so as to fill it with water and to expel the common air from it; and then holding its mouth over the gas while rising under the water from another vessel or pipe:— FLOATING —GA8 APPARATU8. 211 d represents a long-necked vessel, used to contain the ingredients for the pro- duction of gases by chemical action. The gas of course rises to the top of the jar b, and gradually displaces the water. During the operation of filling, the jar may be supported by the hand or by resting upon the shelf;—in the latter case the gas is allowed to rise into it through a hole in the shelf, pro- vided with a small funnel gaping doAvnwards to catch the air more readily. The shelf may have room on it for many jars, and it may have more holes than one ; and if the gas under operation be such that water absorbs or changes it, some other liquid, as mercury, may be used instead of water. A gasometer or gas-holder, is merely a larger jar or vessel, as a, dipping into Avater, with its mouth doAvnwards, in a trough of its own shape, b c, and so sup- Fig. 107. ported or counterpoised by a Aveight at d, ________ over pulleys, that very little force suffices to f^ ' (2J move it up or down. Air forced into \C ______^______ ! through a pipe f opening under it, causes it I to rise or float higher in proportion to the j quantity. The air is made to pass from it ; again when wanted, either through the same j tube or through another, as e. The huge gasometers, exceeding in size fr| an ordinary house, and containing the supply a cL of gas for the lamps of a toAvn, are vessels _c suspended as above represented, in great pits or troughs,1 filled with water. The gas issues Avith force proportioned to the downward pressure of the containing vessel, which may- be nicely regulated in a variety of ways, and is generally made to equal the action of a column of water of two inches in height; that is to say, such, that a pipe issuing from the gas-holder, and dip- ping into water at its other end, shall allow gas to escape, if immersed less than tAvo inches perpendicularly. It Avould be encroaching on the province of the chemist to treat here par- ticularly of the substances which most generally exist in the aeriform state ; but to give an increased interest to the description of the gas apparatus, a few leading facts may be mentioned. (>i about fifty distinct substances known as the materials of our globe, five, Avhen uncombined, and under common circumstances of heat and pressure, exist as airs or gases. The water used to fill the apparatus above described is a compound of two of the substances, viz., oxygen and hydrogen. By directing an electrical current through Avater, it is gradually decomposed, and from one side, a stream of aeriform oxygen may be received, and from the other a stream of hydrogen. The tAvo gases may again be united to form water, by mixing them in a proper vessel, and passing an electric spark through them. They combine Avith explosion. This oxygen, so called from its relation to acids, (the name consisting of tAvo Greek Avords, signifying acid and to form,) has been accounted, for many reasons, the most important substance in nature. It forms eight- ninths, by Aveight, of the ocean ; one,-fourth of the atmosphere ; and per- haps, one-fourth of the solid matter of the globe: possibly, therefore, although most persons think of it only as an air or gas, there is not a mil- lionth part of the quantity of oxygen in the Avorld, existing as air. It unites readily Avith most other substances, and generally Avith such intense 212 PNEUMATICS. t action as to produce the phenomena of fire or combustion; the Avord com- bustible chiefly applies to substances that quickly combine Avith oxygen. Oxygen assumes a singular variety of character in its different combina- tions. Thus with hydrogen, it forms Avater; Avith lead, it forms the sub- stance called red-lead; with nitrogen, in one proportion, it forms atmospheric air, in another proportion, the nitrous oxide, or what is called the laughing gas, in a third, the acid called aqua fortis ; with sulphur, it forms the sulphuric acid or oil of vitriol; with iron, and all metals, it forms their ores called oxides ; and so forth. But the most important character in which we knoAv it, is as that ingredient of our atmosphere, Avithout which animals and vegetables cannot live, and fire cannot burn. Oxygen, from this part of its history, Avas long named vital or pure air. Pure oxygen, in the state of air, is a little heavier than common air ; but when holding a quantity of charcoal in solution, it forms aeriform carbonic acid, which is nearly twice as heavy as common air, and may be poured out of one vessel into another like water. Carbonic acid is what issues from soda-water, brisk ale, champagne, &c, while they sparkle. If drawn into the lungs in breathing, it is fatal to life. A charcoal fire left in a close room with sleeping persons, has often been fatal to them, because carbonic acid gas is the product of the combustion. So likewise, houseless wretches in Avinter lying down in a brick-maker's field to leeward of a burning heap of bricks, often fall asleep for ever. The famous Grotto del Cane, in Italy, is a cavern always full of carbonic acid, which springs into it from below, as water springs into a well, and runs over like water from a well:—it received its name from the circumstance of dogs dying instantly when thrown into it. Carbonic acid rising in fermentation has often proved fatal to persons leaning over the edge of fermenting vats. It is common to see a rat die instantly, in the attempt to run a plank laid across the mouth of a fermenting tub. Hydrogen, the other ingredient of water, and so called from its relation to water, (the name consists of the Greek Avords for water and to form,) when in the state of air, is sixteen times as light as oxygen. With it balloons are filled. When it holds in solution a certain quantity of carbon or charcoal, it becomes the common gas used for illumination, and is the fire-damp of mines, of which the burning and explosion are so terrible. It forms one-ninth of the ocean, and much of animal and vegetable bodies. Nitrogen, so called from its relation to nitric acid, is the third and last substance which Ave shall mention. It is what remains of the atmosphere when the oxygen is removed. It forms about four-fifths of the atmosphere, one-fourth of the animal flesh, and is found in small quantities in the other combinations. It will not support life by itself, and therefore formerly was called azote: Avith a larger proportion of oxygen, it forms nitric acid or the aquafortis of old. The last feAy paragraphs may serve to show how many of the manipula- tions of chemistry are directed by the principles of physics or mechanical philosophy; and therefore, how essential to the chemist the preliminary study of physics becomes. DISCHARGE FROM APERTURES. 213 PART III. OR THE PHENOMENA OF FLUIDS. (continued.) SECTION III.—HYDRAULICS—PHENOMENA OF FLUIDS IN MOTION. ANALYSIS OF THE SECTION. Ulielher the particles of matter exist in the form of solid or fluid, the cir- cumstance does not affect their properties of inertia and gravity.— Hence liquids and airs, in proportion to their quantity, resist, receive, and impart motion, and have weight and friction, as is true of solids. This is seen in the phenomena of I. Fluids issuing from vessels, or moving in pipes and channels. 2. Waves. 3. Fluids resisting the motion of bodies immersed in them; or themselves moving against other bodies. 4. Fluids lifted, or moved in opposition to gravity. "Fluids issuing frOm vessels, or moving in channels." Water admitted to a tube ascending from near the bottom of a reservoir, will rise in it, as already explained, to the level of the liquid surface in the reservoir. If such a tube be afterwards cut off, except a-small part at the bottom, then prepared as a jet-pipe, the Avater will spout from this still to the same height, with a certain deduction for the resistance of the air and friction. Noav as a body shot upwards to any height has that velocity in departing, Avhich it again acquires by falling back to the same place or level, (with a certain deduction for the resistance of the air,) as explained at page 60, it follows that fluid issues from any orifice in a reservoir Avith velocity equal to Avhat a body acquires in falling as far as from the level of the fluid surface in the reservoir to the orifice. By referring then to the law of falling bodies, as explained at page 59, we may learn the velocity of the issue of Avater in any case, and therefore the quantity delivered by an opening of a given magni- tude. 15 214 HYDRAULICS. Thus, a body by gravity falls sixteen feet in the first second, with speed gradually increasing, and at the end of the second has a velocity of thirty-two feet per "second; therefore a reservoir Avith an opening of an inch square at sixteen feet beloAV the Avater's surface, will deliver, in one second of time, with a certain deduction for resistance of air, friction, &c, thirty-tAVO feet of a jet of AA'ater of an inch square ; and according to the same rule, an opening at four times the depth should deliver a double quantity; at nine times the depth, a triple quantity; and so on, as really happens. An inquirer is at first surprised that the quantity should not be quadruple, where the height of column or pressureforcing.it out is quadruple, ninefold Avhen the pressure is ninefold, &c.; but on reflection, he may perceive that the real effects, as stated above, are still exactly proportioned to the causes ; for, Avhen only twice as much Avater is forced out in the same time, there is still an effect four times as powerful, because each particle of the double quantity issues with tAA*ice the force or velocity, and increase of velocity costs just as much force as increase of quantity. Similar reasoning holds with respect to the triple or other quantities. Because a body shot upward Avith a double velo- city gains a quadruple height, (see page 60,) the jet, issuing with only double velocity from four times the depth, still reaches the level of the surface of the reservoir. The knoAvledge of this rule for discharging orifices is of the greatest import- ance in the construction of Avater-works, because, Avhen joined Avith other rules assigning the effects of friction, bending, unequal Avidth, &c, in pipes, it ascertains the quantity of Avater Avhich a conduit of any magnitude, length and slope, A\rill deliver. It is a curious fact, that more water issues from a vessel through a short pipe, than through a simple aperture of the same diameter as the pipe ; and still more if the pipe be funnel-shaped, or Avider towards its inner extremity. The explanation is, that the issuing particles coming from all sides to escape, cross and impede each other in rushing through a simple opening, as is proved by the narroAv neck Avhich the jet exhibits a little beyond the opening; but in a tube, this narroAving of the jet cannot happen without leaving a vacuum around the part, and the pressure of the atmosphere, resisting the vacuum, causes a quicker flow. The funnel-shape again leads the Avater by a more gradual inclination to the point of exit, and thus considerably prevents the crossing among the particles; besides that, because its mouth surrounds the narrow neck of the jet, it allows that part to be deemed the commence- ment of the jet. Another remarkable effect of atmospheric pressure on running liquids is, that in a tube of considerable length, descending from a reservoir, it much quickens the discharge. AVater naturally falls like any other body Avith acce- lerating velocity, but if it so fall in a tube which it fills like a piston, either portions of it beloAV must outstrip portions above, leaving vacuous spaces between, or water from above must be pressed into the tube by some other force than its Aveight. Now the atmospheric pressure becomes this force, and it prevents^ a vacuum, partly by impelling water more rapidly into the top of the tube, and partly by resisting the discharge from below. The forcing in of the Avater at the top of the tube causes that depression of the water- suriace in the reservoir over it, which becomes more conspicuous as the depth in the reservoir diminishes, and at last is a deep hole in the water extending far into the tube, and sometimes even as in a common funnel ex- tending quite through. The friction or resistance which fluids suffer in passing along pipes is DISCHARGE FROM APERTURES. 215 much greater than might be expected. It depends on the cohesion of the particles to the surface of the pipe and among one another, and on the parti- cles near the outside being constantly driven from their straight course by the irregularities in the surface of the pipe. An inch tube of two hundred feet in length, placed horizontally, is found to discharge only a fourth part of the water which escapes by a simple aperture of the same diameter. Air passing along tubes is still more retarded. A person who erected a great belloAVs at a water-fall, to bloAV a furnace two miles off, found that his appa- ratus was totally useless. When gas-lights were first proposed, some engi- neers feared that the resistance by friction to the passing air would be fatal to the enterprise. Higher temperature in a liquid increases remarkably the quantity discharged by an orifice or pipe,—apparently by diminishing that cohesion of the par- ticles which exists in certain degrees in all liquids, and affects so much their internal moAements. The addition of 100 degrees of heat will, in certain cases, nearly double the discharge. The flux of water through orifices under uniform circumstances is so steady, that before the invention of clocks and Avatches, it Avas employed as a means of measuring time. The vessels Avere called clepsydrae. That of Ctesibius is famous, in Avhich the issuing water took the form of tears from the eyes of a figure, deploring the rapid passing of precious time ; and these tears being received into a fit vessel, gradually filled it up and raised another floating figure, Avho pointed to the hours marked on an upright scale. This vessel Avas daily emptied by a syphon, when charged to a certain height, and its dis- charge Avorked machinery which told the month and the day.—The common hour-glass of running sand is another modification of the same principle, Avith this remarkable difference, however, that depth of the sand does not quicken the flux. The progress of Avater in an open conduit, such as the channel of a river or aqueduct, is influenced by friction, &c, in the same manner as in close pipes. But for this, a river like the Rhone, draAving its Avaters from the elevation of 1,000 feet above the level of its mouth, would pour them out, with the velo- city of A\*ater issuing from the bottom of a reservoir, 1,000 feet deep ; that is to say, at the rate of about 170 miles per hour. The ordinary Aoav of rivers is about three miles per hour, and their channels slope three or four inches per mile. The velocity of a AA-ater current is easily ascertained by immersing in it an upright tube, of which the bottom bent at right angles becomes an open mouth turned toAvards the stream. The AA-ater in the tube will stand above the surface of the stream, as much as AA*ould Fig. 108. be necessary in a reservoir, according to the explanation given above, to cause a velocity of jet equal to the velocity of the stream. A modification of this contrivance may be ct - made to measure the velocity of the Avind.—A common mode of telling the velocity of an open stream, is to observe Avith I a stop-Avatch the progress of a body floating in some part of it from which its medium speed may be known ; and know- j ing that speed and the depth and width of the channel, the j quantity deliA'ered in a given time becomes a matter of sim- CV—*V, *, pie calculation. The speed of the Avind may be ascer- ~^- tained by observing how long the shadoAv of a cloud takes to pass across a field of known dimensions. The friction of water moving in AA-ater is such, that a small stream directed 216 HYDRAULICS. through a pool, with speed enough to rise over the opposite bank, will soon empty the pool. Extensive fens have been drained on this principle. The fric- tion betAveen air and water is also singularly strong, as is proved on a great scale by the magnitude of the ocean-waves, which is a consequence of it; and on a small scale, by the amusing experiment of making a light round body dance or play upon the summit of a water-jet,—a chief cause of its remain- ing there being, that the currentof air which rises around the jet by reason of the friction, presses it inwards again, whenever it inclines to fall over. Oil thrown upon the surface of water, soon spreads as a film over it, and defends it from farther contact and friction of the air. If oil be thus spread at the windward side of a pond where the waves begin, the whole surface of a pond soon becomes as smooth as glass; and even out at sea, where the commencement of the waves cannot be reached, oil thrown upon them smooths their surface to leeward of the place, and prevents their curling over or breaking. It is said that boats having to reach the shore through a raging surf, have been preserved by the creAvs first spilling a cask of oil in the offing. The most magnificent examples that ever existed, or probably ever will exist, of artificial Avater-courses, Avere the aqueducts of ancient Rome, about twenty in number. Several of them exceeded forty miles in length, passing through hills in their Avay, and resting on tiers, of splendid arches across the valleys. They were constructed of such durable materials, and so skilfully, that the principal of them remain perfect to this day. Considered as one object, they rank, in point of magnitude, with any other Avork of human labour, not excepting the pyramids of Egypt. While the aqueducts are cited as specimens of grandeur, we may mention the fountains in the gardens of France and Italy as specimens of beauty. Those at Versailles are well known. In them the most magical effects are produced by varying the ways in which water is made to spout from orifices. In one place it is seen darting into the air as a single upright pillar: in others many such pillars rise together, like giant stalks of corn: sometimes an in- clination given to the jets makes them bend so as to form beautiful arches, of which a portion appear as the roofs of apartments built of water, while others mingle together with endless variety: here and there water-throAving wheels send out spiral streams, and hollow spheres Avitha thousand openings are the centres of immense bushes or trees of silvery boughs. Such effects, amidst cascades, smooth lakes, and scenes of lovely landscape, constitute a whole as enchanting, perhaps, as art by moulding nature has ever produced. " Waves." The form, magnitude and velocity of waves, are subjects admitting of deep mathematical research ; and are rendered the more interesting, because cer- tain phenomena of sound and light are of kindred nature. Here, however, they must be treated with great brevity. A stone throAvn into a smooth pond, causes a succession of circular waves to spread from the spot where it falls as a common centre. They become of less elevation as they expand, and each new one is less raised than the pre- ceding, until gradually the liquid mirror becomes again perfect as before. Several stones falling at the same time in different places, cause crossing circles, which, however, do not disturb the progress of one another,—a phenomenon seen in beautiful miniature at each leap of the little insects which cover the surface of our pools in the calm hours of summer.—The rationale WAVES. 217 of the formation of waves in such cases is as folloAvs : When the stone falls into the water, because the liquid is incompressible, a part of it is displaced laterally, and becomes an elevation or circular wave around the stone. This wave then spreads outwards in obedience to the laws of fluidity, already ex- plained, and the circle is seen to Aviden. In the mean time, where the stone descended, a hollow is left for a moment in the water, but owing to the sur- rounding pressure, is soon filled up, chiefly by a sudden rush from beloAV. The rising water does not stop, however, at the exact level of that around, but like a pendulum sweeping past the centre of its arc, it rises almost as far above the level as the depression was deep. This central elevation noAV acts as the stone did originally, and causes a second Avave, which pursues the first; and when the centre subsides, like the pendulum still, it sinks again almost as much below the level as it had mounted above : hence it has to rise again, again to fall, and so on for many times, sending forth a new wave at each alternation. Owing to the friction among the particles of the water, each new wave is less raised than the preceding, and at last the appearance dies away. A wave passing through any gap or opening, spreads from it as a neAv centre ; and a wave coming against a perpendicular surface of wall or rock, is completely reflected from this, and acquires the appearance of coming from a point as far beyond the reflecting surface, as its real origin or centre is distant on the side where it is moving. So absolutely level is a liquid surface, and so sensitive or mobile, that the effect of any disturbing cause is perceived at great distances. A boat roAved across a still lake, ruffles its surface to a great extent; and although the widening waves become at last such gentle risings as not to be perceptible to the eye, they still produce a rippling noise where they fall among the pebbles on shore. In seas liable to sudden but partial hurricanes, the roar of breakers on distant coasts often tells of the storm Avhich does not othenvise reach them. The author once, in the eastern ocean, had an opportunity of contemplating AA-aves of extraordinary magnitude rolling along during a gloomy calm, and therefore with unbroken surface, appearing like billows of molten lead. At that very time, about a hundred and fifty miles to the north- east, four of the finest ships of the India Company Avere perishing in a storm.—In the polar seas, Avhich are comparatively tranquil, because partially defended from the Avind by the floating islands of ice, a few sudden Avaves are occasionally observed, and quickly all is calm again. Such a phenomenon announces, that the occurrence described at page 153 has happened some- Avhere, of an island of ice turning over, Avhen the place of its centre of gra- vity is changed by partial melting. The common cause of waves is the friction of the Avind upon the surface of the water. Little ridges or elevations first appear, Avhich, by continuance of the force, gradually become loftier and broader, until they are the rolling mountains seen Avhere the Avinds SAveep over a great extent of water. The heaving of the Bay of Biscay, or still more remarkably, of the open ocean beyond the southern capes of America and Africa, exhibits one extreme, and the stillness of the tropical seas, Avhich are sheltered by near encircling lands, exhibits the other. In the vast archipelago of the east, where Borneo and Java and Sumatra lie, and the Molucca islands and the Philippines, the sea is often fanned only by the land and sea breezes and is like a smooth bed, in which these islands seem to repose in bliss—islands in Avhich the spice and perfume gardens of the Avorld are embowered, and Avhere the bird of para- dise has its home, and the golden pheasant, and a hundred other birds of 218 HYDRAULICS. brilliant plumage, among thickets so luxuriant, and scenery so picturesque, that European strangers find there the fairyland of their youthful dreams.— One Avho has visited these islands in his early days, may perhaps be pardoned for thus adverting to their beauties. In rounding the Cape of Good Hope, waves are met with, or rather a swell, so vast, that a feAV ridges and a few depressions occupy the extent of a mile. But these are not so dangerous to ships, as what is termed a shorter sea, with more perpendicular waves. The slope in the former is comparatively gentle, and the rising and falling are much less felt; while among the latter, the sud- den tossing of the vessel is often destructive. When a ship is sailing directly before the wind, over the long swell noAV described, she advances as if by leaps ; for as each Avave passes, she is first descending headlong on its front, acquiring a velocity so wild that she can scarcely be steered; and soon after, AA-hen it has glided under her, she appears climbing on its back, and her mo- tion is slackened almost to rest, before the folloAving Avave arrives. To a pas- senger perched at such a time on the extremity of the boAVsprit, and looking back on the enormous body of the ship, with perhaps its thousand of a crew, a hundred feet behind him, heaved by these billows as a cork is on a ruffled lake, the scene is truly sublime. When a coming wave lifts the stern and in the same degree depresses the bow, he is deep in the hollow or valley between the waves, and sees only the ship rushing headlong doAvn towards him as if to be engulfed ; but soon after, Avhen the stern is down, and the bow is raised, he looks from his station in the sky upon an aAvful scene beneath him and around. The velocity of Avaves has relation to their magnitude. The large waves just spoken of, proceed at the rate of from thirty to forty miles an hour.— It is a vulgar belief that the Avater itself advances with the speed of the wave, but in fact the form only advances, Avhile the substance, except a little spray above, remains rising and falling in the same place, with the regularity of a pendulum. A wave of water, in this respect, is exactly imitated by the wave running along a stretched rope when one end is shaken ; or by the mimic Avaves of our theatres, which are generally undulations of long pieces of car- pet, moved by attendants. But when a Avave reaches a shallow bank or beach, the water becomes really progressive, for then, as it cannot sink directly downwards, it falls over and forwards, seeking the level. So aAvful is the spectacle of a storm at sea, that it generally biases the judgment; and, lofty as Avaves really are, imagination pictures them loftier still. Noav no Avave rises much more than ten feet above the ordinary sea- level, Avhich, with the ten feet that the surface afterwards descends below this, give twenty feet for the whole height, from the bottom of any water- valley to an adjoining summit. This is easily verified by a person who tries at what height on a ship's mast the horizon remains ahvays in sight over the top of the Avaves—allowance being made for accidental inclinations of the ves- sel, and for her sinking in the water to considerably below her water line, at the time when she reaches the bottom of the hollow between the two Avaves. The spray of the sea, driven along by the violence of the wind, is of course much higher than the summit of the liquid wave ; and a wave coming against an obstacle, or entering a narrow inlet, may dash to an elevation much greater still. At the Eddystone light-house, which is about ninety feet high, placed on a solitary rock ten miles from land, Avhen a surge breaks which has been growing under a storm all the way across the Atlantic, it often dashes to 100 feet above the lantern at the summit. The magnitude of Avaves is Avell judged of when they are seen breaking WAVES. 219 on an extended shore or beach. In the deep sea the AA-ave is only an eleva- tion of the water, sloping on either side ; but as it rolls towards the shore, its front becomes more and more perpendicular, until at last it curls over and falls Avith its Avhole weight, and Avhen several miles of it break at the same instant, its force and noise may shake the country abroad. Along the east, or Coromandel Coast of India, at certain seasons, vast Avaves are constantly breaking ; and as there are no good harbours there, com- munication betAveen the sea and land is rendered impossible to ordinary boats. The natives of the coast, at Madras, for instance, have hence become almost amphibious. They reach ships beyond the breakers by the help of what are called catamarans, consisting of three small logs of wood tied together. On these they secure themselves, and boldly advance up to the coming wall of water, Avhich they shoot into, and rise to the smooth surface beyond it, like Avater-fowls after diving. Boats unsuited to the breakers often perish in them. The author of this work had gone on shore with a watering party on the coast of Sumatra, and during the hours spent there, a swell had risen in the sea, which on their return was already bursting along the beach and across the river's mouth in lofty breakers. The boat in Avhich he happened to be, regained the high sea in safety, but a larger boat which followed at a short distance was ovenvhelmed, and an officer and part of the crew perished. There is a phenomenon observed at the mouths of many great rivers, called the Boar, Avhich has resemblance to a Avave. When the tide returning from the sea meets the outward current of the river, and both have the force which in certain situations belongs to them, the stronger mass from the ocean assumes the form of an almost perpendicular wall, moving inland Avith resistless sweep. This is called the boar. It is in fact the great sea-wave of the tide, produced tAvice a-day by the attraction of the moon, rolling in upon the land and inlets, where contracting channels concentrate its mass. In the different branches of the Ganges the boar is seen in a remarkable degree. Its roaring is heard long before it arrives. Smaller boats and skiffs cannot live where it comes ; and as it passes the city of Calcutta, even the large ships at anchor there are thrown into such commotion, as sometimes to be torn away from their moor- ings.—The nature and effects of this boar are strikingly illustrated upon cer- tain coasts Avhere extensive tracts of sand are left uncovered at low Avater. In such situations, of AA-hich there are many on the Avestern shores of Britain, the returning tide is seen advancing with steep front, and with such rapidity, that the speed of a galloping horse can scarcely save a person Avho has in- cautiously approached too near. Many, every year, are the victims of temerity or ignorance on these treacherous plains. In the end of the year 1831, on the Ioav flat coast of the Indian peninsula, north of Madras, one great wave of the kind noAV described was produced during a very high spring-tide of midnight, by an extraordinary Avind, and spread ten miles in upon the inhabited land. It had retired Avith the ebbing tide before morning, but the next day's sun disclosed a scene of devastation rarely matched. Amidst the total wreck of the villages and fields, there lay the droAvned carcases of more than ten thousand human beings, mixed with those of elephants, horses, bullocks, Avild tigers and the other inhabitants of the land. It has been proposed lately to construct sub-marine boats, or vessels cal- culated to swim so deep in the water as to be below the superficial motion of the waves, and therefore beyond the influence of storms at the surface. Such a boat has been tried Avith considerable success ; and men's increasing fami- liarity with sub-marine matters since the invention of the diving-bell, may 220 HYDRAULICS. ultimately lead to improvements rendering the sub-marine vessel, for certain purposes, commodious and safe. " Fluids resisting the motion of bodies immersed in them, or themselves moving forcibly against other bodies." (See the Analysis.) The same force is required to give or to take away, or to bend motion, in a fluid, as in an equal quantity of solid matter. A pound of Avater enclosed in a bladder is not more easily thrown to a given height than a pound of ice or of lead; nor, if falling into the scale of a weighing beam, does it require less as a counterpoise; nor, if made to revolve at the end of a sling, does it render the cord less tight. A convenient measure of the force of moving water on an obstacle, or of the resistance of still-Avater to a moving body, exists in the facts already ex- plained, that the pressure of a known height of fluid column produces from an orifice a certain velocity of jet, while conversely, that jet, or a current of equal speed, directed against the orifice, supports the column. The impulse given or received, therefore, by a flat surface in water, such as the vane of a water-wheel, whether that of a steam-boat pressing against the water, or that of a corn-mill pressed by it, is measured by the Aveight of the column alluded to, the height of which is, according to the velocity and the breadth or diameter, according to the breadth or extent of the solid surface concerned. This estimate supposes that the pressure of or upon the surface is direct; if it be oblique, there is a diminution according to the rule given under the head of " resolution of forces." Many persons, looking carelessly at the subject of fluid resistance, would expect that if a body, as a boat, moving through a fluid at a given rate, meets a given resistance, it should just meet double resistance when moving twice as fast. Now the resistance is four times greater with a double rate. This fact is but another example of a principle already explained, and when more closely examined, is easily understood. A boat Avhich moves one mile per hour, displaces or throAvs aside a certain quantity of water, and Avith a certain velocity ;—if it move tAvice as fast, it of course displaces twice as many particles in the same time, and requires to be moved by twice the force on that account; but it also displaces every partiole Avith a double velocity, and requires another doubling of the power, on this account; the poAver then being doubled on tAvo accounts becomes a poAver of four. In the same manner with a speed of three, three times as many particles are moved and each particle Avith three times the velocity ; therefore, to overcome the resistance, a force of nine is Avanted ; for a speed of four, a poAver of sixteen; for a speed of five, a power of twenty-five, and so forth: the relations being that Avhich mathematicians indicate by saying that the resistance increases as the square of the speed. The corresponding numbers, up to a speed of ten, are as here shown. sPeed -.123456789 10 Corresponding, resistance £ 1 4 9 16 25 36 49 64 81 100 Thus, even if the resistance at the bow of a vessel Avere all that had to be considered, the force of one hundred horses would only drao* the vessel ten times as fast as the force of one horse. But there is another important element in the calculation, viz., the lessening, as the vessel's speed quick- WAVES. 221 ens, of the usual water pressure on the stern,—which pressure, while she is at rest, is equal to the pressure on the bow, and the force therefore required to produce an increased velocity is still considerably greater than as noted in the table. There is not a more important truth in physics than the law of fluid re- sistance to moving bodies here treated of; it explains so many phenomena of nature, and becomes a guide in so many matters of art. We will now set forth some interesting examples. It explains at Avhat a heavy expense of coal high velocities are obtained in steam-boats. If an engine of about 50 horse power would drive a boat 7 miles an hour, tAvo engines of 50, or one of 100 would be required to drive it 10 miles, and three such to drive it 12 miles; even supposing the increased resistance at the bow, as already stated, to be the measure of the whole work done, which it is not, and that engines Avorked to the same advantage with a high velocity as with a low, which they do not.—For the same reasons, if all the coal which a ship could conveniently carry were just sufficient to drive her 1,000 miles, at a rate of 12 miles per hour, it would drive her more than 3,000 at a rate of 7 miles per hour; and more than 6,000 at a rate of 5 miles per hour. This is a very important consi- deration for persons concerned in steam navigation to distant parts. The same law shows the folly of putting very large sails on a ship; the trifling advantage in point of speed by no means compensating for the addi- tional expense of making and working the sails, and the risk of accidents in bad Aveather. The ships of the prudent Chinese have not, for the same ton- nage, one-third so much sail as those of the Europeans, and yet they move but little slower on that account. A European ship under jury-masts does not lose so much of her usual speed as most people would expect. This law explains also why a ship glides through the Avater one or tAvo miles an hour when there is very little wind, although with a strong breeze she would only sail at the rate of eight or ten miles. Less than the 100th part of that force of wind which drives her ten miles an hour, will drive her one mile per hour, and less than the 400th part will drive her half a mile. Thus, also, during a calm, a few men pulling in a boat can move a large ship at a sensible rate. These considerations show strikingly of AA-hat importance to navigation it might be to have, as a part of a ship's ordinary equipment, one or two water- wheels, (or ready means of forming them,) to be affixed upon the ship's side Avhen required, like the paddle-wheels of a steam-boat,and by turning which, the crew might easily deliver themselves from the tedium, or even disastrous consequences of a long calm at sea.—This idea occurred to the author Avhile in a ship completely becalmed for Aveeks on the Line: during \A*hich weari- some period, the breezes were often seen roughening the Avater a mile or two farther on; and any means that could have enabled the ship's company to advance her that little distance might have saved the delay. The wheels might be driven by connection wilh the capstan, at Avhich, under such circum- stances, the crew would most willingly work. Delay in a large vessel often costs hundreds of pounds per day, and may retard the execution of important projects.—But the propelling of the ship in a calm seems, by no means, the most important purpose Avhich such Avheels might serve. If from disease, fatigue, or other cause, the crew were inadequate to existing necessities, two wheels affixed to the extremities of an axis crossing the ship might be equiA'a- lent in many cases to additional hands, or to a steam-engine of great poAver; 222 HYDRAULICS. for Avhen acted upon by the water as the ship sailed, they would turn with the force of Avater-wheels on shore, and might be made to move the pumps, to hoist the sails, and to do any work Avhich a steam-engine could perform. Many a gallant vessel has perished because the exhausted crew could no longer labour at the pumps, where such water-wheels as now contemplated, or a wind-mill wheel in the rigging Avould have performed the duty most perfectly. The laAv that resistance to a body moving in a fluid increases in a greater proportion than the speed of the body, applies where the fluid is aeriform, as Avell as where it is liquid. A bullet shot through the air with a double velocity, for the reason assigned above, experiences four times as much resistance in front, as with a single velocity: the motion is retarded also by the diminution of the usual atmo- spheric pressure of 15 lbs. per inch on the posterior surface, which diminu- tion is proportioned to the speed. It is farther true, that when the velocities of bodies moving in the air are very great, the resistance increases in a still quicker ratio than in liquids,—probably because the compressibility of air allows it to be much condensed or heaped up before the quick moving body. It is useless to discharge a cannon-ball with a velocity exceeding 1,200 feet in a second, because the powerful resistance of the air to any velocity beyond that, soon reduces it to that at least. The rule of reciprocal action between a solid and fluid, now explained, holds equally Avhen the fluid is in motion against the solid, as when the solid moves through the fluid. If a ship be anchored in a tide's way, where the current is four miles an hour, the strain on her cable is not one-fourth part so great as if the current were eight miles. A Avind moving three miles an hour is scarcely felt: if moving six miles, it is a pleasant breeze; if twenty or thirty miles, it is a brisk gale; if sixty, it is a storm; and beyond eighty, it is a frightful hurricane, tearing up trees and destroying every thing. Supposing the wind to move one hundred miles per hour, there are one hundred times as many particles of matter striking any body exposed to it, as when it moves only one mile per hour, and each particle strikes, more- over, with one hundred times the velocity or force, so that the whole increase of force is a hundred times a hundred, or ten thousand. This explains how the soft invisible air may by motion acquire force sufficient to unroof houses, to level oaks which have been stretching their roots around for a century, and in some West India hurricanes, absolutely to brush every projecting thing from the surface of the earth. The laAv of rapidly increasing resistance assigns a limit to many velocities, both natural and artificial. It limits the velocity of bodies falling through the air. By the laAv of gravity, a body would fall with a constantly accelerating speed, but as the resistance of the air increases still more quickly than the speed, at a certain point, this resistance and the gravity balance each other, and the motion be- comes uniform. ACTION BETWEEN FLUIDS AND SOLIDS. 223 The parachute, by means of which a person may safely descend to the earth from a balloon at any elevation, furnishes a good example. The con- trivance resembles a large flat umbrella. The aeronaut attaches himself underneath it, and when it is let loose from the balloon, he is partly supported by the resistance Avhich its broad expanse experiences in falling through the air, and falls, therefore, in a corresponding degree more sloAvly. After the first second or tAvo, for the reason stated above, it descends Avith a uniform motion ; and its breadth is generally made such, as to allow a velocity of about eleven feet in a second, or that Avhich a man acquires in jumping from a chair tAvo feet high. No ship sails faster than fifteen miles in an hour.—And it is because the resistance to be overcome in steam-carriages on rail-ways, viz., their friction, does not increase with their velocity like the fluid resistance to steam-boats, that the speed of the former may so much exceed that of the latter. No fish swims with a velocity exceeding twenty miles an hour ; not the dolphin, when shooting ahead of our swiftest frigates, nor the salmon, Avhen darting forward with a speed Avhich lifts him over a water-fall. Ancl the flight of birds through the thin air has a limited celerity. The croAV, Avhen flying homeAvards against the storm, cannot face the Avind in the open sky, but skims along the surface of the earth in the deep valleys, or wherever the sAviftness of the wind is retarded by terrestrial obstructions. The great albatross, stemming upon the wing the current of a gale so as to keep company Avith a driving ship Avhere the air is passing at the rate of a hundred miles an hour, often takes shelter momentarily under the lee-side of the lofty billoAvs. The bird called the stormy petrel abides chiefly in the midst of the Atlantic Ocean, but the irresistible violence of the Avind occa- sionally sweeps it from the waves, and causes its appearance on the western shores of Europe. Vessels from the high sea, approaching a coast -from Avhich the Avind blows, generally become resting-places to exhausted land birds driven off the shore by Avind Avhich they have not had strength of Aving to stem ;—sad evidences of the myriads which are constantly perishing Avhere no resting-place is found, and Avhere no human eye notes their fate. The action or resistance betAveen a meeting fluid and solid, is influenced by the shape of the solid. This folloAvs from Avhat has already been said of direct and oblique impulse. If a flat surface directly opposed to the fluid experience a certain resistance, a projecting surface like that of a sphere or short wedge is resisted in a less degree, and a concave surface in a greater. The explanation is, that a flat or plane surface throAvs the particles of fluid almost directly outAvards from its centre to its circumference, and therefore Avith greater velocity, Avhile the convex or wedge-like surface, although displacing them just as far, still does so more sloAvly, and therefore with less expenditure of force, in proportion to the obliquity of surface, or as its point is in advance of its shoulder or broadest part; and a concave surface must give to some of the particles a forward as Avell as lateral motion. The shape of the hinder part of a solid moving through a fluid is of importance for corresponding reasons. The folloAving are instances of projecting or wedge-like surfaces, intended to diminish the=resistance. Fishes are Avedge-like both before, and behind, their form being modified, hoAvever, in relation to other objects than mere speed of motion. Birds are so also ; and they stretch out their necks while 224 HYDRAULICS. flying, so as to make their form perfect for dividing the air. In the form of the under part of boats and ships, men have, in a degree, imitated the shape of fishes. The light wherries which shoot about upon the surface of the Thames, appear the very essence of what imagination can picture of form combining utility and grace. There are boats used in China called snake- boats, which are only a foot or two broad, but perhaps a hundred feet in length, and Avhen moved, as they often are, by nearly a hundred rowers, their swiftness is extreme. The problem of which it is the object to assign for a ship's hull or bottom the best possible form that she may have speed of sailing, is not yet completely solved ; so that a kind of empiricism prevails in the matter, and very unexpected results often arise. Yet the subject merits much attention, for Avhen vessels have to chase and to flee, speed becomes of the greatest importance ; and at all times the sailor's heart swells with delight to find his well-beloved vessel performing well. The folloAving instances exhibit the mutual influence of meeting solids and .fluids, where the surface of the solid is plane or concave.—In a water-wheel, whether the water be moving against the wheel, as is the case where a stream acts to drive machinery, or the wheel be moving against the still water, as in the case of the paddle-wheels of a steam-boat, the extended faces of the vanes or float-boards give or receive a powerful impulse. When a wheel with float-boards has its lower part merely dipping into a stream of water, to be driven by the momentum, it is called an undershot-wheel; when the water reaches the wheel near the middle of its height, and turns it by falling on the float-boards of one side as they SAveep doAvmvards in a curved trough fitting them, the modification is called a breast-wheel; and when the float- boards are shut in by flat sides, so as to become the bottoms of a circle of cavities or buckets surrounding the Avheel, into which the water is allowed to fall at the top of the wheel, and to act by its weight instead of its momen- tum, the modification is called the over shot-wheel. To have a maximum of effect from Avheels moved by the momentum of water, they are generally made to turn Avith a velocity about one-third as great as that of the water; and Avheels moved by the simple weight of water usually have their circum- ference turning Avith a velocity of about three feet per second. The subject of Avater-wheels is one of the most important in practical mechanics ; for moving Avater performs a great deal of labour for man. Oars for boats are made flat, and often a little concave, that the mutual action between them and water may be as great as possible. The webbed feet of water-fowl are oars ; in advancing, they collapse like a shutting um- brella, but open outwards in the thrust backwards, so as to offer a broad concave surface to the Avater. The expanded Avings of birds are in like man- ner a little concave towards the air Avhich they strike. The sails of ships, when they are receiving a fair wind, are left slack so as to swell and become holloAV. The resistance betAveen a meeting solid and fluid being nearly proportioned to the breadth of the solid, it follows that large bodies, because containing more matter in proportion to their breadth or surface than smaller bodies of similar form, are less resisted, in proportion to their weights, than smaller bodies. 8 The science of measures tells us that a bullet or other solid of two inches diameter, has eight times as much matter in it as a similar solid of one inch ACTION BETWEEN FLUIDS AND SOLIDS. 225 diameter, while it has only four times the breadth or surface. Thus, by putting eight dice or little cubes together, as here represented, Ave have a larger cube, of Avhich compared with a single dice, the edge is evidently twice as long, the surface four times as great, and the quantity of matter eight times as great;—again, twenty-seven dice simi- larly put together form a cube with sides three times as long, and the surface nine times as great; and sixty- four dice form a cube Avith sides four times as long, and a surface sixteen times as great. All solids similar have to each other this kind of relation, which, in the language of the science of quantity, is called the rela- tion of cubes : they are said to be to each other as the cubes of any of their corresponding lines. Hence, if a bullet of eight pounds, and a bullet of one pound be shot off with equal velo- city, because that of eight pounds has only half as much surface in propor- tion to its weight, and therefore to its motal inertia or force, as the other, it Avill go much farther than the other. This important rule explains why shells and large shot may be thrown four or five miles, while smaller cannon-balls, musket-bullets, pistol and swan shot, and the common small-shot of the sportsman, all of which are generally discharged from their respective pieces with the same commencing A-elocity, have a shorter range, as the size of the projectile is less. Even water is sometimes throAvn from a gun or poAverful syringe to stun birds, that they may be obtained Avith uninjured plumage ; but it soon divides in the air so minutely that it reaches only to a short distance. Water falling through the air from a great height, goes on suffering a gradual division into smaller and smaller portions, which at last may be said to be nearly all surface : and then the resistance of the air lets them fall very slowly indeed. The relation of the size and resistance is well shown by the difference of celerity in the descent of a minute fog, a drizzling mist, and common rain. The toy called the water-hammer, is merely a little Avater enclosed in a tube exhausted or empty of air; and Avhen, by turning the tube, the AA-ater is made to fall from one end to the other, as there is no air to impede or divide it in its descent, it falls as one mass, and makes a sharp noise like the blow of a hammer. The same laAv explains Avhy a spider's thread or a single filament of silk floats so long in the air before it falls ;—Avhy there is almost constantly sus- pended in the air, wherever active man resides, that immense quantity of very minute solid particles, Avhich, Avhen rendered visible by the sun's light passing directly through them, are called motes in the sunbeam—particles Avhich are constantly settling on household furniture, and rendering necessary the daily operation of dusting or cleaning:—Avhy the fine dust sent aloft during the eruption of volcanoes is often carried by the wind to a distance of hundreds of miles ;—Avhy in the deserts of Africa the strong Avinds often transport fine sand from place to place, overwhelming caravans, and forming new mosntains, Avhich succeeding blasts are again to lift;—Avhy in the bot- tom of a riA-er, or in a tides-way, fine mud is found where the current is sIoav ; sand Avhere it is quicker; pebbles, or large stones, where it is quicker still; while in rapids and Avater-falls, only massy rocks can resist the fluid force. Noav rocks, pebble, sand and mud, may all be the same material in portions of different magnitude. This law explains the operation of levigating, by which substances inso- luble in water are obtained in the state of a very fine poAvder. Any such 226 HYDRAULICS. substance is first ground or powdered in the ordinary way, and mixed Avith Avater The grosser parts then soon fall to the bottom, while the fine dust remains longer suspended. This is afterwards obtained separately by jiouring the liquid which bears it into another vessel, and allowing more time for the sIoav subsidence. The fine poAvder of flint used in the manufacture of por- celain is obtained by levigation ; as is also that of calamine stone, and other powders used in medicine and various arts. This laAv farther explains hoAV, by means of air or Avater, bodies of differ- ent specific gravities, although mixed ever so intimately, may be easily separated. If pieces of cork and lead be let fall together through the air, the lead will reach the ground first, and may be swept away before the cork arrives ; but in a vacuum the whole Avould reach the ground at the same time, as is proved by the common experiment of the guinea and feather fall- ing in the exhausted receiver of an air-pump. Again, when a mixture of corn and chaff, as it comes from any threshing machine, is showered doAvn from a sieve in a current of air, the" chaff being longer in falling, is carried farther by the Avind, while the heavier corn falls almost perpendicularly. The farmer, therefore, by winnowing in either a natural or artificial current of air, readily separates the grain from the chaff; and, if he desire it, may even divide the grain itself into portions of different quality. Similar to the operation of separating chaff from corn by wind, is that of separating sand or mud from gold-dust by water :—the soil containing gold-dust is first spread on a flat surface, over Avhich a current of Avater is then made to pass ; which current carries away the lighter rubbish, and leaves the gold. If a mass of metal be affixed on the end of a rod of wood, the rod then, whether simply falling through the air, or advancing as an arrow, will follow the heavier metal as its point. The cork of a shuttlecock is always foremost for the same reason. The instances enumerated under this head serve to show how many and varied the results may be Avhich floAV from a single principle. * When a fluid and a solid meet each other obliquely, the impulse or effect is still perpendicular to the surface of the solid, as if they met directly, but is less forcible as the obliquity of the approach is greater. Suppose a b to represent the upper edge of a smooth board or of any flat polished surface standing in a current, the fluid approaching this surface, in whatever direction, must act upon it as if approaching perpendicularly, because, on account of its smobthness, the fluid can take Fig. 110. no hold of it to push it endways, either towards a or b. n But the impulse of a stream acting on the surface will / j be less forcible if the surface be oblique to the stream, n > both because less fluid will touch, and because the velo- * \ city of the effective approach will be less. The line c d \ marks the breadth, and therefore force, of the part of ------\jc a stream reaching the board directly; and the shorter .-•' 7 line/c marks the smaller breadth that can touch it, of a j stream coming obliquely in the direction c b: in the / | oblique stream, moreover, if the line c. b mark the whole /' j » velocity, the shorter line c a marks the sloAver rate of '# the direct approach of any one particle to. the board. (This subject Avas treated of at page 57, under the head of Resolution of Forces.) Hence the wind bloAving upon the sail of the ship, however obliquely, / OBLIQUE FLUID ACTION. 227 Fig. 112. a 'c always presses it directly fonvard or perpendicularly Fig. ill. to its surface, but acts less forcibly as the obliquity is greater. If the wind be represented, as to direction and strength, by the line e d approaching the sail a b, it Avill act on the sail as if it came from/, but with the smaller force, f d, instead of the whole force e d. The effect, therefore, is the same as if the sail Avere pulled by the rope d c. We gee in this, how a ship can be made to sail in a certain degree against the Avind:—for all the sails being adjusted so as to receive the wind in the direction here shoAvn, they all act to produce the same result as if ropes Avere pulling from each in the direction dc; and a force like fd, or a rope like d c, urging side- ways as Avell as forwards—as instanced in the toAV-rope of a canal boat— makes the vessel advance rapidly forward, but scarcely at all sideAA'ays, be- cause the form of vessels causes them to pass forward at least twenty times more easily Avith their sharp bow than sideways Avith their long keel; and therefore a force urging equally sideways and forwards makes a ship advance twenty miles in the direction of her keel, that isfonvards, for one mile which she deviates sideways.—The deviation sideways, Avhich, in sailing vessels, must take place to a certain extent whenever the wind is at all oblique, is called the lee-way. A vessel having to sail from b to a, Avhile the Avind Woavs directly against her course, or from a to b, is ob- liged to sail close to the wind, as represented in fig. 112, first perhaps to e, as represented by this figure, with the left or larboard side to the wind, then to tack, as it is call- ed, or turn around, at e, and to sail to d, Avith the right or starboard side in the wind: then to go on the larboard tack again to c, and thence to the port at a. In making way against a contrary wind, the sails of a ship are pointed so nearly edgeways to the wind, that unless very flat, a great portion of their surface becomes* useless. nose manner of rigging is, in this respect at least, superior to the European; for in it bamboo reeds attached across the sails, render them as flat as boards. When a Chinese ship has her sails pointed edgeAvays to a spectator, he only sees the masts Avhich support them. The reason A\rhy a ship Avith several masts generally sails faster when the wind is more or less from a side, than when directly astern, is, that in the former case all the sails are acting, although individually not to the best advantage, Avhile, in the latter, the sails in front are becalmed by those behind them. A ship A\ith a side-wind may move faster than the Avind itself, as is often true of the outer extremities of a Avind-milPs vanes. A qorresponding relation of motions is observed when a slippery wedge is forced out two or three inches laterally from its place, by a Aveight Avhich descends only one inch perpendicularly. The law noAV under consideration explains the action of the rudder of ships, —that contrivance, by which a single steersman can direct the course of an enormous vessel through rocks and shoals more steadily and safely that an adroit charioteer can guide his tiny vehicle on a common road. The helm or rudder is a flat projection from the stern-post of the ship, turning on strong hinges, in the manner of a door or gate, and moved by a beam or lever cl,-- b The Chi- 228 HYDRAULICS. Fie 113 calIed the tiUer' which Proceeds from it fonvard to where the steersman stands. In small vessels the tiller is above the deck, and the steersman applies his hand directly to it; but in large J\ ships it is beloAV, and is moved by ropes, rising from it to the f \ wheel on the deck, Avhere the steersman stands, Avith the com- ) pass before him. While the rudder points directly astern, as \ / to a, like a continuation of the keel and stern-post, it does not \ / affect the vessel's course ; but if it be inclined ever so little to c \ , / one side, as to b on the left or larboard side, the water imme- '-A/T diately acts on it in the direction c b, perpendicular to its sur- ' ia face, and pushes the stern to the right or starboard side,—an action equivalent to pulling the boat to the left or larboard. It is possible to make a ship or boat steer itself, by placing a powerful vane on the mast-head, and connecting it with the tiller-ropes by two pro- jecting arms from its axis. If it Avere desired to make the ship sail directly before the Avind, the tiller-ropes would be fixed to the arms of the vane so that the helm should be in the middle position, Avhen the vane was pointing directly forAA*ard : should the vessel then from any cause deviate from her course, the vane, by its changed position Avith respect to her, would have produced a corresponding change on the position of her helm, just such as to bring her back to her course. Again, it is evident that, by adjusting such a vane and rudder to each other in different Avays, any other desired course might be obtained, and Avhich would alter only Avith the wind. The vane, to have the necessary poAver, Avould require to be of large size; it would be a wide hoop, for instance, with canvas stretched upon it; and the rudder, to turn with little force, might be hung on an axis passed nearly through its middle, instead of, as usual, by hinges at one edge. Cases have occurred Avhere shipwrecked persons might have sent intelligence of their disaster to a distant coast, by a small vessel, or even a block of Avood fitted up in this way. The method admits also of other applications, particularly in war. As fluids act on surfaces, in a direction perpendicular to them, the water on the right side of a ship's boAV is alwa}^s pressing it toAvards the left side, but OAving to the equivalent and contrary pressure there, the ship holds her course evenly between the two, or straight fonvard. When a ship, however, owing to a side Avind, lies over, or heels, as it is called, that side of the bow which sinks most is more pressed than the other; and were there not a coun- teracting inclination of the rudder then made, constituting what is called weather-helm, the ship's head would come round to the wind. Noav ships so rarely have the wind exactly astern, that to diminish the almost constant necessity for weather-helm, the mast or masts, and consequently the mass of the sails, are placed more towards the bow than the stern. Again, because the bow of a ship is oblique downwards as well as side- ways, the water, when she moves, is constantly tending to lift the bow; hence when the vessel is dragged by a low horizontal rope, as in the case of a boat attached to a sailing ship's stern, or is moved by paddle-wheels, like steam-boats, the bow rises much out of the water, and the stern sinks in the hollow or furrow of the track: but when she is driven by sails, as these are high on the mast, and are acting therefore on a long lever to depress the bow, the tAA-o opposite tendencies just balance each other, and the vessel sails evenly along. The form of the fore part of a ship has less influence upon her speed of sailing than the form of the hind part, called the run, from the middle to the stern. When a ship is at rest, there is of course as much forward pressure OBLIQUE FLUID ACTION*. 229 of Avater about the stern as of backward pressure on the bow ; but Avhen she sails, she is running away from the propelling pressure, and is increasing the resisting pressure. A gradual tapering of the hind part, therefore, or a fine run, as it is called, Avhich allows the Avater to apply itself readily to it. as it passes along, must influence much the rate of sailing. The fore part of any mass draAvn through the water, hoAvever blunt or square, becomes in effect sharp or rounded by a quantity of water Avhich it pushes on before it. A tree, or the tapering mast of a ship, can be draAvn through the water more easily with the large end foremost than in a contrary way. The common windmill furnishes another illustration of the action of fluids on oblique surfaces. The face of the windmill is turned directly to the wind, but the four flat Fig. 114. vanes or sails, of which the great wheel consists, are individually oblique. Thus the edge a of the vane a e, is more fonvard as regards the coming wind or a spectator in front, than the edge e, and the action of the wind, therefore, being perpen- dicular to the oblique surface a e, pushes it in a degree towards a. The same remark applies to each of the other vanes where the edges b c and d are in front, and those marked by the fainter lines are behind; so that each vane produces an equal effect in turning the Avheel. The laAv of the " decomposition of forces,'' explained in page 57, tells in Avhat proportion the force of the wind is exerted to push the wheel backwards against its supports, and to turn it round. Windmills were first used in Europe in the fourteenth century, and they are still of great importance in countries Avhere there are no water-falls, and little fuel for steam-engines. In some of the richest European landscapes, every height is crowned by its bushy windmill, grinding corn, or saAving wood, or pressing oil-seeds ; and over the plains, similar Avheels are pump- ing water for domestic use, or incessantly draining the land. The smoke-jack of our chimneys is a small windmill, driven by the ascend- ing current of air in the chimney. . The feathering of an arrow acts in part on the principle of the Avindmill. The feathery projection from the shaft is not quite straight, but winds round it a little, like the thread of a screw; and the arrow, therefore, constantly turns as it flies, and goes straight to its object although the shaft itself be bent. because any deviation is constantly correcting itself. The rifle-barrel in fire-arms has spiral furrows or threads along its interior surface, so that the bullet in passing out receives a turning motion corre- sponding to that of an arroAv, and producing similar results. A bullet which receives any other turning motion than round the line of its course—and most bullets from a common barrel do acquire such, owing to the irregularity of their form, or unequal friction at the mouth of the piece—is sure to deviate from its course, because unequally pressed or resisted by the atmosphere. A good rifle fixed to its place will send a succession of shots through the hole made in the target by the first shot, at the distance of 200 yards. Duels have been fought Avith rifles, and the parties having fired at the same moment, have been corpses the moment after. It might be supposed that a wheel Avhich the Avind turned by direct action on the rim, as Avater turns common Avater-wheels, Avould be preferable to the windmill-Avheel above described, Avhich is turned by oblique action on the face; accordingly, a Avheel like a Avater-Avheel only with broader vanes, has 16 230 HYDRAULICS. been placed in a house or cover, so that only one side at a time was exposed to the Avind:—but it is a poAveriess machine. The oblique vane wheel may apply to use only half or less of the force of the air which reaches it, but its Avide expanse receives a stream of air of thirty feet in diameter, while an ordinary AvindoAV Avould admit that required for a wheel of equal size of the other construction. There are some situations Avhere it Avould be an advantage to have water- Avheels like the common windmill-Avheel, viz., where the stream is sluggish, and is deep enough to alloAV a large wheel to be Avholly immersed. A small Avheel of this sort, Avith broad oblique vanes, has been used as a means of ascertaining the rate of a ship's sailing. It is allowed to drag astern in the water; and the number of reA-olutions made in a given time marks the ship's speed. A Avindmill-Avheel made to turn during a calm by force applied to its axle, would be pressed endways, or in the direction of its axle, just as if Avind were bloAving upon it, OAving to the reaction of the still air, through Avhich its oblique vanes Avere made to sAveep. Such a form of Avheel fitted to Avork in water, and called a Avater-screw, has been applied at the bow or stern of steam-boats, to propel them in canals where there was no room for side Avheels. But as from the obliquity of the surfaces only a part of the applied poAver becomes propulsive—the remainder being wasted in the lateral strain or tAvisting of the Avater—the method is not applicable to general purposes. Two small windmill-wheels placed horizontally one above the other, on the same axis, and made to turn in opposite ways by springs or otherwise, would rise in the air, carrying a certain load Avith them, and would consti- tute, therefore, a flying machine. The effect of a single oar projecting from the stern, used to propel a boat or vessel, in the manner called sculling, is referable to the law hoav under consideration. The oar or scull rests on a round-headed prop or nail at the stern, and is made to vibrate from side to side. In all its positions it has the surface Avhich presses the Avater turned obliquely backAvards ; hence the reac- tion of the water drives the boat fonvard.—In China, large vessels are moved by a single sculling oar, which half of the ship's company may be urging at the same time. A sculling oar may be regarded as a single vane of such a propelling Avheel or Avater-screAV as above described, made to sweep across, behind the vessel, alternately to the right and to the left. The action of a fish's tail and of the bending of an eel or snake in Avater, partly resembles that of the sculling oar. Many people believe that the tail of the fish is only the rudder of the body, and that the fins give it forward motion—as is true of a bird's tail and wings,—but the fish's tail is in fact the great instrument of motion, while the fins serve Fi£- 11S- chiefly to steady and direct the motion. £-.. A paper kite rising in the air is another example \~a belonging to this place. Its cord d is attached to it Idg> ^ above the middle of its loop, and therefore so as to J^ -^ make it present ahvays an oblique surface to the wind; jf \^ and by the action of the wind, perpendicular to its f surface, it rises as if pushed up in the direction c a, 1 or as if draAvn up in the direction of a b. A kite / might be made large enough to lift a man. Cats | have been sent up at kites' tails, and have fallen doAvn safely under parachutes from the greatest eleva- tions. It might be safer for a man to rise at a kite's * LIFTING OF WATER. 231 tail to reconnoitre an enemy's position, or to survey an unknown country, than under a balloon, as was practised by the French during the revolutionary wars. He might have the security of a parachute, and the poAver of regula- ting the obliquity of attachment of the rope, so as to command his ascent or descent at pleasure. An exhibition Avas made in October, 1827, between Bath and London, of a car drawn along the highway by kites. That they might ascend to a great elevation, where the Avind is generally stronger than beloAV, they Ave re attached to each other in a row, so that the second kite mounted as if its cord Avere held by a hand at the first, the third as if rising from the second, and so forth. The projector of this novelty hoped that he had pointed out a most valuable means of travelling across extensive plains, sandy deserts, tracks of snow, &c, and in all cases, nearly with the speed of the wind. " Fluids lifted in opposition to gravity." (See the Analysis.) Water, as we have seen in former parts of this work, is to the living uni- verse, in some degree, what the blood is to the animal body, and a constant supply and circulation are required. This supply has been provided for to an extraordinary extent, by the operation of natural causes ; but for many purposes of human society, water is still required where none naturally exists. A great variety of means have been employed for raising it, some of Avhich", sufficient to illustrate the whole, are now to be considered. Water may be raised in a bucket which is attached to a rope to be pulled up by the hand.—The rope carrying the bucket may be drawn up more easily by being Avound round a barrel or axle turned by a winch.—There may be a succession of buckets on a rope, rising one after the other, and Avhen emptied, descending again on the opposite side of the Avheel or axle Avhich lifts them : the rope to Avhich they are attached being a circle or end- less rope, and constituting Avith them what is called the bucket-machine.— Instead of buckets or such an endless rope or chain, there may be a succes- sion of flat nieces of wood, which, on being drawn up through a large tube or barrel, like loose-fitting pistons, will raise a copious stream of water : this is the contrivance called the chain-pump.—Or simply an endless rope of hair, very rough, passing round one Avheel above, another beloAV, may be Avhirled quickly by turning the upper Avheel, so that a mass of AA-ater adhering by friction to its rising half, shall be thrown into a reservoir at the top Avhere it passes over the upper wheel: several such ropes may be joined side by side to increase the effect.—But the most important of all water-raising engines are the lifting and forcing-pumps, already described at pages 171 and 172. They are used to draw from wells, to drain mines, to send a supply over cities, to pump ships, to throw AA-ater for extin- guishing lires. and for many other purposes. Fig 116. A stream of Avater passing through a garden, or in the midst of fields, may haA*e beauty Avith little utility, unless it can be employed to irrigate the vegetable creation around. In the fields and gardens of Persia, Avhere the heat of the sun is very intense, the streams are caused, by their OAvn action, to lift a part of their Avater into elevated reservoirs, from Avhich it again Aoavs in sloping channels to whenever it is required. A large Avater-Avheel is placed so that the stream may turn 232 HYDRAULICS. Fig. 118. it, and around its circumference buckets are attached, to be filled as they sweep along below, and to be emptied into a reservoir as they pass above- or instead of buckets, the spokes of the wheels are themselves made hollow, and curved as here represented, so that as their extremities dip into the water at each evolution, they receive a quantity of it, which runs along them as they rise, and is discharged into a reservoir at the centre. These are usually called Persian wheels, but they are as commonly employed on the banks of the Nile and elseAvhere as in Persia. A pipe wound like a screw upon a sloping barrel, and made to dip its lower mouth into water at each revolution of the barrel, will also raise water : the lower portions of the turning pipe will always be full of it, and it will be rising in them to the top, as if on Fig. in. an inclined plane. Archimedes was the inventor of this beautiful water-screw, and his name has re- mained to it. It may be turned by hand, or by a passing stream Avhich acts on the vanes of a water-wheel affixed upon it. Water may be raised by produ- cing centrifugal force at the upper end of a bent pipe which dips into a reser- voir* Supposing the pipe to be bent as here represented, and the horizontal arm a to turn like the spoke of a Avheel, round the upright portion as the axis,—if the pipe be once filled with water, and be turned with sufficient speed, it will con- tinue to throw out a constant stream from the end a. To increase the discharge there may be several horizontal arms from one larger upright pipe, all emptying themselves into a circular trough or reservoir ; and to prevent the necessity of refilling the apparatus after every interruption of its motion, a valve opening upwards must be placed at the bottom. This contrivance has been called the centrifugal pump, hecause the water is raised at b as in a pump, by the pressure of the atmosphere, to supply the place of that which is throAvn out from a by the centrifugal force. The velocity of rotation must bear proportion to the height of the discharging aperture a, above the surface of the Avater in the reservoir. It had long been observed in household experience and elsewhere, that while water is running through a pipe, if a cock at the extremity be suddenly shut, a shock and noise are produced there. The reason is, that the forward motion of the whole water contained in the pipe being instantly arrested, and the momentum of a liquid being as great as of a solid, the water strikes the cock with as much force as if it were a long bar of metal or a rod of wood having the same weight and velocity as the water. Then as the fluid presses equally in all directions, a leaden pipe of great length may be widened, or even burst in this experiment.—Lately this fonvard pressure of an arrested stream has been used as a force for raising water, and the arrangement of parts contrived to render it available has been called, on account of the shocks produced, the water-ram. The ram may be described as a sloping pipe in which the stream runs, having a valve at its loAver end, to be shut at inter- vals to arrest the stream, and having a small tube rising from near that end toAvards a reservoir above, to receive a portion of the water at each interrup- tion. Now water allowed to run for one second, in a pipe ten yards long, LIFTING OF WATER. 233 Fig. 119. two inches wide and sloping six feet, acquires momentum enough to drive about half a pint, on the shutting of the cock, into a tube lead- ing to a reservoir forty feet high. Such an apparatus, therefore, with the valve shutting every second, raises about sixty half-pints or four gallons in a minute. The valve is so con- trived that the steam works it as desired.—In this figure which represents the lower end of the water-ram, a is the opening by which the steam escapes from it, and the valve or flap seen below the opening is that Avhich by suddenly shutting arrests the stream. The valve is made so heavy, that the stream must run for a certain time to acquire force enough to shut it; and in the instant of its shutting, a little of the advancing Avater passes upwards through the valve b towards the reser- voir. The water in the main pipe then becoming stagnant again, no longer has poAver, by its Aveight alone, to keep the valve a shut: this, therefore, falls open and the stream begins again, again to be arrested as before ; and as long as the supply of water lasts, the action of the apparatus continues. The action of a Avater-ram has been compared to the beating of an animal's pulse. The upright tube has usually a reservoir at the bottom, where it first receives the water, constituting there an air-vessel b, (described at page 161) which, by the air's elasticity, converts the interrupted jets first received, into a nearly uniform current towards the reservoir. The supply of air to this vessel is maintained by the contrivance called a snifting-valve. In the preceding examination of the doctrines of fluidity, we have had to touch on many of those phenomena of nature and art which are the most important to man ; yet we have seen how beautifully simple and intelligible they are all rendered when referred, by a methodical arrangement, to a feAv heads dependent on the " fundamental truths." Each one of the many par- ticulars belonging to this department, and Avhich when now explained appears so simple and obvious, has yet been a distinct step in the slow progress of discovery or invention, and probably when first made has filled some inge- nious mind with intense and purest delight. 234 ACOUSTICS. PART III. (continued.) SECTION IV.—ACOUSTICS, OR PHENOMENA OF SOUND AND HEARING. ANALYSIS OF THE SECTION. 1. Sound is heard when any sudden shock or impulse is given to the air, or to any other body which is in contact directly or indirectly with the ear. 2. If such impulses be repeated at very short intervals, the ear cannot attend to them individually, but hears them as a continued sound, which is uni- form, or what is called a tone, if the impulse be similar and at equal in- tervals, and is grave or sharp, according as they are few or many in a given time ; and all continued sound is but a repetition of impulses. 3. When the number of impulses in a given time producing some uniform continued sound has a simple relation, as of half, third, fourth, fyc, to the number producing some other such sound which is heard either simul- taneously with it, or a little before or after, the ear is generally much and pleasingly affected by the circumstance ; and the sounds are said to have musical relation to each other, or to be accordant, while all others are termed discordant. 4. The shock which causes the sensation of sound spreads or is propagated in all bodies, somewhat as a wave spreads in water, with decreasing strength as the distance increases, but with a velocity nearly uniform, and which in air is about 1,142 feet per second. 5. Sound is REFLECTED/rom smooth surfaces, and hence arise many curious and pleasing effects called echoes, $-c. 6. The structure of the ear illustrates tlte laws of sound. Early inquirers into nature had remarked that in most instances of noise or sound there was present a shock or trembling of the sounding body, often visible, but sometimes only sensible to the touch, or discoverable by other means ; it was noted, for instance, in the string of a harp, in the reed of a hautboy, in the prongs of a tuning-fork, in the lip of a bell: but it Avas reserved for the moderns to understand fully, that the animal organ called the ear, is merely a structure of parts admirably adapted to be affected by the concussions or tremblings of things around ; and that sounds in all their varieties are merely such motions, affecting the ear through the meditm of CONTINUED SOUND. 235 the air Avhich surrounds it, or of some other body, or series of bodies, reach- ing from the trembling thing to the ear. The delicacy and complexity of an organ destined to feel and to distin- guish such light and varying influences, and the vast importance of it to man, as that which makes him capable of using language, besides being his ever-Avatchful monitor of surrounding occurrences, and the channel by which the fascination of music enters, render this subject, to all Avho love to read in nature the attributes of its author, a most favourite study. Because all the bodies around us are immersed, in common with ourselves, in the ocean of air which covers the earth, we are much more frequently warned of the shocks and tremblings of which Ave have been speaking, by their effect on the air, than in any other way ; hence the early prejudice that air was necessary to sound, and hence, in part, the reason why the doctrines of sound have generally been accounted a part of pneumatics. We shall now find, however, that all bodies are more or less fitted to convey these trem- blings, and that air in many cases is neither the quickest nor the best conduct- or. Although our notions on the subject are thus corrected, it is still con- venient to study the theory of sound as a part of Pneumatics. 1. " Sound is heard when any sudden shock or impulse occurs in a body having communication, through the air or otherwise, with the ear." (Read the Analysis.) Common instances of a single impulse are—the blow of a hammer—-the clap of hands—the crack of a whip—a pistol-shot — any explosion — the thunder-clap. The loudness of sound conveyed by air depends on the air's density. A bell enclosed in the receiver of an air-pump is heard less and less distinctly as the air is exhausted, and in a vacuum is not heard at all.—Even the blow of a hammer, in a vacuum, is not heard if care is taken to prevent the shock from being communicated through neighbouring solid bodies.—In the thin air surrounding a lofty mountain-top the report of a pistol is much less loud, and human voices are Aveaker.—In the condensed atmosphere of a div- ing-bell a Avhisper is loud.—When volcanoes and various other resemblances to the constitution of our earth Avere first discovered in the moon, some per- sons fancied that during the stillness of night Ave should hear the thunder there :—but supposing the thunder to happen, and to be ever so loud, it could not be heard on earth, because there is no medium to bear thither the pulses of sound—there is a vacuum between. 2. Impulses quickly repeated cannot be individually attended to by the ear, and hence they appear as one continued sound, of which the pitch or tone depends on the number occurring in a given time ; and all continued sound is but a repetition of impulses. (Read the Analysis.) If a Avheel Avith teeth be made to turn and to strike any elastic plate, as a piece of quill, with every tooth, it Avill, when moved sloAvly, alloAv every tooth to be seen and every bloAv to be separately heard ; but with increasing velocity the eye will lose sight of the individual teeth, and the ear, ceasing to perceive the separate Woavs, will at last hear only a smooth continued sound, called a tone, of Avhich the character will change Avith the velocity of the wheel. In like manner the vibrations of a long harp-string, while it is very slack, are separately visible, and the pulses produced bv it in the air are separately 236 ACOUSTICS. audible; but as it is gradually tightened, its vibrations quicken, so that, where it is moving, the eye soon sees only a broad shadowy bellying line * and the distinct sounds Avhich the ear lately perceived, seeming now to run together on account of the shortness of the intervals, are felt as one uniform continued tone, which constitutes the note or sound then belonging to the string/ Again, if a current of air passing through a tube or opening, be in any way interrupted at regular and very short intervals, as by a little stop-cock placed in the opening, of which cock the plug, instead of being only partially turned by a cross handle, as in a common beer-cock, has a wheel fixed upon it, so that any desired rapidity of rotation-may be given to it,—then at every time when the passage for air becomes open, there will be a certain shock given to the air around, and the repetition of such shocks will constitute a musical tone. This apparatus can produce all tones, and it enables us with great precision to ascertain the number of pulses required to constitute any given tone. It is the elasticity of any string used to produce a tone which causes the repetition of the percussions, and therefore the continuance of the sound, thus :—the string having been pulled at its middle to one side, and then let go, is, owing to its elasticity, carried back quickly to the straight position; but by the time that it has reached this, it has acquired a momentum which, like the momentum of a vibrating pendulum, carries it nearly as far beyond the middle station as the distance whence it came : — it has to return, therefore, by its elasticity, from this second deviation, in the same way; but still passing the middle as before, it has again to return ; and thus continues vibrating uniformly as a pendulum does, until the resistance of the air and friction gradually bring it to rest. A large vibration of any string, like a large oscillation of a pendulum, occupies very nearly the same time as a smaller, because the farther that the string is displaced or bent, the more forcibly, and therefore quickly, is it pulled back again by its elasticity: hence the uni- formity of the tone produced by a musical string is not injured by the differ- ent force with Avhich the finger of the player may touch the string. Accord- ing, however, as the vibrations of a string are more extensive or quicker, the impulses given to the air are more sharp or forcible, and hence the sound becomes louder. And this explains why sharp sounds are generally also loud. Vibrations which are comparatively few and slow, strike the ear very gently, as in the flapping of a pigeon's wing, or in the play of a switch. The most familiar instance of sounding vibration is that of an elastic cord extended betAveen two fixed points, as in stringed instruments of music : but because elastic bodies generally, when by any force their natural form is for a time altered, recover it Avhen allowed, not by a first effort, but like the string of a pendulum, after a series of oscillations, almost all such bodies repeat many times an impulse once given to them, and thus may become the means of producing a continued sound.—If a solid rod of steel, glass, or any other elastic substance, be fixed firmly at one end and left free at the other, and if that other be then pulled a little to one side of its station of rest, and suddenly let go, it will immediately seek its station again, but by the momen- tum acquired in the approach, will go beyond it: it will then return as be- fore, but again to pass, and so will continue to vibrate Avith diminishing force for a considerable time.—A boy at school, thus, sticks the point of his pen- knife into the bench, and by one touch makes it produce a continued uniform sound of considerable duration.—The prongs of a tuning-fork, or of the com- CONTINUED SOUND. 237 mon sugar-tongs, vibrate and sound in the same way.—In the musical snuff- boxes and chimney-clocks, the sounds are produced by the vibration of little rods of steel, fixed by one end, in a row, like the teeth of a comb, and touched by small pins or points projecting from a turning barrel.—Any elastic flap, as of metal or of tough Avood, placed over an opening, so as to stand away from it a little Avhen not pressed by passing air, but to close the opening if so pressed, becomes a sounding reed when air is gently forced through the opening : thus, the air first pressing on the flap to close it causes a moment- ary interruption of the current, but the flap immediately recoiling from the blow, as well as by reason of its own elasticity, again opens the passage, and the continued rapid alternation of the shutting and opening produces the tone.—The reed of a clarionet is a thin plate of elastic wood, made to vibrate in this way.—The drone of the bag-pipe and the common straw-pipe, are reeds of nearly the same kind.—The Chinese organ, and the sweet instru- ment lately introduced under the name of yEolina, have reeds which differ from these, by beating through the opening instead of merely on its face.— Elastic rods simply resting on supports at both ends, or suspended by their middle, will also vibrate ; a musical instrument is thus made of pieces of glass laid upon two strings, and struck by a cork hammer: in the Island of Java, a rude instrument of the same kind is made of blocks of hard elastic wood.—A portion of a hollow sphere of elastic metal very readily takes on a vibration, during Avhich its form is constantly changing from the perfect round to the oval, and conversely ; there are consequently repeated percus- sion of the air, and a continued sound, and the thing is called a bell. A bell admits of great variety of shape, and may be made of any elastic substance, as metal, glass, earthenware, (buyers ring earthenware to ascertain its sound- ness,) and even of hard wood.—The Chinese gong is a metallic vessel shaped like a common sieve, having a manner of vibration very peculiar, and pro- ducing sounds that are rousing and sublime.—The drum has a tense elastic membrane on Avhich the Woavs of the drum-stick are received : its tone ceases quickly, because the motion of so broad a surface is much resisted by the air.—In the flute, flageolet, common organ-pipes, &c, the air is forced through narroAv passages, and is divided by sharp edges, in such a way as to suffer repeated but perfectly regular condensations or interruptions sufficient to affect the ear ; and hence the endless variety of sweet continued sounds Avhich these contrivances are knoAvn to produce. , To the production of a tone, it is of no consequence in Avhat Avay the pulses of the air are caused, provided they follow with sufficient regularity ; witness, in addition to some of the instances given above, the pure sound produced by the motion of a fly's wing—supposed by many to be the voice of the insect. The clacking of a corn-mill, and the noise of a stick pulled along a grating, are not tones, only because the pulses folloAV too slowly. Where a continued sound is produced by impulses AA-hich do not, like those of an elastic body, follow in regular succession, the effect ceases to be a clear uniform sound or tone, and is called a noise.—Such is the sound of a saw or grind-stone—the roar of the waves breaking on a rocky shore, or of a violent wind in a forest—the roar and crackling of houses or of a wood in flames__the mixed voices of a talking multitude—the diversified sounds of a great city, including the rattling of Avheels, the clanking of hammers, the voices of street-criers, the noises of manufactories, &c. ; Avhich rough ele- ments, hoAvever, at last mingle so completely that the combined result has often been called " the hum of men," from analogy to the smooth mingling miniature sounds which constitute the hum of a bee-hive. 238 ACOUSTICS. " Grave and sharp sounds." (Read the Analysis.) The difference of sounds, which depends on the different number of vibra- tions of the sounding body in a given time, divides them into those called bass, low, or grave notes, for comparatively few and slow vibrations ; and those called high, shrill, or sharp, for vibrations more numerous and quick. The frequency of vibrations in strings increases with their shortness, light- ness and tension—for if a string be long or heavy, there is a greater mass of matter to be moved, and hence a slower motion ; and if a string be slack, the force of elasticity which pulls it from any deviation back to the straight line is so much the less. It is found that a string taken of half the length, or of one-fourth the weight, or of quadruple the tension of another string, vibrates twice as fast on any one of these accounts. These truths are familiarly illustrated in the violin. The low or bass string is thick and very heavy from being covered with metallic Avire, and the others gradually diminish in magnitude and weight, up to the smallest or treble. The strings are tuned to each other by being attached by one end to movable pins, which, when tuned, increase or diminish their tension; and the sound produced by each may be afterwards varied to a certain extent, by the performer pressing different parts of it with the finger against the board, so as to shorten the vibrating portion. An analogous law, as to the influence upon tone, of weight and dimensions, holds with respect to bells, glasses, reeds, &c, and enables us to use these also in the construction of musical instruments. 3. " When the number of impulses producing some continued sound has a simple relation, as of half, third, fourth, fyc, to the number producing some other sound which is heard either simultaneously, or a little before or after it, the ear is much and pleasingly affected ; and the sounds are said to have musical relation to each other, or to be accordant, while all others are termed discordant." (Read the Analysis.) Understanding now that all continued uniform sounds are produced by a repetition of similar beats or vibrations, we perceive that in the series from grave, to sharp, there must be such as, with respect to the number of beats in a given time, are related to each other, as the numbers 1, 2, 3, 4, &c, or, which is the same thing, as 10, 20, 30, &c. Now as between two sounds, one of Avhich has 20 beats while another has 10, there will be a coincidence at every second beat of the quicker, and between sounds whose beats are to each other as 30 to 20, there must be a coincidence at every third beat of the quicker, and so forth, Ave should naturally expect the ear to be differently affected by such correspondence than when the coincidence is either less frequent, or is irregular. Accordingly we find that all sounds which have such simple relations to each other, are remarkably agreeable to the ear, either when heard together, or in close succession ; while those in which the coincident beats are farther apart, are heard with indifference, or are felt to be positively harsh and disagreeable. It is in fact offering itself to be noticed here, that the coincident or double pulses of any tAvo concordant sounds be- come the cause or elements of a third sound, perfectly distinct from them, but which is ahvays heard with them, and is called their grave harmonic or resultant: it is the same as a simple sound having as many vibrations in a given time as there are coinciding beats between the two other sounds. If a long musical string be made to sound, and the number of its vibrations in a given time be ascertained, we find that if only half of it be allowed to MUSIC. 239 vibrate at a time, as when a finger presses its middle against a board, that half will vibrate twice as fast : and similarly, a third part three times as fast; a fourth part four times as fast; and so on, producing thesounds or tones most nearly related to each other. A fine illustration of this is afforded by the string of a violoncello, when made to vibrate by a bow moved very gently across it, near the bridge ; for it often divides itself spontaneously into tAvo, three or four, &c, equally vibrating parts or bellies, with points of rest betAveen them called knots : when this happens, there are heard not only the sound or note belong- ing to the Avhole length of the string, but, also, more feebly, the subordinate notes belonging to its half, third, or fourth, &c, according to circumstances, beautifully mingling with the first sound, and forming with it a rich harmony. Often in such a case the subordinate sounds swell with such force as to over- power for a time the fundamental note ; but any one such sound is rarely of long duration. The same harmonic sounds may be produced still more certainly, while drawing the bow across the string, by touching the string lightly with the finger, at one of the points where we wish it to divide. Even a tune may be so played. The sounds thus belonging to a single cord or string, and produced by its spontaneous division into different numbers of equal parts, constitute, AA-hen heard together or in succession, Avhat may be called the simple music of na- ture herself. It is produced pleasingly, as just described, by the single string of a violoncello ; but in the most perfect manner by the instrument called the ^Eolian harp. The vEolian harp is a long box or case of light wood, with harp or violin strings extended on its face. These are generally tuned in perfect unison with each other, or to the same pitch, as it is expressed except one serving as a bass, which is thicker than the others, and vibrates only half as fast; but when the harp is suspended among trees, or in any situation Avhere the fluc- tuating breeze may reach it, each string, according to the manner in Avhich it receives the blast, sounds either entire, or breaks into some of the simple divisions above described ; the result of which is the production of the most pleasing combination and succession of sounds that ear has ever listened to, or fancy perhaps conceived. After a pause this fairy harp may be heard beginning with a Ioav and solemn note, like the bass of distant music in the sky: the sound then SAvells as if approaching, and other tones break forth, mingling with the first, and Avith each other; in the combined and varying strain, sometimes one clear note predominates, and sometimes another, as if single musicians alternately led the band: and the concert often seems to approach and again to recede, until Avith the unequal breeze it dies away, and all is hushed again.—It is no Avonder that the ancients, Avho understood not the nature of air, nor consequently even of simple sound, should have deemed the music of the Mohan harp supernatural, and, in their Avarm imaginations, should have supposed that it Avas the strain of invisible beings from above, come doAvn in the stillness of evening or night to commune with men in a heavenly language of soul intelligible to both. But, even now that we under- stand it avoII, there are few persons so insensible to Avhat is delicate and beau- tiful in nature, as to listen to this wild music Avithout emotion; while the informed ear finds it additionally delightful, as affording an admirable illustra- tion of those laws of sound Avhich human ingenuity at last has traced. As the simple scale of sound, called a chord, Avhich nature thus gives by the spontaneous dividing of a single string, has considerable vacancies in it, human taste or feeling, long before there was any theory of music, had joined to it the notes of two additional strings, one sharper or more acute than it, 240 ACOUSTICS. and the other more grave ; of which additional notes, while part agreed, or were in unison with certain notes of the principal chord, the remainder just served to fill up its larger intervals, and to complete a scale of nearly uniform in- terval—as three ladders havingunequalintervalsbetweentheirsteps,mightstill, if placed together, complete a stair of easy ascent. The relation between these strings or chords is such, that the principal beats thrice for twice of the low chord, and the high chord beats thrice for twice of the principal:—and in the complete scale of notes, the principal is five notes above the lower and five notes below the higher. So truly natural is the scale thus formed, that it has arisen in all nations, however remote or unconnected : and an untutored indi- vidual, in attempting to raise his voice by regular steps, falls into it almost as readily as the learned professor. The scale has eight steps or notes between any tone, and the tone above it vibrating twice as fast, or the tone beloAV it vibrat- ing half as fast; these two tones or notes being hence called the octaves above and below the note with which they are compared, and the intermediate notes which fill up either octave from the fundamental note are distinguished by the names of second, third, fourth, &c, in ascending or descending. The numbers Avhich express the relations of beats among the notes of an octave are easily found, from our knoAving the relative number of beats in the notes of any one simple chord, and the relation as above described of the three chords forming the compound scale. The following table exhibits these num- bers or the arithmetical expression for the notes of an octave, as well as the corresponding lengths of a given string required to produce them, and the English designation of the notes by letters, and the continental designation by names, these names being the first syllables of certain verses sung by learners. Number of vibrations . 1 9 *5 5 4 4 T 3 2 5 X i j 7 2 Length of string . . 1 8 "5 4 7f 3 4 2 -J 3 1 8 i 2 English characters . . C D E F G A B c Continental names . . ut re mi fa sol la si ut The musical scale, however far extended, is a repetition of similar octaves, so that any note in it vibrates just twice as often as the corresponding note in the octave below, and half as often as that in the octave above. The loAvest note which is perceptible to the human ear has about thirty beats in a second, and the highest about thirty thousand ; and there is included between these two, a range of nearly ten octaves. To certain ears the extremes of this range are totally inaudible, as if their poAver did not reach so far. Some persons do not hear at all the sharp note of the grasshopper, while some are equally insensible to the lowest tones of an organ or piano; and yet to all the perception of intermediate sounds may be equally perfect. Few musical instruments comprehend more than six octaves, and the human voice in general has only from one to three, the female voice being in pitch an octave higher than the male. If the intervals in the musical scale were all equal, a performer might choose indifferently any note as a fundamental or key-note, and would only have to attend to the number of intervals above and below it; but, in fact, the relation of the three constituent chords is such that the third and seventh intervals, in ascending from a key-note, are only about half as large as the others. It is OAving to this circumstance that in changing the key on any instrument, certain notes belonging to other keys are half a note too low or MUSIC. 241 too high, that is, too flat or too sharp, and must be changed accordingly. And hence, when an instrument is to be used to play in all keys, its larger intervals must be divided into two parts. The fact of these unequal intervals, ill understood, is what gives an appearance of great complexity and difficulty to musical science. Melody, in music, is when notes, having the simple numerical relations of beat which we have been describing, are played in succession ; harmony is Avhen two or more such notes are sounded together. The effect of both is delightfully increased by what is called measure, A'iz., making the dura- tion of the notes or strain correspond with certain regular divisions of time. This gives to the ear a prescience, to a certain degree, of what is coming, Avith the pleasure of having expectation realized, as happens similarly from the metre and rhyme of poetry: it moreover enables the memory to retain musical combinations of sound—for the airs of the iEolian harp, which observe no time, cannot be learned or repeated. The music of a single drum is that of time only. Melody, harmony, time and varying intensity of sound, are the four con- stituents of music, and it seems that almost every state of mind has, in some combination of these, an appropriate expression, intelligible to the general feeling of the human race. The exact relation betAveen the movements of the animal spirits, as it has been expressed, or the fluctuating stream of feeling, and the varying flow of sound in a musical composition, is not clearly understood, but the fact of their correspondence and its consequences are most remarkable. Under many circumstances, the association between the feeling and expression is so strong, that the latter is often spontaneously be- traying itself;—Avitness the almost constant humming, or low song of some contented beings—the singing and Avhistling of careless childhood, or of the light-hearted rustic living among the beauties of nature—the heart-rousing strain of the hunter or warrior—and the tender expression of many of the modifications of anxiety and sorroAv. The musical sensibilities are by no means limited to the human race, for there is no expression more exquisite than in the song of the nightingale during the evenings of spring, or of the thrush and blackbird, in the same season, amid the quiet retreats of our Avoodlands,—the music of Avhich untutored songsters is made up of the same elements as our oAvn. The accompaniment of an air afforded to a singer by one or more instru- ments, and which is so pleasing, is chiefly the sounding, simultaneously, in a subdued manner, some other notes of the chords to which the several vocal notes belong. Duetts and more complicated concert-pieces have their origin from the same source: and highly cultivated musical sense can even folloAV and enjoy seAreral melodies played together. Musical notes, by Avhatever instrument produced, have to each other the same numerical relations in the beats or A-ibrations Avhich constitute them. The different qualities of tone, therefore, from different instruments, can only depend on the peculiarities of the single beat, as to Avhether they are sharp or soft, strong or Aveak, &c. Such is the extraordinary nicety of per- ception Avhich the human ear possesses in this respect, that it can not only distinguish different kinds of instruments, as a flute and clarionet, playing the same note, but different instruments of the same kind, even to the extent, for instance, of recognizing each one of a hundred voices singing the same air. One of the greatest charms of concert music is, that the voice and the different instruments may take up separately, part of the strain suited to their individual expression—the flute and clarionet, for instance, breathe soft- 242 ACOUSTICS. ness ; the trumpet and drum arouse ; the harp rolls forth its brilliant chords; the violin leads the floAving sound through rapid and endless variety; and so of the rest. That there might be correspondence in instruments when played together and a known pitch Avhen played apart, it ^became necessary to fix on some tune or number of vibrations as a point of comparison. Hence, tuning-forks have been made of steel, with length of prongs calculated to produce a certain note. This note is usually the fourth, A or la from the bass of the piano- forte, and vibrates about 430 times in the second;—and Avhen the note of the same name on any instrument is tuned in unison with this, the other notes can be easily adjusted according to the harmonic relations above explained. Almost every substance or contrivance that can produce a uniform con- tinued sound may enter into the composition of a musical instrument: hence the almost endless variety Avhich the world has seen. The chief classes of instruments are stringed instruments, wind instruments and bells or rods. Of the stringed instruments, we may mention the harp, the lyre or lute, the guitar, the viol of all sizes, and piano-forte. The harp, lyre and lute were the inventions of antiquity, and have brought down with them to the present times a thousand delightful associations. They awakened to inspi- ration the bards and poets of the young world, and they were the beloved companions of many of the noblest spirits of succeeding times. Their great charm appears to have been in their power to heighten the emotions produced by music's twin sister, poetry ; and the combined effects seem to have been miigical.—The other instruments mentioned are of comparatively modern invention, particularly the piano-forte ; and their perfection has assisted in carrying the combinations of musical sound to degrees of com- plexity and difficulty of Avhich antiquity dreamt not. It is a question, how- ever, whether the style of much of the music now in vogue does not prove rather a degeneracy, than a desirable refinement of musical taste. Music is a language of nature, intelligible at once to all susceptible minds, and, in a degree, even to inferior animals ; but modern art is attempting to make of it an artificial and conventional language, in which there may be fashion and change. The ornaments and accompaniments are noAV often so overwhelm- ing, that the melody, in Avhich the idea and sentiment really reside, is masked and almost lost; and an unpractised ear, particularly if listening to an organ, often discovers only an unmeaning succession of chords. And Avhen a singer, abandoning the natural simplicity of melody, strains to exe- cute with the voice the complicated movements which belong properly to instrumental accompaniments, the attempt destroys the poetry, by either ren- dering the Avords inaudible, or by sacrificing their natural expression to some supposed appropriate expression of the ornamental music. These considera- tions may account in part for the insensibility of so many highly-endowed per- sons to what is now called excellent music. Some of the tricks on the voice and on instruments, at present so common, are, to natural or graceful music, Avhat tumbling and rope-dancing are to natural or graceful gesture. And when AA-e hear noted professors avoAV their inability to sing a simple ballad, or to play an unadorned melody, must Ave not conclude that the natural sense of music has left them, as the relish for simple but the most invigorating fare has left the morbid epicure ? The guitar, as affording an accompaniment to vocal music, has many ad- vantages. It is not too loud, yet the strains are very distinct; it admits of most touching expression; it is very easily learned by any one who should attempt to learn music; it is portable and cheap. The great facility of ac- MUSIC. 243 companiment on it depends on thi«, that the player is able by one position of the hand to touch the strings so that the sounds of all the six shall belong to the same chord ;—three positions of the hand, therefore, for one key, pro- duce all the notes and chords which a simple accompaniment requires ; and the hand soon falls into these so readily, that the player is hardly sensible of exerting volition. Among wind instruments are the flute, the flageolet, the organ, the clario- net, the hautboy, the horn, the trumpet, &c. The pitch or tone of a tubular wind instrument, just as of a musical string, has relation to its length ; and the vibrations causing the sound seem to be Avaves or condensations of air passing from the mouth to the extremity of the tube ; being more frequent, therefore, as the tube is shorter:—when the bottom of the tube is closed, the Avave has to come back again, and thus renders the note twice as grave. It appears, also, that on blowing more strongly, the air in the tube divides into separate vibrating portions, as a string may divide to produce its har- monic sounds, and produces thus all the harmonic sounds belonging to the fundamental note of the tube. By blowing into a common German flute, for instance, it is possible to produce five ascending harmonies without mov- ing the fingers at all. The music of a trumpet is limited to these five notes of the same chord ; but in the flute, and other instruments Avith holes, the effective length of the tube is calculated from the upper end to the nearest hole left open ; and each length has its harmonic.—If a tuning-fork, Jew's harp, or any such sounding body, be held at the open end of a tube or other empty space of dimensions calculated to produce a frequency of undulation, in its contained air, according with the pulses of the sounding body, then the tube or space will immediately give out its own beautiful tone ; and if the space be enlarged or diminished in a double, triple, or any other simple pro- portion—as a tube may be, by a piston moved up, or doAvn in it—then >vill its note become the fifth, octave, twelfth, &c, above or below the original tone, although that tone continues unchanged. The tones of the JeAv's-harp are well knoAvn to depend altogether on the varying dimensions of the player's mouth : but to obtain perfect music from it, three harps at least, to be substi- tuted one for the other during the performance, are required to produce the notes of the three constituent chords of the common musical scale. In Avind- instruments Avith reeds, the tone depends on the stiffness, Aveight, length, &c, of the vibrating plate or tongue of the reed, as Avell as on the dimensions of the tube or space Avith Avhich it may be connected. This truth is Avell illus- trated in that instrument, the iEolina, already mentioned, Avhich, in improved and varied forms, promises to become common, and one of the most express- ive of wind instruments.—The sounds of the human voice are the sAveetest of all, and are produced by the vibrations of tAvo delicate membranes situated at the top of the windpipe, Avith a slit or opening, called the glottis, left be- tAveen them, for the passage of the air. The tones of the voice are grave or acute according to the varying tension of these membranes, and to the size of the opening.—In the organ there is a pipe for each note, and Avind is ad- mitted from the belloAvs to the pipes, by the action of keys, like the keys of a piano-forte. The organ may be played also very perfectly by a barrel, made to turn slowly under the keys, and to lift them in passing, by pins projecting from it at the required situations. Very complicated pieces of music are thus set on barrels, but at great cost of study and labour, and, therefore, of money; now a plain barrel, made to turn near the keys of an organ during perform- ance on it by the hands, might be made to record, Avith mathematical accuracy, every touch of the most finished player, by receiving marks of some kind 244 ACOUSTICS. from the keys as they AA*ere lifted: and to repeat, with absolute accuracy, there- fore, any performance, hoAvever delicate and exquisite, it would only be far- ther necessary to drive pins into the barrel where the marks remained, and afterwards to make these pins lift the keys. Bells are often conjoined in sets, having the musical relations, and to some persons their music is very agreeable. There are, in the tolling of a single bell, a loudness and solemnity rendering it a fit accompaniment of funeral rites. The Chinese gong partakes of the nature both of the bell and of a great drum, and has something in its sound which is singularly affecting. In its OAvn country it bears a part in one of the most imposing ceremonies which man has ever imagined. On certain festivals, as the sun is sinking in the west, the whole population of China, a host of more than a hundred millions, issues forth under the single canopy of heaven, to testify, amid the thunder of gongs and the continued discharge of fire-works, that adoration and grati- tude tOAvards the Deity Avhich human nature, in all ages and climes, has felt to be due, and has eagerly sought to express, however blind as to the sublime simplicity of religious truth. Bells or goblets of glass sound still more perfectly than those of metal, and by gentle friction on their edges with a bow or the Avetted finger, their tones may be continued for any length of time, and may be made to swell and diminish like the human voice or the Fig. 120. notes of a violin. A set of glasses, there- fore, attuned to each other, according to the harmonic scale, becomes, for certain species of music, the most perfect of all instruments. It is in fact an iEolian harp at command. Dr. Franklin, who first constructed a set, doubled the long line of glasses upon itself, and placed the half- notes as outside rows. The author of this Avork, hoAvever, during some experiments on sound, found the zig-zag arrangement here represented to possess certain advan- tages. The small open circles represent the mouths of the glasses standing in a, box a b c, and the relation of the glasses to the written musical notes is shoAvn by the common music lines and spaces Avhich connect them. The learner dis- covers immediately that one row of the glasses produces the notes written upon the lines, and the other row the notes Avritten between the lines: and he is mentally master of the instrument by simple inspection. This ar- rangement also renders the performance easy, for the notes most commonly sounded in succession are contiguous ; and the relations of the notes forming a tune are so obvious to the eye, that the theory of musical combination and accompaniment is learned at the same time. The set of glasses here repre- sented has two octaves, and with the additional flat seventh and fourteenth, seen at a and c, which, when required, maybe substituted for the correspond- ing glasses m the rows, it is capable of playing the greater part of our simple melodies. All the half-notes, if desired, may be placed in outside rows. Ihe player stands at the side of the box between a and b, and has the notes ascending towards the right hand, as in a piano-forte. MUSICAL EAR. 245 Musical ear. Philosophers have not yet been able to account for a remarkable difference among individuals, as regards their perception of the musical relations of sounds. Many persons, Avithout understanding any thing of acoustics, or having studied music as a science, can.lell instantly Avhether various notes heard together or in succession, have the mutual relations which we call musical—and Avhich we now knoAV to depend on the comparative numbers of beats in a given time: and they quickly recognize and learn to repeat tunes, and to sing a fit second or bass to the performance of another;—while there are persons, again, Avith an equally perfect sense of hearing, Avho can neither know if an air