PHYSICO-CHEMICAL 
METHODS 
BY 
DR. J. TRAUBE, 
PRIVATDOCENT IN THE TECHNICAL HICTT SCHOOL OF BERLIN 
AUTHORIZED TRANSLATION 
s 
BY 
WILLETT L. HARDIN, Ph.D., 
HARRISON SENIOR FELLOW IN CHEMISTRY, UNIVERSITY OF PENNSYLVANIA 
ICUtb ffilustrations 
PHILADELPHIA 
P. BLAKISTON’S SON & CO. 
1012 WALNUT STREET 
1898 Copyright, 1898, by P. Blakiston’s Son & Co. 
Press of Wm. F. Fell & Co., 
1220-24 Sansom St., 
PHILADELPHIA. PREFACE. 
In the preface to the German edition the author calls attention 
to the ever-widening application of physico-chemical methods in 
the various branches of chemistry. He says the vapor density, 
melting point, boiling point, and specific gravity are no longer the 
only constants the determination of which is necessary in organic 
chemistry. The electric conductivity, specific refraction, thermal 
constants, depression of the freezing point and vapor pressure, etc., 
are of fundamental importance in determining the constitution 
and molecular weight of substances, as well as in determining their 
identity and degree of purity. 
The theoretical significance of physico-chemical constants, and 
the fact that their application has been extended to almost every 
branch of chemistry, renders it desirable, if not necessary, for all 
students of the science to become more or less familiar with the 
methods of measurement. 
In this book the author has systematized the more important 
physico-chemical methods. The very complete descriptions of 
apparatus and the minute details in the methods of operation, as 
well as the large number of references given throughout the book, 
seem to warrant its translation. 
In the preparation of the English edition no additions have 
been made to the text. The few references which have been added 
are inclosed in brackets. 
The Translator. CONTENTS. 
I. THE CHEMICAL BALANCE, 9 
11. DENSITY (Specific Gravity), 13 
1. Density of Solids, 14 
(a) The Pyknoraeter, 14 
(£) The Crystal-float Method, 17 
2. Density of Liquids 19 
[a] The Pyknometer, 19 
The Mohr-Westphal Balance, 24 
(r) The Araometer, 27 
(1d) Determination of the Specific Gravity at Elevated Tempera- 
tures as well as the Molecular Volume of Liquids at Their 
Boiling Points, 28 
(if) Contraction and Dilation, 31 
3. Density of Gases (Vapor Density), 32 
(rt) Method of Dumas, 32 
(ib) Method of Gay-Lussac-A. W. Hofmann, 34 
(<;■) Method of V. Meyer (Air Displacement), 38 
[d) Method of Lunge and Neuberg, 41 
111. CAPILLARITY, 45 
1. The Rise in a Capillary Tube (The Capillarimeter), ... 45 
2. The Drop-method (The Stalagmometer), 49 
IV. THE CONSTANT OF VISCOSITY, 53 
1. Method of Poiseuille-Ostwald, 53 
V. SOLUBILITY, 56 
VI. THE ELECTRIC CONDUCTIVITY OF LIQUIDS, 58 
1. Method of F. Kohlrausch, 58 
2. Calibration of a Wire (Method of Strouhal and Barus), . 73 
v VI 
CONTENTS. 
VII. EXPANSION OF LIQUIDS, 75 
1. Determination of the Coefficients of Cubical Expan- 
sion of Glass and Liquids, 76 
VIII. MELTING POINT AND SOLIDIFYING POINT, 79 
IX. DEPRESSION OF THE FREEZING POINTS OF SOLU- 
TIONS, 81 
1. Method of Beckmann, 81 
2. Method of Raoult, 86 
X. BOILING POINT AND VAPOR PRESSURE, 90 
1. Ordinary Method for Determining the Boiling 
Point, 91 
2. Determination of the Boiling Points of Liquids in 
Small Quantities, 93 
(a) Method of Siwoloboff, 93 
3. Determination of the Boiling Point at Different 
Pressures, 95 
(/>) Method of Jones-Schleiermacher, 93 
XI. ELEVATION OF THE BOILING POINTS OF SOLUTIONS, 97 
1. Method I of Beckmann, 97 
2. Method II of Beckmann, 103 
XII. SPECIFIC PI EAT, 109 
1. The Method of Mixtures, no 
(a) Specific Heat of Solids, ill 
(1b) Specific Heat of Liquids (Methods of Kopp, Schiff, 
and Andrews), 117 
2. The Ice-calorimeter (Method of Bunsen), 121 
XIII. HEAT OF FUSION, 126 
XIV. HEAT OF VAPORIZATION 129 
Method of R. Schiff, 129 
XV. THERMOCHEMICAL CONSTANTS, 132 
1. Heat of Neutralization, 133 
2. Heat of Solution,. 137 
3. Heat of Dilution, 139 
4. Heat of Hydration, . . 140 
5. Heat of Combustion, 141 
The Calorimetric Bomb (Method of Berthelot), 141 CONTENTS. 
XVI. MEASUREMENT OF CRYSTALS, 153 
1. The Reflection Goniometer of Wollaston, .... 153 
2. The Microscope with Polarizing Attachments, . . 160 
(«) Measurement of Plane Angles, 163 
(.b) Testing for Double Refraction and Determination of 
the Directions of Vibration in Crystals, 164 
(c) Investigations in Convergent Light, 165 
XVII. INDEX OF REFRACTION, 168 
x. The Refractometer of Abbe, 168 
2. The Refractometer of Pulfrich, 172 
XVIII. SPECTRUM ANALYSIS, 182 
1. The Direct-vision Spectroscope, 182 
2. The Spectroscope of Bunsen, 183 
3. The Universal Spectroscope of KRtiss, . 189 
4. The Universal Spectroscope as Spectrophotometer 
(Method of Vierordt), 193 
XIX. ROTATION OF THE PLANE OF POLARIZATION, ... 201 
1. The Polariscope of Mitscherltch, 207 
2. The Polaristrobometer of Wild, 209 
3. The Half-shadow Apparatus of Laurent, 211 
4. The Half-shadow Apparatus of Lippich, 2x4 
XX. GENERAL CONTRIVANCES FOR MEASUREMENTS, . 215 
1. The Vernier (Circular Vernier), 215 
2. The Cathetometer, 216 
3. The Thermometer, 218 
XXI. TABLES, 226 
4. The Barometer, 224 ERRATA, 
Page 21, line 9, read 76 for 69. 
“ 28, “ 2, “ are for is. 
“ 49, “ 20, “ (p. 45) for (p. 39). 
“ 57, “ 39, omit comma after reaction. 
“ 153, “ 27, read (p. 215) for (p. 218). 
“ 160, “ 16, and foot-note, read (p. 201) for (p. 203). 
“ 174, “ 24, read 205 for 207. 
“ 178, “ 18, 226 for 229; line 19, read 232 for 235 
“ 194, lines IX and 35, read 233 for 229. I. THE CHEMICAL BALANCE. 
General Rules for Weighing.—The balance is placed so 
that it is protected from the direct rays of the sun and other 
sources of heat which would produce an inequality of temperature 
in the different parts. 
The balance is brought into a horizontal position by means of 
foot-screws on the bottom of the case. The horizontality is indi- 
cated by a spirit-level or a plumb-line. 
It must also be free from the influence of vibrations. 
The interior of the balance case is always kept dry by means of 
calcium chloride, etc. 
With constant load a good balance should always take the same 
position when allowed to come to rest. The extent of the swing 
for any load should diminish slowly. 
After the arrestment of the balance the pointer should remain 
at the middle division of the scale; in raising the arrestment the 
two supports of the beam should be removed at the same instant. 
In regard to the equality in the length of the two arms, see page 11. 
The weights should be placed on the balance only after the arrest- 
ment of the beam, and should in no case be touched with the fin- 
gers. Rapid swinging of the beam will cause error in the weighing. 
For accurate weighing, the balance case should be kept closed. 
Adjustment of the Balance.—The sensibility and hence 
the vibration period of the balance are regulated by means of a 
gravity-bob situated near the middle of the pointer. The adjust- 
ment is so made that the vibration period for a short-armed balance 
is from six to ten seconds, and from ten to fifteen seconds for a long- 
armed balance. 
The adjustment of the balance so that the pointer will swing 
equal distances on both sides of the middle division of the scale is 
made by means of movable weights attached to the ends of the THE CHEMICAL BALANCE. 
beam or, when these fail, the unsymmetrical weight at the middle 
of the beam is given such a position that the inequality in the 
weights of the two arms is counterbalanced. 
Determination of the Resting Point. Method of 
Weighing.—lt is not necessary nor desirable in weighing, that 
the weights be adjusted so that the pointer will swing equal dis- 
tances on both sides of the middle division of the scale; e.g., if 
10 is the middle division, the resting point may be 9 or 9.5. 
The resting point is calculated from several turning points of the 
pointer. The arithmetic mean of the turning points is taken for 
each side, and the mean of these two is taken as the resting point. 
The first and last observation used in the calculation must be made 
on the same side; therefore, an uneven number of swings are 
observed. The observation of 3 -f- 2 or 4 -)- 3 turning points is 
sufficient for accurate weighing; the resting point in this case is 
determined to the second decimal place. It frequently happens 
that the position of the resting point changes, especially after the 
weighing of heavy loads. 
Suppose the resting point to be 9.53 on the scale, then in the 
process of weighing it is unnecessary to adjust the weights so that 
the second resting point will be exactly at the same position. 
Assuming, when the weighing is made to one centigram, the 
weight = 10.28 gm., let the rider be placed at 5 mg., and suppose 
the resting point then to be 9.20. Let the rider be next placed at 
6 mg., and suppose the resting point to be 10.16. Then 1 mg. 
corresponds to 0.96 scale divisions, and hence 10.285 gm- are too 
light by an amount which corresponds to 9.53 9.20 = 0.33 
scale divisions, i.e., |-;|-| = 0.34 mg. The true weight therefore is 
equal to 10.28534 g. 
It is even unnecessary to make this double adjustment of the 
rider. Apart from the determination of the resting point, a single 
observation near the correct weight will suffice when the operator 
has once constructed a sensibility table. 
By the sensibility of a balance is meant the deviation in scale 
divisions produced by an increase of 1 mg. in the load. The 
amount of deviation is always more or less dependent on the load. 
For different loads the balance is adjusted with equal weights in 
each pan. A small excess of a mg. is then placed in the one pan. THE CHEMICAL BALANCE. 
The resting point is thereby removed n scale divisions, and the 
sensibility for the given load is —. When this value has been de- 
a 
termined for loads of 5:5 or 10 : 10 gm, and a curve constructed 
with the loads as abscissas and the corresponding sensibilities as 
ordinates, the operator can, with the help of this curve, easily make 
the necessary correction for any weighing which is approximately 
correct. 
Relative and Absolute Weighing.—The chemical balance 
is generally employed to determine relative and not absolute 
weights. This being the case, a slight inequality in the lengths of 
the arms can be neglected if the weights are always placed upon 
the same pan. 
On the other hand, if the absolute weight is to be determined, it 
is desirable to know the ratio of the lengths of the two arms. This 
is found by the method of double weighings. If p represents the 
weight of the load q placed upon the left pan of the balance, and 
px the weight of the same load placed upon the right pan, then the 
ratio of the lengths I and r of the left and right arms is found 
from the simple equation of the lever: 
ql=p r and pxl= qr; _A__ 
The weight of a load obtained by placing the weights on the right 
pan of the balance must be multiplied by the above ratio in order 
to obtain the absolute weight. 
The absolute weight can also be determined from a double 
r 
weighing without a knowledge of the ratio —. 
From the equations q I—pr and pxl=q r, we have q= Vp p1; 
or, simplified =\ (p p\ )*,—i. e., the true weight of the load qis 
the arithmetic mean of the weighings on the right and left pans of 
the balance. 
The tare method is also applicable. The load qis brought into 
equilibrium with a second set of weights, or another load, and then 
instead of q is placed enough weights to bring the balance again 
into equilibrium. 
* Kohlrausch, Prakt, Phys. VII, 35, 1892. THE CHEMICAL BALANCE. 
Reduction of Weighings to a Vacuum Standard.—When 
brass weights (density = 8.4) are used, this reduction is made ac- 
cording to the formula,— 
P=p + 0.0012 * J; * 
where P represents the weight of the substance in vacuo, p is the 
apparent weight obtained by weighing in air, and d is the density 
of the weighed substance. 
The error introduced by neglecting this reduction to a vacuum 
standard is greater, the greater the difference between the specific 
gravity of the weighed substance and that of the weights. Even 
for relative weighings in chemical analysis, where it is unnecessary 
to determine the absolute weight, this reduction is too often 
neglected. 
Calibration of a Set of Weights and Preparation of 
a Correction Table.—Let the larger weights of the set be desig- 
nated as 50', 20', 10', 10", s', 2', T, 1", T", and let the arms of 
the balance be of unequal length. 
In this case, by the method of double weighings of the weights 
against each other, suppose we have,— 
Left. Right. 
sc/ correspond to 20/ -)- 10/ . . . a mg. 
20/ -j- xo/ -(- 10// I) mg. correspond to sc/. 
Then according to page 11 : 
In the same manner we obtain 
sc/ = 20/ ic/ + 10" -f . . . \{a4* b) mg. 
20' ic/ 4- 10" 4- \ (c -f d); 
lo" = io/ -j- \ {e 4-/), etc., etc. 
Representing the corrections \(a 4- \(T (<? /), 
. . . by a, /9, y, . . . we have the following relations: 
sc/ = 20' -) io7 -f- io// 4- ... a 
20/ - io/ -t- 10// 4- . ./3 
10" io/ -j- ... y 
5' 4- 2/ 4- i/ 4- i" 4- x"' iq/ 
in which a, ft, y, and 8 can be positive or negative. 
* Kohlrausch, Prakt. Phys. VII, 36, 1892, and Landolt-Bornstein, p. 4, 1883, 
Tables. DENSITY. 
Comparing all the weights against the xo' gm. weight, we have,— 
sq/5q/ =5 X IQ/ +a+P+ 2 7 + J 
20/ =2 X 10/ +P + 7 
io// =i X xc/ -f 7 
ic/ ' = i X io/ 
5' +2; +i' + i// + i/7/ =i X >o' 4- (! 
■S = 50/ -)- 20/ + XC/ -)- XO'' -|- 5/ +27 -f- I/ + -)- I/// =IO X XC/ 
+ (« + 2/3 + 47 + 2 (5)- 
If the correction table is to be drawn up with reference to the 
standard gram, one of the weights must be compared with a standard 
weight. For most work in chemistry (analysis, specific gravity 
determinations, etc.) this is not necessary. 
In such cases the corrections for the single weights are assumed 
to be so small that the sum Sof the larger weights is correct; then 
5= 10 X io'-|- (a -(- 2 /? -f 4 y -j- 2 d) 100 gm. 
Let (o. —[— 2ft —4 y-: 2 4 then 
io/ =io g. a 
10" =. xo “ + y 
5/ + 2' -f- i/ -)- IO “ a -f 6 
20/ =2O “ 2(T4-/? -f y 
sq/5q/ =s° “ 5 +a+/? + 2 7 + 
In a similar manner the five weights s', 2', I', 1", and 1"' are 
compared with each other, and likewise the smaller weights. For 
the latter, however, a single weighing is sufficient, even though the 
balance-arms are of unequal length. If the balance-arms are 
equal, a single weighing is sufficient for any of the weights. 
11. DENSITY (Specific Gravity). 
General.—The density of a body is the mass of unit volume. 
For solid and liquid bodies the mass of 1 c.c. of water at 40 is con- 
sidered the unit of mass. The density, then, of a body may be 
defined as the ratio of its mass to the mass of an equal volume ot 
water at 40. DENSITY OF SOLIDS. 
The specific gravity of a body is the weight of unit volume. As 
the ratio of the weights of bodies in a vacuum is the same as the 
ratio of their masses, the numerical value of the density and specific 
gravity is the same. 
The densities of gases are usually spoken of as vapor densities. 
The vapor density of a gas is the ratio of the mass of unit volume 
of the gas to the mass of unit volume of a standard gas at the same 
temperature and pressure. Dry air is usually taken as the standard 
gas. 
By specific volume is meant the reciprocal of the specific 
gravity,—the volume of unit mass. 
The atomic and molecular volumes are the volumes which the 
weights corresponding to the atomic and molecular weights 
occupy. 
Let p represent a given weight of substance in grams, v the 
volume in cubic centimeters, d and s the density and specific 
gravity, <p the specific volume, a and m the atomic and molecular 
weights, va and vm the atomic and molecular volumes, then from 
the above definitions we have the following relations: 
7 p iv a , m 
d— s = ; <P=~y =—- ; va = a<p =—7 and vm = 
v d p d d 
i. DENSITY OF SOLIDS. 
(a) The Pyknometer. 
Principle and Calculation.—The pyknometers represented in 
figures i and 2 are usually employed. 
The pyknometer is weighed, filled (1) with air, (2) with water, 
and (3) with water plus the substance to be investigated. 
Let the weight of substance taken be represented by ps, the 
weight of the water required to fill the pyknometer at the tempera- 
ture tby pw [(pyknometer -|- water) (pyknometer air)], 
and the weight of the substance and water in pyknometer by pws 
[(pyknometer -f- water -f substance) (pyknometer -(- air)], then 
the uncorrected specific gravity 
Ps 
ps + piv pw S THE PYKNOMETEk. 
15 
Reducing this to a vacuum standard and to the temperature 40, the 
specific gravity .$• becomes 
s = ■{Q —X)+ 7i * 
Ps -f~ pw pws 
Q represents the specific gravity of water at the ordinary tem- 
perature t, j- and b = 0.0012, the average density of the air com- 
pared with water at 40. 
If the temperature at the time of weighing the water is different 
from that at the time of weighing the water plus the substance, a 
correction must be introduced for the expansion of the water and 
glass ; and the formula becomes 
,= A (0-») 
Ps -f* pw pws ~f~ pw [(? Qw ~h 3 P )1 
t and Q represent the temperature and specific gravity of water at 
the time of weighing the water plus the sub- 
stance, 4 and Qw represent the corresponding 
values at the time of weighing the water alone, 
and 3 /? is the coefficient of cubical expansion of 
glass = 0.000025 (for Jena glass = 0.0000237). 
For substances which are soluble in water other 
liquids are used,—alcohol, benzene, petroleum, 
turpentine, etc. In such cases the above expres- 
sion must be multiplied by the specific gravity of 
the liquid employed. 
Method of Operation.—The pyknometer 
(Fig. 1) consists of a glass vessel A and a 
ground-glass stopper b, through which passes 
a capillary tube. When the pyknometer is 
filled with the liquid, the cork is inserted in 
such a manner that no air-bubbles remain in 
the flask, and so that the liquid rises to the 
Fig. i. 
top of the capillary opening or to a definite mark on the cork 
A more complete pyknometer is represented in figure 2. The 
* Kohlrausch, Prakt. Phys. VII, 47, 1892. 
f Landolt-Bornstein, Tables, pp. 33-35, 1883. 
J Kohlrausch, Prakt. Phys. vn, 49, 1592 ; also Graham-Otto, in, 1. Abt., p. 371. DENSITY OF SOLIDS. 
thermometer inserted through the neck h of the vessel A is 
graduated to iO. When the vessel is filled with liquid the air- 
bubbles are completely removed and a portion of the liquid is re- 
moved from the small tube c by means of filter-paper, until the 
surface of the liquid just reaches 
the top of the mark m. The tube 
c is closed with a small stopper. 
The pyknometer is next dried by 
means of alcohol and ether, and 
weighed ; it is then filled with 
boiled water and reweighed, the 
temperature being noted at the 
same time. From these two weigh- 
ings the weight of the water pw is 
calculated. Finally, the substance 
is w-eighed, either in or outside of 
the pyknometer, and its weight 
represented by ps. The value pws 
is then determined by weighing 
the pyknometer containing the 
substance and water. The pykno- 
raeter can be previously brought 
to a constant temperature in a 
water-bath when the observations 
can not be made at the tempera- 
ture of the room. After inserting 
the stopper or thermometer the 
pyknometer is carefully dried by 
means of filter-paper and a piece 
of silk; heating must be avoided. 
If the substance whose specific 
gravity is to be determined is too 
light, it is made to sink in the 
Fig. 2. 
liquid by placing it in a vessel made of glass, metal, or wire net, 
which remains in the pyknometer during all the weighings. 
The pyknometric method gives far less accurate results for solids 
than for liquids. Greater errors can be introduced for pulverized 
substances by the absorption of air at the surface, and for crystals METHOD OF FLOATING CRYSTALS. 
17 
or minerals by the inclosure of air or the mother-liquor, or by other 
heterogeneities. 
Great care is therefore necessary in the selection of the sub- 
stance ; a previous microscopic examination is sometimes necessary. 
The adhering air can often be removed by shaking or frequently 
immersing the substance, or even wetting it with a brush. 
In the investigation of pulverized substances the pyknometer, 
when filled, is placed under an air-pump and exhausted so far that 
bubbles of air no longer rise in the liquid. It is still better to boil 
the liquid while under the air-pump. For this purpose use is made 
of a simple apparatus described by von Petersen (Zeitschr. 
physik. Chem. 8, 602, 1890). If the homogeneity of a crystal 
is uncertain, it is better to powder it for pyknometric obser- 
vations. 
The removal of the inclosed air or mother-liquor by heat is 
not to be recommended, as the density in such processes frequently 
undergoes a change. 
(6') The Method of Floating Crystals 
This method * in many cases is capable of greater accuracy 
than the pyknometric method, and a smaller quantity of substance 
is necessary for its execution. 
For reasons given on page 16, the pyknometric method, even for 
apparently homogeneous, well-formed crystals, is sometimes accom- 
panied by such errors that the determinations of the specific gravity 
show a variation of several units in the second and even in the 
first decimal place. 
A microscopic separation of the crystals would in most cases be 
a waste of time. 
On the other hand, homogeneous crystal fragments free from 
inclosures are easily obtained by the following method : 
A small, separatory funnel is half filled with a liquid of rather 
high specific gravity. For most crystallized substances methylene 
iodide (specific gravity = 3.3) is used. Suppose the specific gravity 
of the crystals under investigation to be less than 3.3, then the 
crystals which are placed in the separatory funnel will float on the 
*Retgers, Zeitschr. physik. Chem. 3, 289 and 298, 1889; 9, 328, 1883. 18 
DENSITY OF SOLIDS. 
liquid. A liquid of low specific gravity, as benzene, is allowed to 
drop into the first liquid until a point is reached where the specific 
gravity of the liquid is equal to or less than that of the crystals. 
The crystals then begin to sink into the liquid. Those crystals 
which inclose either none or the smallest quantity of mother-liquor 
and air will sink first. 
When the sunken crystals are examined under a microscope they 
are found to consist mostly of single, and often very small, crystal 
fragments, which prove to be so pure and homogeneous that they 
can be used in the investigation. 
The determination is carried out in the following manner, 
according to the principle already developed. 
The separatory funnel is again filled with methylene iodide and 
one of the purest crystal fragments placed upon the surface of the 
liquid. Benzene is added until the crystal just floats in the middle 
of the liquid. The specific gravity then, of the liquid mixture, 
is equal to that of the crystal. If a small pyknometer (Fig. 2) 
be placed under the separatory funnel and filled with the liquid 
mixture as quickly as possible to prevent any change in the con- 
centration, the specific gravity of this liquid is the same as that of 
the crystallized substance. 
As it is difficult to adjust the conditions so that the crystal will 
float exactly in the middle of the liquid, it is better to conduct the 
experiment so that (1) the crystal slowly sinks, (2) slowly rises, 
and (3) approximately floats. The three values thus obtained for 
the specific gravity must agree within one unit in the third decimal 
place. Heating should be avoided in drying the pyknometer, as a 
difference of i° in temperature changes the specific gravity of 
methylene iodide about 0.002. The observation temperature should 
always be noted. 
If the substance under investigation is heavier than methylene 
iodide, it is made to float by attaching to it a glass or platinum 
shell. * 
The method, however, in such cases is not to be recommended. 
The rather costly methylene iodide (100 gm. = $2.50) is separated 
from the benzene by simple evaporation or fractionation ; the 
* Retgers, Zeitsclir. physik. Chem. 4, 189, 1889. DENSITY OF LIQUIDS. 
crystals are freed from methylene iodide by washing with benzene 
until the red color disappears. 
Potassium sulphate or sodium chloride, the specific gravities of 
which were shown by Retgers to be 2.666 (at 20°) and 2.167 (at 
170), are well adapted to this or the pyknometric method. 
It is sufficient to carry the determinations of the specific gravities 
of solids to the third or at most to the fourth decimal place; the 
fourth decimal is always unreliable. 
The floating method is also applicable for the investigation of 
minerals. For this purpose, as well as for insoluble artificial crys- 
tals, use is made of Thoulet’s solution,—i. e., an aqueous solution of 
potassium mercuric iodide,—in which the mineral fragments are 
made to float by diluting the solution with water, stirring well at the 
same time (Goldschmidt, Neues Jahrb. fur Mineral., Beil. Bd. 
1, p. 179 ; also Rosenbusch, Mikrosk. Physiogr. der Mineralien, 
sec. 231, 1892, and Retgers, Zeitschr. physik. Chem. 4, p. 189, 
1889). 
For other methods of determining the specific gravity of solids, 
see the application of the hydrostatic balance (Retgers, Zeitschr. 
physik. Chem. 3, p. 301, 1889). The volumenometer is appli- 
cable, especially for powdered substances. (Wiedemann and 
Ebert, Phys. Prakt., p. 79, 1890, and Kohlrausch, Prakt. 
Phys. vu, p. 50, 1892. Tables of the Specific Gravities of Solids, 
Landolt-Bornstein, Physik. Chem., p. 78, 1883.) 
2. DENSITY OF LIQUIDS.* 
(a) The Pyknometer. 
Principle and Calculation.—A suitable glass vessel is 
weighed, filled (1) with air, (2) with water, (3) with the liquid 
under investigation. 
The apparent weight of the liquid in air is represented byps = 
[(pyknometer -f- liquid) (pyknometer -f- air)]. The weight of 
an equal volume of water by pw = [(pyknometer -)- water) 
* [Kohlrausch and Hallwachs have recently introduced a very accurate method 
for determining the density of solutions, Wied. Ann. 53, p. 14, 1894. hr.] 20 
DENSITY OF LIQUIDS. 
p 
(pyknometer -f- air)]. The uncorrected specific gravity then is —. 
A 
Reduced to water at 40 and to a vacuum standard this becomes 
S = %(Q~X) +X* 
where Q = the density of water at the observation temperature 
t and I 0.0012 = the average density of the air compared with 
water. As Qis usually very slightly less than unity, it is often 
Fig. 3. 
Fig. 4. 
convenient to substitute Q 1 d in the formula, whence we 
have; 
pw Pm 
If the specific gravity of the liquid is determined at a tempera- 
ture different from that at which the water content is determined, 
the specific gravity is then calculated from the formula : 
s C 1 +3 P (/w /)] (Q /I) -j- /I; 
* Kohlrausch, Prakt. Phys. vn, p. 47, 1892. THE PYKNOMETE&. 
2 1 
4 and / represent the temperatures of the water and the liquid at 
the time of weighing. 3/5= 0.000025 = coefficient of the cubical 
expansion of glass. 
If the specific gravity determination is to be made as accurately 
as possible to the fifth decimal place, then A is placed equal to 
0.00119, and the coefficient of expansion of glass is determined 
Fig. 5. 
according to page 69, also the formulae of Winkelmann, Graham- 
Otto, 3. Aufl., 1. Abt., page 371. 
Method of Operation.—Leaving out viscous liquids, for 
which a pyknometer of the form represented in figure 2, page 16, 
with a wider tube is used,* more accurate determinations are made 
* Such a pyknometer is described by Briihl and Scheibler, Ber. d. d. chem. 
Ges. 24, pp. 182 and 357,1891. 22 
DENSITY OF LIQUIDS. 
by using a Sprengel pyknometer, the most common forms of which 
are represented in figure 3 and figure 5. 
In figure 3 is represented a U-shaped glass tube, which termi- 
nates at the top in two small horizontal tubes. A platinum wire is 
arranged in the middle for hanging the vessel to the balance. 
Tube ais smaller than tube b;at m on the tube bis a mark. Both 
tubes in this as well as in figure 5 can be closed with small glass 
caps, thereby preventing evaporation during the weighing. The 
pyknometer (Fig. 5) differs essentially only in that through the 
top of the tube is fused a thermometer graduated to 4° or -4g-°, which 
must be carefully adjusted. Figure 4 represents a pyknometer * 
which possesses certain advan- 
tages for determining the specific 
gravity of highly volatile or ex- 
pansible liquids, and also for in- 
vestigations made at tempera- 
tures lower than that of the 
room. 
The wider capillary tube b is 
provided with a globular en- 
largement c, the capacity of 
which is so large that it will 
suffice even for highly expan- 
sible liquids. 
Fig. 6. 
The tubes are closed by means 
of rubber or glass caps. 
The pyknometer is usually of from sto 20 c.c. capacity. When 
there is sufficient liquid for the investigation, the capacity is chosen 
with reference to the greatest accuracy of results. 
The pyknometer is dried by means of alcohol and anhydrous 
ether. The filling is accomplished either by means of the mouth 
or a caoutchouc pipette as represented in figure 6, where the 
smaller tube a is connected to a glass globe g by means of a small 
cork, or finally with the help of a knee-tube (Fig. 5) which is 
slipped onto the larger tube b and immersed in the liquid. The 
* Perkin, Jour, prakt. Chem., N. F. 31, p. 486, 1885. THE PYKNOMETER. 
23 
filling must proceed in such a manner that all the air-bubbles are 
removed from the apparatus. 
When completely filled, the pyknometer is placed or hung in a 
water-bath (or thermostat), so that only the upper tubes are free 
from the water, and indeed for the pyknometer figure 4, so that 
the wider tube b is in a vertical position. 
If the specific gravity determination is to be made accurately to 
the fourth decimal place, the temperature of the water-bath must be 
kept constant to within 0.20. For that reason a large water-bath 
is used, and to it is fastened a thermometer graduated to when 
necessary, very near the pyknometer. For a complete equalizing 
of temperature, eight to ten minutes are necessary. 
The quantity of liquid in the pyknometer, while in the water-bath, 
is so regulated that the smaller tube a is completely filled, and the 
tube b filled to the mark m. If the tube b contains too much liquid 
a small piece of filter-paper is brought to the end of the smaller 
tube a, and by carefully manipulating the same, the quantity of 
liquid can be adjusted so that it fills the tube b exactly to the mark 
in. If the quantity of liquid in the tube is too small, or if the filter- 
paper has removed too much liquid, then a glass rod with a drop 
of the liquid on the lower end is brought to the filled tube a. The 
amount of liquid in b increases immediately. When the quantity 
of liquid is properly adjusted the tubes a and b are carefully wiped 
with filter-paper and a piece of silk, to remove the liquid on the out- 
side. The small glass caps are next placed on the tubes a and b, and 
the apparatus, after removing from the water-bath, is carefully dried, 
heating from the hand being carefully avoided. In no case should the 
liquid, from expansion by heat, be allowed to enter the small caps. 
With the pyknometer figure 4 the liquid, after being adjusted to 
the mark in, is allowed to run back in a until the liquid in b stands 
at the mark mv 
The water and other liquids, before the operation, are as far as 
possible freed from the dissolved air by boiling; the water used in 
preparing solutions must also be boiled, preferably after the prep- 
aration of the solution. 
The determination of specific gravities at higher temperatures 
can be made according to the method of Ramsay-L. Meyer, page 
28, or according to the method of Schiff. 24 
DENSITY OF LIQUIDS. 
The relation of the density of solutions to the percentage content 
see, among others, Gerlach, Specific Gravities of Salt Solutions, Frei- 
berg, 1859, and Bremer, Zeitschr. phys. Chem. 3, page 425, 1889. 
Tables of Specific Gravities of Liquids, Landolt-Bornstein, Phys. 
Chem. page 88 ; of salt solutions, Gerlach, Fresenius, Zeitschr. anal. 
Chem. 8, page 279, 1869 ; 27, page 271, 1888, and 28, page 466, 
1889. 
(3) The Mohr-Westphal Balance. 
It frequently happens that one wishes to make an approximate 
specific gravity determination quicker than is possible by the time- 
consuming pyknometric method. In this case use is made of either 
a Mohr-Westphal balance or of the araometric method, page 27. 
The Mohr-Westphal balance (Fig. 7) is supplied with a screw P 
for lengthening and shortening the stand, and a balance-beam which 
rests on the sharp edge at H. On one end of the beam is hung a 
glass float with a thermometer, while on the other end is a weight 
K which is really an enlargement of the beam. By proper adjust- 
ment of the foot-screw .S' of the stand, the weight K can be made to 
just balance the glass float in the air. The proper adjustment is 
shown when the two points J and K are exactly opposite each other. 
Sometimes a vertical scale is placed at J and the point K brought 
to the middle division. 
The balance-beam between the point where the thermometer is 
suspended and the point of support is divided into ten equal parts. 
The balance is provided with three and often four riders, Ax A, 
B and C, the weights of which stand in the ratio 1:10: 100. 
If, after the balance has been carefully adjusted in the air, the 
glass float be sunk into water and then into some other liquid, it is 
evident that equal volumes of the water and liquid will be displaced, 
and the equilibrium of the balance will be disturbed. To restore 
this equilibrium, sufficient weight must be placed on the beam in 
each case to exactly counterbalance the weight of the displaced 
liquid. The ratio of the weight of the liquid to that of the water 
represents roughly the specific gravity of the liquid. 
The weights Al = A are of such magnitude that when one is 
hung on the end of the beam, its weight exactly counterbalances 
the weight of the water at 150, displaced by the glass float; hence 
when the balance is adjusted in the air and the glass body placed THE MOHR-WESTPHAL BALANCE. 
25 
in water at 15°, and the rider Ax hung on the end of the 
beam, the balance is again brought into equilibrium with the 
points exactly opposite each other. The weight therefore is rep- 
resented as A 1 = A = 1; likewise the weights of B and C hung 
at the same point on the beam would be o. 1 and 0.01, and accord- 
Fig. 7. 
ing to the known laws of the lever, each of these weights in the 
divisions 9, 8, 7. . . . of the beam would be .9, .8, .7. . . . of the 
original weight. If therefore, the glass float, after being adjusted 
in the air and water, is sunk into the liquid to be investigated, it is 
only necessary for obtaining the specific gravity to determine what 
positions of the riders produce equilibrium in the balance, dhe 26 
DENSITY OF LIQUIDS. 
position of A gives the first, JB the second, and C the third decimal 
place in the specific gravity. Ax is used only when the specific 
gravity of the liquid is greater than unity. As an example, the 
positions of the riders in figure 8 and figure 9 represent the specific 
gravities 0.747 and 1.846 respectively. 
With the better class of instruments determinations can be made 
to within about two units in the fourth decimal place. This degree 
of accuracy, however, requires a careful construction of the balance. 
Fig. 8. 
The distance between the divisions on the beam must be larger and 
the weights must stand exactly in the ratio given. The adjustment 
in air and water must never be omitted. If the adjustment for water 
is not perfect when Ax is hung at the tenth division of the beam, 
the final adjustment must be made with the help of the other weights. 
If the weight is 0.992 instead of 1, then all the readings of the 
balance are incorrect and must be divided by 0.992. The sensi- 
Fig. 9. 
bility of the balance is sometimes lowered by the collection of rust 
and dirt on the knife edge on which the beam rests. This can be 
detected by readjusting the points of the balance after moving the 
beam with the hand ; the position of the points should be the 
same when the balance comes to rest.* 
* According to an article published by Kohlrausch and Hallwachs (Nachrich- 
ten Ges. Wiss., Gottingen, p. 350, 1893) the method of hydrostatic weighing is 
capable of great accuracy, being possible to determine the specific gravity to the 
sixth decimal place. THE ARAOMETER. 
27 
(c) The Araometer. 
The araometer consists of a glass stem weighted usually with 
mercury; the more accurate instruments are provided with a ther- 
mometer. The instrument is placed in the liquid to be examined, 
into which it sinks to a definite mark on the stem. 
The same instrument will stand at different positions in different 
liquids depending upon their specific gravities. 
The araometer is sunk into liquids of known specific gravities ; 
the stem is marked in each case at the surface of the liquid and 
provided with an empyrical scale which represents the specific 
gravities. The instrument can then be used for liquids of unknown 
densities. When the determination is to be made with greater accu- 
racy the temperature is taken into account, and the reading should 
be made so as to exclude any error due to parallax. 
Sometimes the apparatus is used to determine the percentage 
content of certain solutions or mixtures, and is then called alcohol- 
ometer, saccharimeter, etc. The scale gives directly in these cases 
the percentage of alcohol, sugar, etc. 
The araometric method, with good instruments, is capable of 
an accuracy which is but slightly inferior to the pyknometric 
method. 
It has recently been shown that the heretofore neglected influ- 
ence of the surface tension, which is different for different liquids, 
at the place where the stem comes in contact with the surface of 
the liquid, produces an error of from two to four units in the 
third decimal place. The same araometer then is not applicable, 
as was previously supposed, for liquids of different surface tension, 
but only for a single liquid, or by using a correction table for a 
group of liquids with nearly equal surface tensions. Such araom- 
eters for definite liquids are constructed by the physico-technical 
Reichsanstalt, and are supplied with the necessary tables. These 
are at present in the market, and are capable of an accuracy of one 
unit in the fifth decimal place in the specific gravity.* 
* Fock, Zeitscbr. physik. Chem. 2, p. 296, 1888, and Weinstein, ibid. 7, p. 79> 
1891. 28 
DENSITY OF LIQUIDS. 
(ff) Determination of the Specific Gravity at Higher Tem- 
peratures AS WELL AS THE MOLECULAR VOLUME OF 
Liquids at Their Boiling Points. 
METHOD OF RAMSAY-LOTHAR MEYER.* 
Principle and Calculation.—The specific gravity and molec- 
ular volume of a liquid at the boiling point is determined by this 
method, in which a pyknometer (Fig. 10) is filled with the liquid 
and heated to the boiling point in the vapor of the 
same liquid in a boiling-vessel. 
As the volume of the pyknometer changes with the 
temperature, the coefficient of the cubical expansion 
of glass must be known. If the pyknometer is made 
of Jena standard glass (No. 14), then, according to 
Weidmann,f 3/? 0.0000237. The value of 3/9 can 
be determined in the manner described on page 75. 
The pyknometer is next weighed filled with air and 
Fig. 10. 
then with distilled water at two temperatures, t and 
tv rather far apart, about the temperature of the room 
and the boiling point of water; then from page 14 we have : 
-vt and vtx —l- 
where v, p, and .y represent the volume, weight, and specific 
gravity of water at the temperatures given ; 
therefore ; 
pt 1 _pt 
Pt\ Pt 1 r) Sti 
For the specific gravity of water at different temperatures see 
Landolt-Bornstein’s Tables, pp. 34-36, 1883. 
If 3 /? is known, the volume for any given boiling point $ be- 
tween t and tx is : 
v$ vt -f 3 p (1? —t) + 3 p (1? t), 
* Neubeck, Zeitschr. physik. Chem. I, p, 651, 1887, and Feitler, ibid. 4, 
p. 66, 1889. 
jWeidmann, Inaug. Dissert., Jena, 1886. MOLECULAR VOLUME OF LIQUIDS. 
29 
pt is the weight and st the specific gravity of the water in the 
pyknometer at t°. By making a larger number of determinations 
the corresponding volumes for temperatures between t and tx can 
be calculated according to the above formula. 
If ft- represents the boiling point of the substance to be investi- 
gated, then the specific gravity at that temperature is s$ = £fL 
where p& is the weight of the liquid at the boiling point [(pyk. -j- 
Hq.) —(pyk. + air)], and is the volume of pyknometer at 
the temperature ft. Then the molecular volume vm = --, where m 
represents the molecular weight of the substance. The reduction 
of the weighings to a vacuum standard can here be omitted. For 
molecular weights see table at end of this volume. 
Apparatus and Method of Operation.—The pyknometer 
(Fig. 10) of about 2.5 c.c. capacity consists of thin glass (Jena 
standard glass, No. 14). 
The wider, closed cylindrical part is united with a somewhat 
longer, rather narrow capillary tube with a turned-up point. 
The filling of this pyknometer with a liquid can be accomplished 
with the help of the apparatus shown in figure 11. 
A wide tube closed with a rubber stopper is connected through 
a side tube with an exhaust pump and the outer air by means of 
two stop-cocks. The air, before entering from the outside, must 
pass through a calcium chloride tube. 
The bottom of the tube is filled with the liquid, into which the 
pyknometer is sunk by means of a wire which passes air-tight 
through the rubber stopper. The pyknometer is lowered into the 
vessel until the point of the capillary tube is immersed in the 
liquid. By repeated opening and closing of the pump and letting 
in air, it is an easy matter to fill the pyknometer with liquid, with 
the exception of a small air-bubble which, upon subsequent heat- 
ing, disappears. Simultaneous heating of the liquid and apparatus 
hastens the filling. 
The subsequent emptying of the pyknometer is accomplished in 
the same apparatus. The pyknometer is hung with the point up- 
ward, and the two stop-cocks alternately opened and closed. It 
is then dried by means of alcohol and anhydrous ether. DENSITY OF LIQUIDS. 
The almost filled vessel is hung in the boiling-flask* represented 
in figure 12, by means of a nickel wire y which passes air-tight 
through the cork k. 
The rather wide boiling-flask, in which the liquid in the 
pyknometer is allowed to boil, is connected with a reflux con- 
denser, which in turn can be connected with a Stadel-Hahn 
or some other form of pressure regulator. With this arrangement 
the liquid can be made to boil under in- 
creased or diminished pressure. The 
method permits then of a determination 
of the specific gravity and molecular 
volume at different pressures and tem- 
peratures. By means of the regulators 
mentioned, the pressure can be measured 
accurately to within about 2 mm. 
Fig. 11. 
Fig. 12. 
The thermometer a fastened in the cork must be tested and ad 
justed as described under Section xx. 
For liquids which cause bumping, it is advantageous to have a 
capillary tube /? passing through the stopper to the bottom of the 
flask, through which a current of air or carbon dioxide is passed. 
* Of course, the filling and emptying of the pyknometer can also be accomplished 
in this flask ; however, it is less convenient. CONTRACTION AND DILATION. 
31 
The pyknometer filled completely, with the exception of a small 
air-bubble, is hung in the flask so that the point of the capillary 
tube remains in the vapor. The desired pressure is then obtained 
and the liquid in the boiling-flask brought to boiling. The liquid 
in the pyknometer expands and drops out of the capillary tube, 
taking with it the last trace of air, until it has assumed the constant 
temperature equal to that of the boiling point of the liquid. 
The boiling is then stopped. The liquid in the pyknometer 
cools and draws back through the capillary tube, with the excep- 
tion of a small drop which hangs on the end of the tube; the 
vessel is then dried and weighed. 
If the substance becomes stiff on cooling, the pyknometer may 
break. This danger can be avoided by repeatedly melting the 
outer layer, thereby distributing the mass uniformly, or by weighing 
before the complete stiffening of the substance. Substances for in- 
vestigation, see Neubeck, Zeitschr. physik. Chem. 1, p. 651, 18187. 
A second method which is to be recommended for determining 
molecular volumes is that of R. Schiff (see p. 76). 
Literature on Molecular Volumes.—Ostwald, Allgemeine Chemie, 2. Aufl., 
Bd. I, pp. 357 and 838; R. Schiff, Lieb. Ann. 220, pp. 71 and 278, also Ber. d. d. 
chem. Ges. 14, p. 2761, 1881; Ramsay, Jour. Chem. Soc. 35, p. 463, 1879; 
Thorpe, ibid. 37, pp. 141 and 327, 1880; Lessen and his students, Lieb. Ann. 
214, p. 81 ; 221, p. 61 ; 224, p. 56; 225, p 109; Gartenmeister, Inaug. Dissert., 
Konigsberg, 1885, and Lieb. Ann. 233, p. 249; Stadel, Ber. d. d. chem. Ges. 
15, p. 2559, 1882; Elsasser, Lieb. Ann. 218, p. 302, 1883; Vollmar, Ber. d. d. 
chem. Ges. 15, p. 2560,1882 ; Horstmann, ibid, ig, p. 1579, 1886, and 20, p. 766, 
1887 ; Bartoli, Ann. chim. phys. (6), ser. VII, p. 394,1886 ; Kopp, Memoires sur les 
vol. mol. des liquides (Winter, Heidelberg, 1886), and Lieb. Ann., 250, p. 1, 
1889; Neubeck, Zeitschr. physik. Chem. 3, p. 649, 1889; Feitler, ibid. 4, p. 66, 
1889; Lessen, 243, p. 64, and 254, p. 42, 1889; Gro.vhans, Kosmos, 1891, Ref. 
Zeitschr. physik. Chem. 8, p. 431, 1891. 
[See also the recent investigations of J. Traube, Zeit. f. anorg. Chem. 3, 
p. 11, 1893, and 8, p. 12, 1895; Ber. d. d. chem. Ges. 28, p. 2924, 1895; 
28, p. 3296, 1896; 30, p. 273; and 33, p. 130, 1898; Wied. Ann. 61, pp. 380 
and 395, 1897.—Tr.] 
(<?) Contraction and Dilation. 
By the contraction or dilation, produced in the mixing of liquids 
or the solutions of solids in liquids, is meant the change of volume 
per unit volume of the original substances. 32 
DENSITY OF GASES. 
If, for example, two liquids of volumes vx and v 2 are mixed and 
the volume of the mixture is v 3, then the volume change per unit 
volume is: 
_ v\ + v-i ya 
+ 
A contraction has taken place when c is positive, and a dilation 
when cis negative. From page 14 we have v% —, where p3 and s% 
h 
represent the weight and specific gravity of the mixture. p3 is equal 
topx p2, the weights of the original liquids, and these in turn 
are equal to vx sx -j- z>2 V We have then the equation : 
c _ K + V,) S3 {vx Jt +vt S2) _ 
K + w2j J« 
For the determination of contraction or dilation according to this 
equation, it is only necessary to note the volumes vx and v 2 of the 
original liquids, and to determine, by known methods, their specific 
gravities sx and 2, as well as the specific gravity ss of the mixture. 
For solutions of solids the same formula holds good. On con- 
traction of solutions, see Ostwald, Allgem. Chem., 2. Aufl.,Bd. i, 
p. 782 et seq., 1891. 
3. THE DENSITY OF GASES (Vapor Density). 
(.a) Method of Dumas. 
Principle.—The weight of a given volume of a gas is determined, 
and then, according to the known laws of Boyle and Gay-Lussac, 
the vapor density is calculated, i. e., the weight of unit volume of 
the gas compared with dry atmospheric air at the same temperature 
and pressure. 
Apparatus and Method of Operation.—A thin-walled glass 
balloon of about xoo to 300 c.c. capacity, with a side tube (Fig. 
13) is, after drying, drawn out at a into a smaller tube of about 
1 mm. in diameter. Let the weight of the dry balloon be repre- 
sented by p. While gently warming the balloon several grams of 
the liquid to be investigated are allowed to enter. The balloon is 
placed in a water-, oil- or paraffin-bath up to the narrowed part a. METHOD OF DUMAS. 
33 
The temperature of the bath is regulated so as to be at least io° 
above the boiling point of the liquid at the end of the experiment. 
When the liquid in the balloon has been completely changed to 
vapor, there being enough of the substance present to expel all the 
air, the balloon is melted off at a by means of a blow-pipe flame, 
after which the barometric pressure b and the temperature t of the 
water-bath are observed. After cooling, the balloon, together with 
the melted-off glass tube, is weighed. Let this weight be repre- 
sented by ps; let the barometric pressure and the temperature at the 
time of weighing be bx and tx. To test for the presence of air in 
the balloon, the point is then broken off under recently boiled water 
which is free from air. The balloon is filled completely with water 
only in cases where the previous removal of air had been complete. 
If the filling with water is complete, the balloon together with 
the water and the melted-off glass tube is placed upon a balance 
and weighed to within one centi- 
gram. Let the weight be pw and 
the temperature of the water again 
be tx. 
the empty balloon can be taken 
Calculation.—The weight of 
equal to p, since the quantity of 
Kig. 13. 
air displaced by the thin-walled balloon is nearly the same as that 
present in the balloon at the time of weighing. 
pw—p can be taken as the weight of the water at t°, since the 
weight of the air displaced by the balloon in comparison with the 
weight of the water can be neglected. If Qis the specific gravity 
of water at /x°,* then the volume of the balloon is : 
_ pw —P 
1 Q ' 
The volume vt at the temperature of the water-bath may be calcu- 
lated from vtx by the formula vt =tx -)- 3/? (t— tx), where 3/5 is 
the coefficient of cubical expansion of glass, and can be taken as 
o, 000025. 
The weight g of the vapor contained in the balloon is found from 
* Landolt-Bsrnstein’s Tables, pp. 33 and 34, 1883. 34 
DENSITY OF GASES 
the expression g = ps—/ +/, where /is the weight of the air 
displaced by the balloon. 
At the ordinary pressure temperature tx we have : 
I K 0-001293 
76 (1 + a/) 
where vtx is the volume of the balloon at t°, 0.001293 is the weight 
of 1 c.c. of air at o° and 76 cm. pressure, and a the coefficient 
of expansion of gases = 0.00366. 
The vapor density d is then given by the formula 
d = K. 76 (1 +« 0 
Wt £ 0.001293 
and the molecular weight m is equal to 28.9 d. 
It frequently happens in the vaporization of the substance that 
the air is not completely removed from the balloon, as can easily 
be seen from the subsequent filling of the vessel with water. If 
the error introduced in this manner is to be neglected, fill the 
balloon completely and calculate according to the above for- 
mula. Otherwise the balloon is sunk into the water after break- 
ing off the point, until the inner and outer surfaces of the water 
stand at the same level. The balloon with this quantity of water 
is weighed and the weight represented by pwl; it is then filled com- 
pletely with water and again weighed; this weight =pw. The 
calculation of the exact vapor density, taking into account all 
sources of error, follows from the equation : 
{ps /) —y + pml pa 
d= —— 
b I 4- 0.00367/. 
jt 11+313 {‘-'M -{p- 
)! represents the density of the air at the temperature and pres- 
sure by. * 
(£) Method of Gay-Lussac-A. W. Hofmann. 
Principle.—A quantity of substance weighed off in a small 
glass vessel is introduced into a barometer tube, the lower end of 
* Kohlrausch, Prakt. Phys. vn, 55 ; ibid. Table, p. 406, 1892. METHOD OF GAY-LUSSAC-A. W. HOFMANN. 
35 
which is immersed in mercury. This tube is surrounded by a 
glass jacket, which is heated to constant temperature by means of 
boiling vapors. Taking into account the pressure and temperature, 
the volume occupied by the vaporized substance is read off, and 
from this volume for a given weight of substance the vapor density 
is calculated. 
Apparatus.—An accurately calibrated * wide barometer tube, 
A (Fig. 14), of about 76 cm. in 
length, is set upright in a mercury 
trough' and fastened below in a wider 
glass jacket B by means of a cork. 
The jacket is heated by means of 
the vapors of boiling liquids (water, 
anilin, etc.), which are conducted in 
through the tube « and out through 
the tube b, and finally condensed in a 
coiled tube cooled with water. 
The arrangement for reading off the 
volume of gas consists of a metallic, 
upright bar C. This is provided with 
a nut in which are fastened, in vertical 
positions, two metallic bars, one of 
which is graduated in millimeters; 
these can be raised or lowered by 
means of the screw c. The second 
bar ends in a point which forms the 
zero of the scale, and is lowered 
toward the surface of the mercury in 
the trough w until the point seems to 
Fig. 14. 
touch its image formed by the reflection of the mercury, without 
actually coming in contact with the surface of the mercury. The 
height of the mercury in the barometer tube is determined by means 
of cross-wires in two vertical metallic rings, the height of which is 
so adjusted by means of the screw d that the two horizontal cross- 
wires and the top of the mercury are brought into the same plane. 
*For method of calibration, see Wiedemann and Ebert, Phys. Prakt. 1, p. 99, 
1890. 36 
DENSITY OF GASES. 
The height of the mercury in the barometer tube is given directly 
by the distance from the metallic point of the scale to the point 
where the screw d is situated on the same scale. 
The substance is weighed in a small glass-stoppered flask 
(Fig. 15) which is placed on the balance in the small metallic or 
glass vessel represented in the figure. 
Method of Operation.—The barometer tube A, cleaned and 
dried by means of alcohol, is filled with dry mercury free from air- 
bubbles. The air-bubbles clinging to the sides of the tube are 
removed by allowing the mercury to flow in and out several' times. 
The tube, completely filled with mercury, is closed by means of the 
finger, inverted and placed upright in the mercury trough, so that 
a perfect vacuum is formed in the upper part of the tube. It is 
then fastened in the glass jacket by means of a cork near the lower 
end, and the weighed substance with the vessel is introduced into 
the barometer tube. The quantity of substance is so 
chosen that when vaporized it fills the tube almost to 
the stopper at the lower end of the jacket. This 
quantity is easily calculated from the formulas which 
follow. The tube, owing to the danger of breaking 
Fig. 15. 
by the sudden vaporization of the substance, should 
be slightly inclined when the substance is introduced. The stopper 
must always be placed loosely in the small glass flask. After intro- 
ducing the substance, which immediately vaporizes either wholly or 
in part, the vapor jacket is fastened in position and connected with 
the vessels attached to a and b. In the former is a liquid, the boil- 
ing point of which is at least io° above that of the substance in the 
tube A. Water or anilin (B. P. 183°) is usually employed. The 
vapor of the hot liquid must be conducted in carefully at first. 
When the temperature has become constant the height h of the 
mercury in the barometer tube above the surface of the mercury in 
the trough is carefully determined by the method already described. 
The length hl of the barometer tube from about the middle of the 
lower cork to the surface of the mercury in the trough is also 
determined. 
Calculation.—The vapor density d is calculated from the gen- 
eral equation : 
d g + 0.0 0367^) 
0.00129 SVO W/0.001293 METHOD OF GAY-LUSSAC-A. W. HOFMANN. 
37 
g is the weight of the substance in grams, v 0 the volume of the 
vapor at o° and 76 cm. pressure, 0.001293 the weight in grams of 
1 c.c. of air, and v the observed volume of the vapor in the barom- 
eter tube at the temperature t of the experiment and pressure p. 
The pressure p is equal to the barometric pressure b reduced to 
o° minus the column of mercury h reduced to o°. As the tem- 
perature of the interior of the jacket and likewise the mercury 
within the jacket is t and that of the lower part of the mercury 
column tv the temperature of the room, we have : 
b h. h h, 
? 1 f 
I -(- O.OOOISI fx I -j- O.OOOISI tl I -f- O.OOOISI^ 
where f represents the vapor pressure of mercury at the temperature 
t, hx the height, and tx the temperature of the column of mercury from 
the middle of the stopper to the surface of mercury in the trough, 
and h /q the height of the column of mercury in the vapor jacket 
at the temperature t. The above formula then can be written : 
p—(b hx) (I 0.000181 q) (h kx) (l 0.000181 /) —f* 
For exact measurements the expansion of the 
barometer tube when heated must be taken into 
account. As the tube is calibrated for 150, its vol- 
ume vt at t° is : 
Vt vl5 (i -f 0.000025 [t 15)) 
vt should therefore be substituted for v in the above 
expression for finding d. 
An appreciable error is also introduced by the fact 
that the mercury column consists of two parts, which 
are heated to different and not accurately measured 
temperatures. For exact determinations, therefore, 
the recent modification of the apparatus (Fig. 16) 
is doubtless to be preferred. As the entire column 
of mercury in this case is heated to the tempera- 
ture t, the expression for p is much simplified. 
Application of the Methods of Dumas and 
Hofmann,—The advantage of the Gay-Lussac- 
Hofmann method over that of Dumas consists prin- 
Fig. 16. 
* For the redaction of the mercury column to <s°, see Landolt-Bornstein, Tables, 
p. 26, 1883; pressure of mercury vapor, ibid. p. 58. 38 
DENSITY OF GASES. 
cipally in that the substance is vaporized in a vacuum and, there- 
fore, at a lower temperature than if vaporized at the atmospheric 
pressure. The method is preferable, therefore, for all compounds 
which at a higher temperature and pressure have a tendency to 
decompose or dissociate, and also in cases 
where only a small quantity of material is 
to be had. On the other hand, the appli- 
cation of the method is restricted to tem- 
peratures not much exceeding 200°, for 
the reason that mercury must be used in 
the experiment. 
(V) Method of V. Meyer (Air Dis- 
placement). 
Principle.—A definite quantity of sub- 
stance is introduced into an air chamber 
which is kept at constant temperature and 
provided with an arrangement by which 
water may be displaced by the air. If the 
temperature of the air is higher than the 
boiling point of the substance, the latter 
vaporizes and displaces a volume of air 
equal to the volume of the vapor formed. 
From this volume and the quantity of sub- 
stance used, the vapor density may be easily 
calculated (see below). 
Apparatus.—A cylindrical glass vessel 
A (Fig. 17) is provided at the top with a 
longer tube a. This vessel is placed in an 
outer glass jacket B, in which some suitable 
substance is heated to boiling, in order to 
maintain a constant temperature for the 
Fig. 17. 
vessel A. For substances with high boiling points (sulphur, di- 
phenyl, etc.) it is better to use a copper jacket instead of the glass. 
The tube a is closed with a rubber stopper, and is connected with 
a calibrated tube e filled with recently boiled water. The air dis- 
placed by the vaporization of the substance is collected in this tube 
and its volume measured. METHOD OF V. MEYER. 
39 
Solid or liquid substances are weighed in small flasks (Fig. 15) 
with or without corks. Volatile compounds are handled in thin- 
walled glass bulbs, each supplied with a small tube. 
The introduction of the small flask into the vapor chamber can 
be accomplished in various ways. In figure 17 is represented 
the side tube c arrangement, which is usually employed. The 
small flask containing the substance is placed upon a glass rod 
which is introduced into the side tube, and the entrance to the 
vapor chamber finally closed by means of an elastic rubber tube 
which allows the glass rod to pass in and out. When the desired 
temperature is obtained the small vessel is dropped from the glass 
rod into the heated vapor chamber, the bottom of which is covered 
with glass-wool or asbestos. 
Method of Operation.—The vapor chamber is dried with 
alcohol and ether, and the apparatus then set up. 
The glass or copper jacket contains a sufficient quantity of the 
heating substance, the boiling or melting point of which must be 
at least 30-40° higher than the boiling point of the substance in 
the vapor chamber. (Heating substances: Water, ioo° ; anilin, 
183°; nitrobenzene, 2110 ; diphenylamine, 300° ; paraffin-bath, 
350°; sulphur, 448°.) 
The jacket is then carefully heated ; as soon as air-bubbles cease 
rising in the liquid which serves as the outlet to the vapor chamber, 
the small flask is introduced and supported by means of the con- 
trivance at c. When the temperature of the vapor chamber be- 
comes constant and the graduated tube e filled with water remains 
free from air for a considerable time, the substance is introduced in 
the manner already described. 
The vaporization which follows immediately is shown by the 
rising of air-bubbles in the tube e. Each molecule of displaced 
air corresponds to one molecule of the substance vaporized. 
From the volume of air contained in e the volume of the vapor 
at o° and 76 cm. is then determined. 
When air no longer escapes from the vapor chamber into <?, the 
connection between the two is broken. 
The volume of displaced air should be at least 30-40 c.c. The 
quantity of substance to be used, therefore, must be estimated. 
Ordinarily from 0.1 to 0.2 gm. are sufficient. Knowing the dimen- 40 
DENSITY OF GASES. 
sions of the apparatus and the temperature required, the quantity 
of substance can be easily calculated from the formula below. 
The vapor chamber may be filled with hydrogen, nitrogen or 
carbon dioxide instead of air. 
Calculation.—Let the weight in grams of the substance used 
in the experiment be represented by g, the volume in cubic centi- 
meters of displaced air by v, the height of the water column in e 
by h, the temperature of the water = temperature of the room by 
t, and the barometric pressure by b; then the vapor density dis 
given by the expression ; 
d _ g _ 76 (I + 0-00367 0 . 
z/0 0.001293 w/0.001293 
p is the pressure, in centimeters of mercury, at which v is measured. 
This pressure is found from the expression : 
4) = (I) (I O.OOOISI t) /I 
r V 13596/v ’ J 
where f is the vapor pressure * of water at the temperature t. 
Application of the Method.—The method just described is 
characterized by its extreme simplicity. 
In contrast with the Hofmann method, this procedure is appli- 
cable to higher temperatures. On the other hand, the Hofmann 
method is preferable for accurate determinations, and also for com- 
pounds which are easily dissociated or decomposed. For dissociable 
compounds the method of V. Meyer must be carried out with great 
care and sometimes rejected entirely. In other cases varying 
values are obtained for the vapor density, depending upon the size 
and form of the vapor chamber and the quantity of substance 
used.f 
On the application of higher temperatures, see, among others, V. Meyer and 
Langer, Pyrochemische Untersuchungen, Vieweg, 1885 ; Mensching and V. 
Meyer, Zeit. phys. Chem. 1, p. 145, 1887; Nilson and Pederson, ibid. 1, p. 
34; 2, p. 657, 1888, and 4, p. 208, 1889, and Jour. pr. Chem. (2), p. 33, 1886; 
Griinwald and V. Meyer, Ber. d. d. chem. Ges. 21, p. 687, 1888; Biltz and 
V. Meyer, Zeit. phys. Chem. 4, p. 249, 1889. 
Method of metal-displacement (Wood’s metal); V. Meyer, Ber. d. d. chem. 
Ges. 11, p. 2253, 1878, and Kohlrausch, Prakt. Phys. vil, p. 59, 1892. 
* Landolt-Bornstein’s Tables, p. 40, 1883. 
J Biltz, Zeit. phys. Chem. 2, p. 944, 1888. METHOD OF LUNGE AND NEUBERG. 
41 
(d) Method of Lunge and Neuberg.* 
( Victor Meyer's Procedure under Reduced Pressure.) 
Principle.—The air displaced by vaporizing a weighed quantity 
of substance is collected over mercury instead of water in the tube 
C, which can be brought into connection with the vapor chamber 
A or with the outer air by means of the cup a. The tubes C 
and D, connected by means of a flexible tube, form a mercury 
pump by means of which any pressure can be produced in the 
chamber A. 
Apparatus (Fig. 18).—The arrangement of the vapor chamber 
A, as well as the contrivance at c and the outer jacket B, is the 
same as that described on page 38. 
The apparatus is of larger dimensions than the simple apparatus 
of V. Meyer. The delivery tube dis at least 30 cm. long, and is 
connected with the tube e by means of a rubber tube, so that it 
can be brought into connection with the mercury pump C b D by 
means of the stop-cock h. The stop-cock, which is a Geissler 
obliquely-bored stop cock, can, by properly turning, be made to 
connect e with C or a with C, or can be entirely closed from C to e 
as well as to a. 
The calibrated tube C (zero point at the top) is connected with 
D by means of the flexible tube b. 
The flexible tube must be thick-walled and interwoven or 
wrapped with canvas. The rubber connections at e and c must be 
carefully chosen and frequently renewed. They should be wrapped 
with wire, and the stop-cock h should always be greased. 
The reading of the top of the mercury in C and D is accom- 
plished, for accurate measurements, by means of a cathetometer 
or by means of the Hofmann contrivance (p. 35). 
A wooden millimeter-scale is fastened in a vertical position on C 
by means of the ring r which is placed in such a position that the 
upper edge, which is the zero point of the scale, is in the same 
horizontal plane as the top of the mercury. 
Ordinarily the arrangement shown in figure 18 is sufficient. 
A pointer s is fastened to the scale and is adjusted so that the 
* Lunge and Neuberg, Ber. d. d. chem. Ges. 24, p. 729, 1891. Fig. 18. METHOD OF LUNGE AND NEUBERG. 
43 
upper edge is in the same horizontal plane as the top of the mer- 
cury in D. The position of the upper edge of the pointer is then 
read on the scale. 
Method of Operation.—The two parts of the apparatus, after 
drying with alcohol and ether, are firmly fastened to a stand and 
connected air-tight by means of a rubber tube. 
The stop-cock h is then turned so that C is connected with a. 
The tube D is filled with recently boiled mercury and raised to 
such a height that the mercury flows into a. his then closed and 
D lowered until a Torricellian vacuum is formed in C; the differ- 
ence in height then of the upper surfaces of the two columns of 
mercury represents the ordinary barometric pressure. When 
filling the apparatus, air-bubbles cling for some time to the 
sides of the glass tube, and especially to the walls of the rubber 
tube, so that D must be frequently raised and lowered. It is 
better, therefore, after once filling, to allow the mercury to remain 
in the apparatus. For accurate determinations it is preferable to 
use a special barometer. 
Suppose the barometric pressure to be 750 mm., and that the 
vapor density determination is to be made at 50 mm. The air in 
the apparatus is exhausted so far that, by connecting A with C, the 
perpendicular distance between the tops of the mercury columns 
in C and Dis 750— 50 = 700 mm. The pointer zon the con- 
trivance for reading off the pressure is fastened on 700 mm. C 
is then connected with A and the air which passes from A into C is 
removed, in that the connection C— Ais closed and the connec- 
tion C—a opened ; by raising D until the mercury enters a, the 
air is completely removed, h is then closed so that Cis neither 
in connection with A nor a, D is lowered and C is again con- 
nected with A; C— Ais then closed and C—a opened and the 
air in C removed by raising D. By repeating this operation four 
or five times the desired exhaustion of the apparatus is practically 
attained. Ais then connected with C and the upper edge of the 
ring ris placed at the top of the mercury column in C. At 
the same time D is fastened in the stand so that the top of the 
mercury column in D coincides with the upper edge of the 
pointer z, placed at 700 mm. If the pressure of 50 mm. in the 44 
DENSITY OF GASES. 
apparatus remains constant for five minutes, the stop-cock and 
rubber connections are tightly closed. 
If the pressure remains constant, the connection C— Ais closed 
and C—a opened, then by raising D the air in C is completely 
removed. If, then, after the vaporization of the substance in the 
chamber A, the pressure again becomes 50 mm., it is evident that 
for each molecule of substance vaporized one molecule of air passes 
from A into C. From the volume of air in Cat 50 mm. pressure, 
the volume and vapor density of the vaporized substance is calcu- 
lated by known methods. 
The heating of A (p. 39) can be carried on during the exhaus- 
tion of the apparatus. To protect C from the heat, a card-board 
or asbestos screen is placed between A and C. 
If a constant temperature has been attained and C has been 
exhausted to 50 mm. pressure in the above manner, A is connected 
with C and the experiment is begun. 
The mercury in C falls immediately; as soon as the top of the 
column becomes stationary, the pressure in the apparatus is brought 
to exactly 50 mm. by raising and lowering D. The connection 
between C and D is then closed, the rubber stopper is taken out 
and the flame removed. 
Calculation.—Let g represent the weight of the substance in 
grams, v the volume in cubic centimeters of displaced air contained 
in C, p the pressure, in centimeters of mercury, of the air in Cat 
the time of reading the volume v, and t the temperature of the 
mercury (equals temperature of the room), then the vapor density is : 
d__ (i + 0-003670. 
vp 0.00x293 
If h is the perpendicular distance between the tops of the columns 
of mercury in C and D at the time of readings, b the barometric 
pressure, and /the vapor pressure of mercury at t°, then,— 
p (b— h) (1—0.000181 t)—f* 
Application of the Method.—While the air-displacement 
procedure, in the simple form of V. Meyer, is not applicable for 
compounds which dissociate under the atmospheric pressure, the 
* See Landolt-Bornstein’s Tables, pp. 26 and 58, 1883. CAPILLARITY. 
45 
working under reduced pressure has the advantage mentioned 
before for the Hofmann apparatus. Besides the greater simplicity 
in the method of operation, this method possesses another advan- 
tage over that of Hofmann in that the mercury is not heated. 
Naphthalene (B. P. 218°) can be investigated in the vapor of 
xylene (B. P. 140°), and mercury (B. P. 3590) in the vapor of 
diphenyl (B. P. 2540). 
111. CAPILLARITY. 
I. FROM THE RISE IN A CAPILLARY TUBE 
(The Capillarimeter). 
Calculation.—The constant of capillarity, y {= a), may be 
defined as the weight of liquid suspended per linear unit of con- 
tact between a liquid and a solid wall (mg. mm.). 
Its value is given by the expression : 
„ rhs 
y cos it = . * 
2 
$ represents the angle formed by the uppermost particle of liquid 
and the walls of the tube ; r is the radius of the tube, and h the 
capillary rise, both measured in millimeters; and jis the specific 
gravity of the liquid. 
Cos # can not (as the earlier theory admitted) be placed equal 
to lin all cases; one must be content, therefore, in establishing 
the constant y cos ft. 
The constant is frequently calculated from a 2 cos ft —r h, where 
a 2 is the specific cohesion. 
For aqueous solutions, the lowering of the capillarity of the 
solvent is usually considered ; it is : 
7w cos -&w —yi cos =\ r (hw sw —hxst ). 
The corresponding constants for water and the solution are repre- 
* Ostwald, Lehrb. Allgem. Chem., 2. Aufl., Bd. 1, p. 514, 1891. 4 6 
CAPILLARITY. 
sented by the indices w and I. (J. Traube, Lieb. Ann. 265, p. 28, 
1891.) 
Apparatus.—The capillarimeter (Fig. 19) consists of a capillary 
tube 15 to 20 cm. long, and a scale made of porcelain or metal. 
The tube and scale are fastened together by means of small screws, 
so that the tube extends from 2 to 3 cm. beyond each end of the 
scale. 
The scale, from 1 to 2 cm. wide, is graduated to 0.5 mm.; it 
terminates below in two points which coincide with the zero point 
of the scale. The position of these points must be adjusted with 
considerable care. 
The stand A carries the clamp a ; by means of the fine screw I), 
the clamp, and likewise the capillari- 
meter fastened in it, can be raised or 
lowered. 
The capillary tube should have a 
radius of from 0.15 to 0.2 ram. The 
walls of the tube should be as thin as 
possible and, above all, the diameter of 
the tube should be uniform throughout. 
This is especially necessary inasmuch as 
the calculation of the capillary constant 
is made from the diameter of the tube at 
the place where the meniscus is situated. 
The uniformity of the bore of the tube 
is tested by passing a thread of mercury 
into the clean, well-dried tube of greater 
Fig. 19. 
length. For this purpose the tube is fastened to a scale ;* errors 
due to parallax in reading the scale should be avoided. If the tube 
is not sufficiently uniform, another is chosen or a correction table 
is calculated. 
The mean radius is best determined by means of pure mercury. 
The clean, dry tube, after being fastened to the scale, is re- 
peatedly filled as full as possible with mercury, and the total 
length of mercury threads is measured (avoiding errors due to 
* Since the work of Lothar Meyer, Berberich has introduced a mirror-scale 
which enables the observer to easily eliminate the error of parallax. THE CAPILLARIMETER. 
47 
parallax). If the total length = I mm., the total weight = p 
mg., and the temperature of the mercury is t, then the radius of 
the tube is ; 
r = J/(X + o-oooxBi t) 
> 13.596W 
in millimeters. The variation in several measurements should not 
amount to more than one unit in the fifth decimal place. 
The tube should always be kept perfectly clean. 
At the end of the investigation the tube should be closed with 
black rubber ; from time to time it should be cleaned with concen- 
trated nitric acid. After each observation the tube should be 
cleaned and dried by sucking into it water and alcohol (not ether) ; 
this is accomplished by connecting one end of the tube with a 
sulphuric acid bottle and the other with the mouth or a pump. Saliva 
or rubber should never be allowed to enter the tube. 
If the necessary precautions are always observed, the same tube 
can be used for several years. 
An unclean tube is usually the cause of an imperfect wetting of 
the walls by the liquid, and of the irregular, jerky movements of 
the liquids. In such cases the cleaning can frequently be accom- 
plished with nitric acid. 
Method of Measurement.—The scale is placed in the sup- 
port so that the tube stands as vertical as possible. The error 
introduced by a slight inclination of the tube is inappreciable. 
The vertical position is determined simply with the eye or by 
means of a plumb-line. 
The liquid is placed under the tube in a small glass vessel. The 
dry points of the scale should touch the surface of the liquid simul- 
taneously. The inclination, however, amounts to less than 0.1 
mm. if the two points are not immersed simultaneously in the 
liquid; it is then desirable to always bring the same point to the 
liquid first. 
When the points are adjusted, the liquid is slowly sucked up 
into the tube. The operation should be conducted so as to pro- 
duce a perfect wetting of the tube. 
The liquid is sucked (carefully avoiding the entrance of saliva 
into the tube) three times from 3 to 4 cm. above the final position 48 
CAPILLARITY. 
of the liquid meniscus, and is allowed to fall from 5 to 8 cm. 
When the liquid has been sucked up three times, it is allowed to 
fall in the tube, and the height assumed by the lower edge of 
the meniscus after one-half to one minute is read off (care 
being taken to avoid any error due to parallax). A microscope 
may be advantageously employed; or a cathetometer may be used 
in making the reading. Heating of the tube should always be 
prevented. 
Ordinarily, the position of the liquid remains constant during 
one or several minutes, and then a gradual sinking begins, owing 
to a lack of perfect wetting of the tube ; or a rising for volatile 
liquids. For exact measurements, a small correction must be 
applied to the observed height of the meniscus; the observed 
value should be increased by yi r. The true value then is 
= & + V. 
Care should be taken in all observations that small air-bubbles 
do not occur in the liquid in the tube, and that the column of 
liquid should at no place be separated. Especially for the more 
viscous liquids or with very narrow tubes it is important, after the 
capillary rise has been determined according to the above method, 
—by sucking the liquid up and allowing it to fall,—to confirm the 
result by sucking the liquid up once, forcing it down, and allowing 
it to rise of its own accord. The height attained by this capillary 
rise should not be more than of a mm. lower than the height 
attained by the first method. 
The liquid and the tube should be warmed to the same tempera- 
ture as that of the room before the experiment; it is also very impor- 
tant, in most cases, that liquids should be sucked up only from the 
surface ; a change of concentration influences the result. 
The observations are always made at a definite temperature, 
usually at 15 or 20° ; the temperature coefficient for most liquids 
and for tubes of from o. 15 to o. 2 mm. radius amounts usually to only 
0.1 to 0.2 mm. for i° Celsius. 
The observations should be repeated after cleaning and drying 
the tube with alcohol. The variations should not, at most, amount 
to more than 0.2 to 0.3 mm. About twenty observations may be 
made in an hour. THE STALAGMOMETER. 
49 
The constant a 2 cos ■& =r h is, for water at 150 : 
= 15.09 (according to Volkmann), 
= 14.7° ( “ Quincke), 
= 14.88 ( “ Brunner), 
= 15.12 ( “ Hagen), 
= 15.24 ( “ Wolff), 
= 14-77 ( “ Traube). 
Weinberg, Zeit. phys. Chem. 10, p. 34, 1892 ; ibid. p. 38, literature. 
Principle and Calculation.—If different liquids under defi- 
nite pressures are allowed to drop from a horizontal, smooth sur- 
face of from 6 to 8 mm. in diameter, the weights of the drops are 
proportional to the weights of the liquids in the capillary tubes. 
If, therefore, definite volumes of different liquids drop from the 
same surface, the number of drops in the volume v are inversely 
proportional to the rise of the liquids in capillary tubes. 
2. THE DROP METHOD (The Stalagmometer). 
If zw and zr represent the number of drops contained in the 
volume v of water and some other liquid dropping from the surface 
a (Fig. 20), and ajl cos -&w and ajl cos &r represent the corres- 
ponding capillary constant (p. 39), we have from the above pro- 
portion the equation : 
COS &w • zw zw 
ar2 cos xrr aw* = 14.90 ——, 
and 
yr cos &r = 7-45 > 
zr sr 
where sw and sr represent the specific gravities of the water and the 
liquid. 
Apparatus.—The apparatus consists of an outflow'arrangement 
A as well as the pressure apparatus B, and is identical in its essen- 
tial parts with Poiseuille’s apparatus for determining the constant 
of viscosity; hence the constants of capillarity and viscosity may 
easily be determined together. 
The stalagmometer A consists of a tube bent twice into a knee 
shape, the upper end of which expands into a globe in which a CAPILLARITY. 
definite volume v, of 6 to 8 c.c. capacity, is divided off by the two 
boundary lines b and c. The middle and lower limb of the tube 
is a capillary tube, the outer diameter of which is from 6 to 8 mm., 
while the inner diameter is chosen according to the height of the 
pressure column and length of the tube, so that the time of forming 
Fig. 20. 
a drop will be at least four to five seconds. The drop-surface a 
(6 to 8 mm. in diameter) should be well polished, and the outer edge 
made as conical as possible (see Fig. 20) to prevent any drawing 
away of the liquid by the sides of the tube, so that only the under 
surface where the drop is formed will become thoroughly wet. 
The flow of liquid to the drop-surface must take place through a THE STALAGMOMETER. 
51 
capillary tube, otherwise an irregular whirling motion will be pro- 
duced in the drop. 
The conical grinding of the sides of the tube at the surface is 
unnecessary; by carefully greasing the outer walls of the tube near 
the surface the drawing away of the liquid can be prevented. 
By means of the pressure apparatus the liquid can be made to 
flow out under constant or any desired pressure. 
A wide glass tube about one meter high is connected with a 
Wulf bottle, in which the air is compressed, corresponding to the 
height of the pressure column. The filling with water takes place 
through the stop-cock d. The level of the water in the pressure 
tube is kept constant by means of the water in the vessel f, which 
gradually flows in, owing to the tilting of the piece of ground-glass 
at g when the surface of the water in the 
pressure tube is lowered. The stop-cock 
e is connected with an air-pump, which 
makes it possible to suck the liquid 
through a into the apparatus. The glass 
parts should be connected by means of 
black or red rubber tubing. 
If the apparatus is also to be used for 
determining the constant of viscosity (p. 
53), it is better to divide A into two 
portions, connected by means of rubber 
Fig. 21. 
(as in Fig. 21). bis a capillary knee- 
tube which must be removed in the determination of the con- 
stant of viscosity, in case its inner radius is not considerably 
greater than that of a. The knee-tube a (volume v, length and 
radius of the capillary tube) is then carefully measured by means 
of mercury and placed in a cylindrical glass water-bath. For 
determining the capillary constant alone, the water-bath (Fig. 20) 
is not necessary. For the simultaneous determination of constants 
of capillarity and viscosity, see J. Traube, Ber. d. d. chem. Ges. 
19, p. 871, 1886. 
Method of Operation.—The liquid at the temperature of the 
room and as free as possible from dust is sucked up into the 
apparatus by connecting the stop-cock e with the pump, until the 
level of the liquid reaches the mark b. The connection is then CAPILLARITY. 
made with the pressure apparatus and the number of drops con- 
tained in the volume v counted. 
If the outflow is sufficiently slow, the operator with a little care 
and practice can determine the exact moment when the lower edge 
of the meniscus passes the marks b and c, and estimate the corre- 
sponding quantity of liquid with certainty to o.i to 0.2 of a drop. 
If the observation of the moment when the liquid passes the mark 
b is not made sharp enough, connection is again made with the 
air-pump, until finally for the mark b a whole drop separates. 
This method leads to accurate results; repeated observations 
should not show variations of more than 0.2 or 0.3 in the number 
of drops contained in the volume v. The drop-surface and capil- 
lary tube should be absolutely clean. A variation in the speed of 
the outflow, due to the presence of dust in the capillary tube, 
gives rise to appreciable errors; the rate of outflow, therefore, is 
always fixed as nearly constant as possible. The larger air-bubbles 
in the drop should be avoided. 
For the majority of liquids, whose constants of viscosity and 
rates of outflow do not differ more than fifty per cent, from the 
corresponding values for water, the pressure, under which the 
liquids flow out slowly (one drop in five seconds), can be kept 
constant. If, however, very viscous liquids are to be compared 
with easily flowing liquids (aqueous glycerin, cane-sugar solu- 
tion with water), the pressure columns are to be shortened or 
lengthened so that the speeds of outflow are not very different. 
The error introduced by using equal pressures in such cases 
seldom amounts to more than one to two per cent. The difference 
between the capillary constants y calculated by the capillary-rise 
method and the drop method amounts to less than one per cent. 
The determination of the capillary constant at higher tempera- 
tures is best accomplished by the drop method ; at the boiling point 
by the capillary-rise method: R. Schiff, Lieb. Ann. 223, p. 47, 
and Gazz. chim. Ital. 14, p. 1, 1884. Determination at the 
melting point; J. Traube, Ber. d. d. chem. Ges. 24, p. 3074, 1891. 
Application of Capillary Constants.—The constant of 
capillarity has hitherto been of little use for chemical purposes. 
On the relation to the constitution of homogeneous organic 
liquids, see the work of Schiff, already cited. The constant of VISCOSITY. 
53 
capillarity is of still greater use in the domain of (aqueous) solu- 
tions. 
i. The constant for water is often considerably lowered by dis- 
solving organic compounds in it. The constant is closely related 
to the constitution of the dissolved substance; for isomeric com- 
pounds it is frequently very different. The constant is of consider- 
able value, therefore, in determining the constitution of com- 
pounds. J. Traube, Lieb. Ann. 265, p. 28, 1891. 
2. The capillarity constant is of importance from an analytical 
standpoint. 
Many compounds (especially electrolytes) in concentrated solu- 
tion influence the constant of water very little, while other sub- 
stances in dilute solutions often lower the constant considerably. 
The capillarity constant makes it possible, therefore, to deter- 
mine, often very accurately, the concentration of a solution, and 
hence may be used in the approximate quantitative determination 
of many substances present in small quantities in a solution which 
may at the same time contain large quantities of other substances 
(mineral acids and bases as well as salts). The constant is also of 
value in determining the degree of purity of a dissolved substance. 
Dudaux, Ann. chim. Phys. (5) 13, p. 76, 1878; J. Traube, Jour, pralct. 
Chem., N. F. 31, p. 177, 1885. Application to the determination of the basicity 
of acids, J. Traube, Ber. d. d. chem. Ges. 24, p. 3074, 1891. 
IV. THE CONSTANT OF VISCOSITY. 
I. METHOD OF POISEUILLE-OSTWALD. 
Principle and Calculation.—The constant rj of viscosity may 
be defined as the work required to move, in unit time, two layers 
of liquid of unit surface in parallel and opposite directions ; the 
distance moved being equal to the distance between the two layers 
of liquid. 
The constant is determined by different modifications of the out- 
flow method of Poiseuille. The time required for a definite volume 54 
VISCOSITY. 
of liquid under a definite pressure to flow through a capillary tube 
is determined, and the constant of viscosity calculated according 
to the formula of Finkener : * 
r4 7T h s vs I 
v— t . 
8/ v 87T g I t 
where tj is the constant of viscosity of the liquid ; 
s the specific gravity of the liquid ; 
r and / the radius and length of the capillary tube (in cm.) ; 
v the volume of liquid flowing out in the time t (cm. sec.) ; 
h the height of the pressure column in centimeters, under which 
the liquid flows out; 
g the acceleration due to gravity = about 981.2 and tt the 
known constant value. 
As all the values except s and t are constant for the same appa- 
ratus, the above formula may be written ; 
, c, s 
)/ = C St 
t 
The constants c and cx are to be determined for each apparatus. 
The dimensions of the apparatus are so chosen that the value of 
cx— is only a small per cent, of the value t]. Instead of ij, it is 
frequently sufficient to determine the “specific viscosity ” z of the 
liquid. By this is meant the time of outflow of the liquid (multi- 
plied by 100) at any temperature, divided by the time of outflow 
for water at o°. We have, therefore, 
r 100 t 
' tw 
The determination of the constants of the apparatus is not 
necessary in this case. 
Apparatus (Fig. 22).—A vertical capillary tube b is fused at 
the ends to the two wider tubes e and d, so that the change from 
the capillary to the wider tubes is as sharp as possible. A bulb k 
is blown in the upper tube d, in which a definite volume v of 
liquid can be measured off by means of the two marks a and c. 
* Gartenmeister, Zeit. phys. Chem. 6, p. 525, 1890; also Wilberforce, Phil. 
Mag. (5) 31, p. 4°7, 1891. METHOD OF POISEUILLE-OSTWALD. 
55 
This simple apparatus is fastened by means of a rubber stopper in 
a large glass bell-jar of 15 to 20 liters capacity, which is filled 
with water and arranged so that the temperature may be determined 
accurately to o.i°. 
The pressure under which the liquid flows out in this apparatus 
is found by multiplying the specific gravity 
of the liquid by the varying height of the 
pressure column during the investigation. 
The mean height of the pressure column 
may be placed equal to the height h of the 
lower mark a above the lower opening of the 
capillary =hn increased by half the distance 
from ato c = hu, therefore h=. h, -j- hu. 
For exact measurements it is desirable 
to use two or three different outflow tubes. 
The volume of the bulb and the dimen- 
sions of the capillary tube are accurately 
measured by means of mercury,—best be- 
fore the apparatus is set up. For the meas- 
Fig- 22> 
urement of capillary tubes, see page 46. 
The dimensions of the separate parts of the apparatus best 
adapted to this work lie between the following limits ; 
v =4to 8 c.c. 
r = 0.025 to 0.030 cm 
/ =3oto 40 cm. 
hj, = 1 to 2 cm. 
The time occupied in the investigation is determined either with 
the help of an ordinary seconds watch or better, a chronograph; 
in the latter case the time is measured to the fraction of a second. 
Method of Operation.—After carefully cleaning the capillary 
tube, the apparatus is filled with the clear liquid free from dust by 
means of a pump from below. By closing the black-rubber tube 
with a glass rod, the outflow of the liquid is prevented until the 
temperature of the liquid is the same as that of the water-bath. It 
is to be observed that the constant of viscosity, in most cases, 
varies to a high degree with the temperature. 
When the experiment is to be commenced the glass rod is re- 
moved, and the time required for the passing of the meniscus from 56 
SOLUBILITY. 
the upper mark c to the lower mark b is measured by means of the 
chronograph. The liquid is not allowed to drop from the lower 
end of the tube, but the outlet end is immersed in a liquid con- 
tained in a small vessel. 
The experiment is always repeated. Greater differences than 
0.2 per cent, in the values of t are usually to be traced to the 
lodging of small solid particles at the top or in the capillary tube. 
The tube is therefore frequently examined with a microscope. 
Before using, the apparatus is first tested by experimenting with 
water. The following table contains the constants of viscosity for 
water at different temperatures : 
Temperature. 
Poiseuille. 
Sprung-. 
Traube. 
V 
V 
V 
o 
0.018 142 
0.018136 
0.01 824 
xo 
I335I 
13271 
i 333 
20 
10 296 
10 214 
1 032 
3° 
08 212. 
08 186 
0819 
40 
06 718 
06725 
0 669 
Poiseuille’s apparatus for the simultaneous determination of the constants of 
viscosity and capillarity, see p. 43, and Ber. d. d. chem. Ges. 19, p. 872, 1886 ; 
a recent form of apparatus especially adapted to high temperatures, see Ostwald, 
Lehrb. allgem. Chem., 2. Aufl., Bd. I, p. 55°) J^px. 
Relation of the constant of viscosity to the constitution of a liquid, see Garten- 
meister, Zeit. phys. Chem. 6, p. 524> lB9°> and Handl and Prihram, ibid. 9, 
p. 529, 1892. Constant of viscosity for solutions, Arrhenius, Zeit. phys. Chem. I, 
p. 285, 1887; Reyher, ibid. 2, p. 744, 1888; Wagner, ibid. 5, p. 31, 1890; 
Lauenstein, ibid. 9, p. 417, 1892. Influence of temperature, Gratz, Wied. Ann. 
31, p. 25. 1888; Stoel, Phys. Revue I, p. 513, 1892. Tables and earlier literature, 
Landolt-Bdrnstein’s Tables, p. 153? 1883. 
V. SOLUBILITY. 
The solubility is referred either to a constant quantity of the 
solvent or, better, to a constant weight or constant volume of the 
solution. It may also be referred to the number of molecules. 
The solubility of a solid compound is determined by shaking the 
solvent for at least two to three hours at constant temperature 
with an excess of the powdered substance. SOLUBILITY. 
57 
The thermostat described by Ostwald (p. 65) may be used for 
this purpose. The flask filled with the solvent is placed in the 
thermostat; the Raabe turbine may be used to advan- 
tage as a stirring apparatus. When the solution in the 
thermostat has become perfectly clear, a definite portion is 
removed by sucking up into the small pipette (Fig. 23) 
proposed by Landolt. The pipette is closed by means of 
a glass cap. If the solubility is determined at higher 
temperatures, the pipette must be previously warmed. 
The quantity of solution is determined from two weigh- 
ings of the pipette ; for determining the quantity of dis- 
solved substance, the contents of the pipette are washed 
into a suitable vessel. 
Fig. 23. 
The accuracy of the result is determined by conducting a parallel 
observation. The relation of the solubility and temperature is 
generally represented graphically. 
See also the apparatus of Reicher and Van Deventer, Zeit. phys. Chem. 5, p. 
560, 1890; for carrying out a huge number of solubility determinations, see the 
apparatus ol Noyes, Zeit. phys. Chem. 9, p. 606, 1892; see aLo Schroder, ibid. 
11, p. 453 1893. 1 teterm nation of solubility by means of the electric conduc- 
tivity. see F. Kohlrausch and Rose, Ber. Beil. Akad. 26, p. 453, 1893. 
Solubility tables : Landolt-Bornstein’s Tai les, p. 154 1883. 
Solubility of salts, see, among others, Engel, Ann. chim. Bhys. (6) 17, p. 338, 
1889; Meyerhoffer, Zeit. phys. Chem. 5, p. 97, 1890; Bodlander, ibid. 7, pp. 
315 and 358, 1891 ; Tresor, ibid. 7, p. 469, and Lobry de Bruyn, ibid. 10, p. 
782, 1892. 
Solubility of organic compounds: Carnelley and Thomson, Jour. Chem. Soc., 
p. 782, 1888. 
Apparatus for determining the absorption of gases: Timofejew, Zeit. phys. 
Chem. 6, p. X4l, 1S90; L. W. Winkler, Ber. d. d. chem. Ges. 24, p. 89, 1891 ; 
Bohr and Bock, Wied. Ann. 44, p. 318, 1891. 
Osmotic pressure. Apparatus ; Adie, Jour. Chem. Soc., p. 344, 1891; Tammann, 
Zeit. phys. Chem 9, p. 103, 1892, and Walden, ibid. Ij, p. 699, 1892. 
Diffusion. Apparatus Scheffer, Zeit. phys. Chem. 2, p. 391, 1888; Chabry, 
Jour, der Phys. (2) 7, p. 115, 1888; Stefan, Wiener Monatshefte, 10, p. 201, 
1889; Wiedeburg, Wied. Ann. 41, p. 675 ; Arrhenius, Zeit. phys. Chem. XO, p. 
52, 1892, and Abegg, 11, p. 249, 1593; Pickering, Phil. Mag. (5) 35, p. 127, 
1892. 
Reaction, velocity, and chemical equilibrium. Recent literature: Warder, 
Ber. d. d. chem. Ges. 14, p. 1361, 1881 ; Reicher, Lieb. Ann. 228, p. 257,1885; 
Ostwald, Jour, prakt. Chem. (2) 35, p. 112, 1887; Landolt, Ber. d. d. chem. 58 
THE ELECTRIC CONDUCTIVITY OF LIQUIDS. 
Ges. 19, p. 1343, l 885; Arrhenius, Zeit. phys. Chem. I, p. 109, 1887, and 4, 
p. 226, 1S89; Menschutkin, Zeit. phys. Cliem. i, p. 61 x, 18S7; 5, p. 589, and 
6, p. 41, 1890; Bull. Ac. Belg. (3) 31, p. 559, 1891 ; Konowalow, Zeit. phys. 
Chem. X, p. 63, 1887, and 2, pp. 6 and 380, 1888; Ostwald, Zeit. phys. Chem. 
2, p. 127, 1888; Meyerhoffer, ibid. 2, p. 585 ; Spohr, ibid. 2, p. 194; Giersbach 
and Kessler, 'ibid. 2, p. 676; Will and Bredig, Ber. d. d. chem. Ges. 21, p. 
2777, 1888; Burchard, ibid. 2, p. 796; Bonz, ibid. 2, p. 865; Lengfeld, Amer. 
Chem. Jour. 11, p. 40, 1889; Hecht, Conrad, and Bruckner, Zeit. phys. Chem. 
3, p. 450, 1S89; 4, p. 273, 1889; 5, p. 289, IS9O, and 7, p. 274. 1891; Walker, 
ibid. 4, p. 3x9, 1889; Fulda, ibid. 6, p. 491, 1890; Montemartini, Rendic. Acc. 
Lincei 6, p. 263, 1890; F.vans, Zeit. phys. Chem. 7, p. 337, 1891; Schiikarew, 
ibid. 8, p. 76, 1891; Bugarsgky, ibid. 8, p. 398, 1891; Wildermann, ibid. 8, p, 
661, 1891; 9, p. 13, 1892 ; Muller and Hausser, Compt. rend. 114, pp. 549 and 
760, 1892; Henry, Zeit. phys. Chem. 10, p. 97, 1892; Uno Collan, ibid, xo, p. 
130; Trevor, ibid. 10, p. 321, 1892; Hjelt, Ber. d. d. chem. Ges. 24, p. 1236, 
1891. 
VI. THE ELECTRIC CONDUCTIVITY OF 
LIQUIDS. 
1. METHOD OF F. KOHLRAUSCH.* 
Apparatus and Method in Generals—The method of Kohl- 
rausch depends upon the use of alternating currents, in connection 
with the Wheatstone bridge. 
The element E (Fig. 24) is connected with the induction coil 
J, the wires of which are fastened to the measuring bridge B by- 
means of binding screws. The circuit of the bridge is made com- 
plete by means of a metallic wire which passes through each of 
the binding screws and finally to the resistance solution W and 
the comparison resistance R. To the binding screw between W 
and R is fastened a telephone wire, the other end of which leads 
to a movable metallic slide on the bridge. 
By closing the circuit the element is set in operation, and the 
slide can be placed at such a position on the bridge that no cur- 
* Kohlrausch, Wied. Ann. 6, pp. I and 145,1879; 26, p. 161, 1885 ; and 49, 
p. 225, 1893; Ostwald, Zeit. phys. Chem. 2, p. 560, 1888. METHOD OF F. KOHLRAUSCH. 
59 
rent will pass through that part ©f the conductor in which the 
telephone is introduced. 
The interposed telephone furnishes a means of determining the 
proper adjustment, instead of the galvanometer or dynamometer, 
in that when the slide is at the proper position the telephone is 
either silent or produces a minimum tone which is augmented by 
moving the slide in either direc- 
tion on the scale of the bridge. 
From the position of the slide 
corresponding to the minimum 
tone, we deduce by means of 
Kirchhoff’s laws* the propor- 
tion W: R—a\b. 
W is the resistance of the 
liquid and the electrode vessel; 
R is the interposed comparison 
resistance ; a and b represent the 
number of divisions on the scale 
Fig. 24. 
of the bridge, to the left and right of the slide when properly ad- 
justed. The unknown resistance of the liquid or the reciprocal 
value, the electric conductivity, may be calculated from the above 
proportion according to page 69. 
The Apparatus in Detail. 
The Element,—A small Bunsen chromic acid element is 
sufficient. For the preparation of 1 1. of solution, 92 gm. of 
pulverized potassium bichromate (or a corresponding quantity of 
the more soluble sodium salt) and 94 c.c. of concentrated sul- 
phuric acid are rubbed together to a uniform pasty liquid ; 900 c.c. 
of water are then carefully added while stirring. 
The Induction Apparatus,—According to Ostwald, the 
smallest induction coil used for medical purposes is best adapted to 
this work. The rapidity of the vibration of the interrupter is 
increased still further by filing the little block of iron on the 
spring down to rather small dimensions (1 or 2 mm.). The mini- 
* Ostwald, Ailgem. Chem. I, p. 537, 1885; and Kohlrausch, Prakt. Pliys. 
VII, p. 255, 1895. THE ELECTRIC CONDUCTIVITY OF LIQUIDS. 
mum tone of the telephone is sharper if the sliding brass tube is 
removed from the apparatus. 
The sharpness of the telephone depends largely on the nature of 
the induction apparatus used,* especially on the speed with which 
the current is alternated. If, therefore, the tone-minimum is not 
sharp, different induction coils should be tested, and the most 
suitable selected. 
The Measuring Bridge.—lnstead of the cylindrical bridge f 
proposed by Kohlrausch, the bridge which is ordinarily employed 
maybe used. The simplest form Jof the same (Fig. 25) is con- 
structed as follows; 
A paper (or wooden) scale, graduated in millimeters, is fastened 
on to a dry board of 110-120 cm. in length and 4—6 cm. in breadth. 
A metallic wire is stretched along 
the scale by means of the screws 
a and ax on the ends of the board. 
Two brass plates are fastened by 
means of the screws b and b' on 
to the board, perpendicular to 
Fig. 25. 
the scale, so that their inner 
edges pass exactly through the 
divisions o and xoo on the scale. The screws b and b' serve also 
for fastening the wires from the induction apparatus and the resist- 
ances. 
The bridge wire, which is about 0.2 mm. in diameter, should be 
made of perfectly clean German silver, or of platinum containing 
iridium. The German silver wire, owing to its gradual oxidation 
in the chemical laboratory, gives rise to irregular sounds in the 
telephone; the wire should therefore be renewed from time to 
time. 
For all exact measurements the uniformity of the wire should be 
tested and the wire calibrated before use. This may be done by 
the method of Strouhal and Bams (p. 73). 
* Kohlrausch, Wied. Ann. 6, p. 8, 1879. 
f Kohlr.uisch, Wied. Ann. 11, p. 653, 1880. 
J A modified form, see Ostwald, Zeit. phys. Chem. 2, p. 562, 1888 ; Wiede- 
mann and Ebert, Phys. Prakt. I, p. 385, 1890. METHOD OF F. KOHLRAUSCH. 
61 
The slide s of the measuring bridge, in its simpler form, con- 
sists of a rectangular, bent-down, metal frame with a small binding 
screw c, with which the telephone is connected. It is adjusted to 
the bridge so that it may be easily moved. In the middle of the 
frame and in contact with the bridge wire, is an elastic German 
silver needle, the flattened point of which is so constructed that it 
is always in perfect contact with the wire. The sensitiveness of 
the telephone depends on the kind of contact.* 
The Telephone.—Care should be exercised in the choice of 
the telephone. The Bell telephone is well adapted to this work. 
Ostwald recommends the telephone of Ericsson, in Stockholm, as 
being very sensitive. 
The sounds proceeding from the induction apparatus are annoy- 
ing at first to the unpracticed. A small bulb or some wadding 
placed in the ear will remove this inconvenience. One learns 
very quickly, however, without this, to distinguish between the 
two sounds. 
The Comparison Resistance.—Three resistances of 10, 100, 
and 1000 units (Ohm or Siemens) are sufficient. More appro- 
priate, however, and far more convenient is the use of a complete 
resistance-box, the greatest resistance of which amounts to 2000 
Siemens-units. By using greater resistances, better results are ob- 
tained ; it is better to work with different electrode distances. 
The best results are usually obtained with resistances of from 100 
to 1000 units. 
The resistances should be wound f bifilar, and should be com- 
pared, at least twice a year, with a standard resistance; at all 
events, one should satisfy himself by testing the apparatus, from 
time to time, with solutions of known resistances. 
As the resistance varies with the temperature, it is necessary for 
accurate determinations to make the small temperature correction 
(see p. 70). 
The Electrode Vessels.—Three different vessels are used for 
f A new kind of winding by Chaperon, Elsas, Wied. Ann. 44, pp. 675 
and 678, 1891 ; and F. Kohlrausch, ibid. 49, p. 233, 1893. 
* Elsas, Wied. Ann. 44, p. 668, 1891. 62 
THE ELECTRIC CONDUCTIVITY OF LIQUIDS. 
this purpose, according to the nature of the liquid to be investi- 
gated.* 
i. For liquids of rather high conductivity (concentrated aqueous 
solutions of salts, mineral acids and bases). 
For such solutions, use may be made of the vessels employed 
by Kohlrausch f (Fig. 26). 
Two cylindrical beakers, which are reduced in size at the lower 
end, are joined together by means of a tube of about 9 mm. in 
diameter. The vessel contains from 12 to 25 c.c. of liquid. The 
electrodes consist of platinum, and are soldered to a copper wire 
which is introduced through a cover of hard rubber. 
2. For liquids of moderate conductivity (dilute aqueous solu 
Fig. 26. 
Fig. 27. 
tions of salts, mineral acids and bases, about -gL to normal; 
also concentrated solutions of many organic acids and bases). 
The resistance vessel best adapted to such solutions is that pro- 
posed by Arrhenius (Fig. 27). 
Two circular plates of heavy sheet-platinum from 3to 4 cm. in 
diameter are soldered, by means of silver solder and borax, to 
heavy copper wires; the distance between the plates should be 
about 1.5 cm. The wires are enclosed in narrow glass tubes 
* [See also Kohlrausch, Wied. Ann. 51, p. 346, 1894, for special forms of 
electrodes and vessels.—Tr.] 
f Kohlrausch, Wied. Ann. 6, p. 6,1879. METHOD OF F. KOHLRAUSCH. 
63 
which are carefully filled with thick liquid asphaltum. The joint 
between the platinum and the glass should be well covered with 
the asphalt glue. The wires are introduced through a cover 
of hard rubber which is fastened by means of a groove on to the 
glass cylindrical vessel. It is advantageous to have two such 
vessels with the electrodes, 1 and 2 cm. apart. 
3. For liquids of low conductivity (most dilute solutions of 
organic acids and bases, especially aqueous 
solutions of neutral organic compounds, as 
well as homogeneous organic liquids and 
their mixtures). 
For such liquids use is made of very 
narrow electrodes with greater surfaces; 
the apparatus of Pfeiffer* (Fig. 28) is well 
adapted to this work. 
Two glass tubes R and Rv of 3 and 3.6 
cm. in their outer diameters, are covered to 
a length of 13 cm. with platinum foils P1 
and P, the smaller tube being covered on 
the outside and the larger tube on the inside. 
The platinum-foil must form complete 
immovable cylinders; these cylinders are 
fastened to the outer glass surface by means 
of platinum wires. The larger platinum 
cylinder (soldered together by means of 
silver) is shoved into the wider tube. The 
smaller tube, after fusing together at the 
top, is then placed in the larger, so that the 
two platinum surfaces form concentric cylin- 
ders. On account of the large area, the sur- 
face of the platinum need not be covered 
with platinum-black (see p. 64). 
Fig. 28. 
The two tubes are then melted together at the bottom, as shown 
in the figure; and at the opposite end the outer tube is drawn out 
into a narrow neck, in which can be placed a glass stopper G 
which, in turn, is covered by the glass covering H. D and D' 
* Pfeiffer, Wied. Ann. 25, p. 233, ISBS. 6 4 
THE ELECTRIC CONDUCTIVITY OF LIQUIDS. 
are the two electrodes leading to the platinum wires fused into B 
and Bv The whole vessel (30 cm. high) is supported by means of 
the glass tubes fused in at the bottom, which are fastened to the 
strong brass foot F. 
If a resistance vessel is to be used, it is best to restrict one’s self 
to the form proposed by Arrhenius (Fig. 27) which, by the 
application of larger resistances, is sufficient for the majority of 
liquids. 
The electrodes must always have a sufficiently large surface; a 
surface which is too small is accompanied by too great a current 
density, which frequently produces the phenomenon of polarization ; 
the sharpness of the minimum tone depends largely on the frequency 
of the replatinizing of the surface.* 
For this purpose the electrodes are immersed in a dilute solution 
of platinum chloride acidulated with hydrochloric acid, and the 
current of a single cell is conducted through, alternating fre- 
quently the direction of the current between the electrodes; or a 
small piece of zinc is brought in contact with the platinum surface 
until the plates are covered with a coating of black, spongy plati- 
num. 
According to Grotrian,f the well-platinized electrodes should 
be saturated with hydrogen by immersing them as kathode in 
dilute sulphuric acid. It is especially necessary that the electrodes 
be well platinized. 
The Thermostat.—On account of the great influence of 
temperature on conductivity,J an accurate measurement of the 
temperature is very important. 
Although Kohlrausch § has observed an influence of liquid 
baths on the minimum tone, and therefore made his determinations 
in air at the temperature of the room, yet the following, essen- 
* Kohlrausch, Pogg. Ann. 148, p. 143, 1873, and ibid. 49, p. 235, 1893. 
•(• Wershofen, Zeit. phys. Chem. 5, p. 486, 1890. 
J For most electrolytes, a change of one degree Celsius changes the conduc- 
tivity about two percent. 
$ Kohlrausch, Wied. Ann. 26, pp. 172 and 184, 1885; Kohlrausch also ob- 
served that the telephone, if too near the apparatus, was influenced by the 
induction coil. See also Kohlrausch, Wied. Ann. 49, pp. 242 and 247, 1893. METHOD OF F. KOHLRAUSCH. 
65 
tially the arrangement proposed by Ostwald (Fig. 30), is to be 
preferred for convenience. 
The electrode vessel is supported in the iron water-bath A of 
10 to 20 I. capacity, by means of a half-circular wooden cover. 
A temperature regulator B, constructed in the ordinary manner, 
is fastened to this water-bath as shown in figure 30. 
The regulator consists of a U-tube in which is fastened, by 
means of a rubber stopper, a cylindrical tube C. This tube (Fig. 
30) is filled with oil or a concentrated solution of calcium 
chloride, and then connected with the U-tube (Fig. 29). A 
Fig. 29. 
Fig. 30. 
sufficient quantity of mercury is then conducted in through the 
funnel, after which, by suitably inclining the U-tube, the air in 
the part between the mercury and the funnel is completely 
replaced by oil or calcium chloride solution. The inflow and 
outflow of gas is indicated by the direction of the arrows. 
To increase the sensibility, the inner portion of the gas-inlet 
tube is cut off at right angles. A very small side-opening in the 
same prevents the putting-out of the flame. By conducting in or 
removing liquid, by means of the funnel, the position of the top of 
the mercury column near the gas-inlet tube can be so regulated that 
widely varying temperatures may be obtained. 66 
THE ELECTRIC CONDUCTIVITY OF LIQUIDS. 
As a motor, the windmill of Ostwald * may he used. It is 
advantageous in this case to have the fans made of thin aluminium 
plates. 
The use, however, of Raabe’s turbine seems to me, in general, 
to be more appropriate. The everywhere purchaseable turbine D, 
after thoroughly oiling the parts of the apparatus, is connected by 
means of a cork to a double wheel E, which turns on a brass 
axis. From E the motion is transferred to a smaller wheel or, as 
in the figure, directly to the stirrer which consists of a glass rod 
fastened to E and provided at the lower end with a glass or 
wooden paddle ; the glass rod rotates in a wider, well-oiled glass 
tube. By employing this thermostat, it is possible to maintain the 
temperature constant to 0.05°. For temperatures of 50° and over, 
the water is covered with a layer of paraffin ; for temperatures above 
Bo°, an altered thermostat is used as described by Bersch.f 
The Contact.—The connection of the different parts of the 
apparatus is made by means of strong copper wires, which are as 
short as possible and fastened to suitable metallic clamps. A 
perfect contact is, above all, very important. The places of con- 
tact of the wires and the binding screws are carefully cleaned from 
time to time with a file and sand-paper; the binding screws should 
be well tightened, the stopper placed firmly in the rheostat, and the 
needle of the slide brought in good contact with the wire of the 
bridge. The contact with the electrode wires is made by means 
of small cups of mercury which, like the electrode vessel, are 
placed in the opening of the wooden cover of the thermostat. The 
copper wire of the electrodes should be carefully cleaned, moistened 
with hydrochloric acid and immersed in the mercury. 
The Nature of Liquids to be Examined. 
Water.—For establishing the conductivity, aqueous solutions 
are of prime importance; it is necessary, therefore, to exercise 
special care in the selection of the water to be employed. Water 
exhibits very different degrees of conductivity, depending upon 
* Ostwald, Zeit. phys. Chem. 2, p. 565, 18S8. 
f Bersch, Zeit. phys. Chem. 8, p. 384, 1891. METHOD OF F. KOHLRAUSCH. 
67 
the manner of distillation and preservation, while perfectly pure 
distilled water exhibits an extremely low conductivity. 
The purest water obtained by Kohlrausch in a platinum appa- 
ratus had a conductivity of /£ = 0.25 X xo~10, compared with the 
mercury unit of o° = 108 ; however, it is sufficient, in general, to 
have water for which k i.io-10 to 2. xo—I°. For the meaning of 
k, see page 70. 
in a distillation apparatus with a tinned coiled tube.* Such water 
preserves (or diminishes) its conductivity if it is placed in a glass 
'The distillation of water, according to Kohlrausch, is carried on 
flask which has been used for a long time for distilled water. 
In the investigations of liquids of high conductivity (concen- 
trated salt solutions) the correction f for the conductivity of the 
water employed may be neglected ; on the other hand, with dilute 
salt solutions and other aqueous liquids of low conductivity, the 
conductivity of the water must be first determined, just as that of a 
solution (see p. 69), and taken into account. For solutions of 
very low conductivity—e.g., neutral organic compounds—the cor- 
rection, which can be only imperfectly determined, is so great that, 
even with the greater sharpness of the minimum tone, an exact 
determination of the conductivity is not possible. 
Solutions.—The substances employed must be pure, as the 
conductivity is often influenced by very slight traces of impurities. 
The conductivity for acids, bases and salts is referred to the 
number of equivalents in one liter of solution ; Ostwald denotes 
with v 32, 64 1024 those concentrations which contain 
¥2> wt • • • • ttjW equivalent weights in grams, in one liter of 
solution. For chemical purposes, solutions of v—32to v 1024 
are usually employed. 
The introduction of the previously warmed solution into the 
electrode vessel is best accomplished after the solution has been 
* Kohlrausch, Wied. Ann. 26, p. 170,1885 ; Kohlrausch and G otrian, Fogg. 
Ann. 154, p. 3, 1875; Kohlrausch, Wied. Ann. 6, pp. 36 and 49, 1879, and 
11, p. 653, 1880. Nernst, Zeit. phys. Chem. 8, p. 120, 1891, obtained water of 
k 2.10—10 by freezing ordinary distilled water; Van’t Hoff and Reicher, Zeit. 
phys. Chem. 2, p. 778, ISBB. 
j- Kohlrausch, Wied. Ann. 26, p. 191, 1885. 68 
THE ELECTRIC CONDUCTIVITY OF LIQUIDS. 
prepared ready for the experiment. However, the different dilu- 
tions can be obtained (of course, somewhat less accurately) in the 
resistance vessel. To accomplish this, half of the solution is 
removed by means of a suitable pipette, and an equal quantity of 
previously warmed water added. In this manner the dilution is 
increased two-, four-, eightfold, etc. 
All solutions must be investigated in a fresh condition, for the 
conductivity of solutions of most organic compounds as well as 
many mineral salts, acids and bases, after twenty-four hours, 
shows, for unknown reasons, a variation.* 
For dilute solutions of acids and bases (HCI, H2S04. C 2H+02, 
KOH, NaOH, NH3), Kohlrausch f has shown that at the elec- 
trode there is a noticeable absorption of the substance, which 
apparently does not take place with neutral salts. This absorption 
produces, after a time, a perfect constancy in the minimum tone. 
If this phenomenon is of a general nature, and depends upon a real 
change in the concentration of the liquid, the inconvenience can, 
as suggested by Kohlrausch, be removed only by using larger 
resistance vessels of about 500 c.c. capacity. 
Method of Operation.—As soon as the liquid takes on the 
temperature of the thermostat, the element is set in operation and 
the slide given such a position that the telephone is either silent 
or produces a minimum tone, the intensity of which increases with 
the least movement of the slide in either direction. In general, 
the adjustment is made so sharply that the two points on the scale 
at which an increase of tone may be distinctly recognized are not 
more than 2 mm. apart. Midway between these points is the 
correct position which, after some practice, can easily be deter- 
mined accurately to from 0.2 to 0.3 ram. The resistances are so 
inserted that the slide, when adjusted, will be near the middle of 
the measuring bridge ; an error of 0.3 mm. in the adjustment here 
will produce an error of about o. 1 per cent, in the value of the 
conductivity. 
Each determination should be repeated by inserting different 
resistances, and the mean value taken as the basis of the calculation. 
* Kohlrausch, Wied. Ann. 26, p. 175, 1885. 
f Kohlrausch, ibid. 26, p. 220, 1885. METHOD OF F. KOHLRAUSCH. 
69 
An indistinctness in the minimum tone may, as already sug- 
gested, be due to very different causes. The difficulty is usually 
removed by replatinizing the electrodes ; sometimes an increase in 
the electrode surface is necessary, varying according to the concen- 
tration and nature of the solution, as well as the amount of resist- 
ance inserted; frequently also, a more rapid alternation of the 
current is necessary, and in many cases the cause lies in the 
amount of resistance. A resistance of from 100 to 1000 mercury 
units gives, in general, the best results. 
After a little practice, ten to twelve solutions may easily be 
investigated in one-half an hour. 
Calculation.—'The measurements for chemical purposes are 
limited almost wholly, in recent times, to the determination of the 
molecular conductivity represented by the constant // (or X, accord- 
ing to Kohlrausch). For the meaning of this constant, see Ost- 
wald, Allgem. Chem., 2. Aufl., Bd. 11, p. 640, 1893; and Kohl- 
rausch, Wied. Ann. 6, p. 152, 1879, and 26, p. 163, 1885. 
p. is calculated from the formula: 
v b 
Hv 7 ; 
r a 
or, for aqueous solutions, taking into account the conductivity of 
the water employed, according to the formula: 
/ b bw \ * 
P* = vyl I, 
\a 7■ a rw } 
where p. represents the molecular conductivity at the dilution v; 
v the volume in liters, which contains one gram equivalent f of the 
electrolyte; 
a and b the lengths of wire to the left and right of the slide; 
aw and bw the corresponding lengths for water; 
rand rw the resistances in mercury units of the solution and the 
water; 
y the resistance capacity of the measuring vessel. 
* The formula follows directly from the proportion (p. 59b The correction 
for the conductivity of water is somewhat uncertain ; for solutions of low conduc- 
tivity the value of p is doubtful. 
f It is better to refer the conductivity to a gram-molecule of the substance, as 
i lis impossible to separate acids, bases, salts, eic., from indifferent substances. THE ELECTRIC CONDUCTIVITY OF LIQUIDS. 
In order to determine the resistance capacity of the vessel,—i. e., 
the resistance which a liquid with unit conductivity would show in 
the vessel,—a liquid is used whose conductivity is accurately known. 
A normal calcium chloride solution which has kept for a long 
time unchanged has, according to Kohlrausch, a molecular conduc- 
tivity at xB° of 112.2, and at 250 = 129.7. This value placed in 
the above formula will give the value of the constant y. For 
liquids of low conductivity and narrow electrodes, it is better to 
take a more accurately investigated solution of low conductivity,— 
e.g., a solution of tartaric acid. 
The molecular conductivity/* at 250 is according to Ostwald * : 
v 16 32 64 128 256 512 1024 2048 
p 11.40 16.03 22.47 3*-28 43-5° 59-51 81.64 109.50. 
Other suggestions see Kohlrausch, Wied. Ann. 6, pp. 49 and 
50, 1879, and Kohlrausch, Prakt. Phys. vn, p. 304, 1892. 
The reduction of the specific conductivity k to terms of // fol- 
lows from the relation p 107 k• v, where p and v have the meaning 
given above (Ostwald, Jour, prakt. Chem. N. F. 33, p. 353, 1886). 
The ratio ~ is given for a wire 1 m. long in the table of Obach. 
An abbreviated form of this table is given at end of this book. 
If the resistance of the wire is not uniform, the wire must be cali- 
brated, and a corresponding correction applied to the above value. 
The resistance r also requires a small correction. For most 
ordinary German-silver wires, an increase of i° in temperature 
increases the resistance on an average of 0.0004 parts of the whole 
value. The necessary reduction to mercury units at o° is easily 
made. 
If one wishes (which is not always permissible) to establish the 
value poo ,-—i. e., the conductivity at infinite dilution,—it is deter- 
mined indirectly, inasmuch as it does not result from direct obser- 
vation. Zeit. phys. Chem. 2, p. 843, 1888. For the calculation 
of the Ostwald constant,— 
K = . 100 
(l m) v 
(see Zeit. phys. Chem. 2, p. 278, 1888). 
*Ostwald, Zeit. phys. Chem. 3, p. 272, 1889. METHOD OF F. KOHLRAUSCH. 
71 
The value of /j. is usually determined at the temperature 250 
(the measurements of Kohlrausch were referred to 180 C.). On the 
temperature influence or the calculation of the temperature coeffi- 
cient, see Kohlrausch, Wied. Ann. 6, p. 14, 1879, and 26, p. 222, 
1885. If the determinations are made at higher temperatures, the 
error due to the dissolving of the glass must be taken into account. 
It is therefore advantageous to boil water in the electrode vessel 
several times before use. Arrhenius, Zeit. phys. Chem. 4, p. 96, 
1889; Krannhals, ibid. 5, p. 251, 1891; and Sack, Wied. Ann. 
43, p. 212, 1891. 
For the calculation of the velocity of ions and the transport 
numbers from the conductivity, see Kohlrausch, Wied. Ann. 6, p. 
160, 1879, and 26, p. 170, 1885; Lob and Nernst, Zeit. phys. 
Chem, 2, p. 948, 1888 ; Kistiakowsky, ibid. 6, p. 105, 1890; and 
Bein, Wied. Ann. 46, p. 29, 1892. 
Instead of the method of Kohlrausch, another method is usually 
employed in France (Lippman’s capillary electrometer, Wiede- 
mann, Elektrizitiit 1, pp. 468 and 480, 1882 ; Compt. rend. 83, p. 
192, 1876 ; and Ann. chim. phys. (6) 3, p. 439, 1884, and ibid.- 
(6) 23, p. 5, 1891). 
Applications of Conductivity.—Organic liquids and their 
mixtures show such a low conductivity* that this constant, in such 
cases, is of little significance. The same is true for aqueous solu- 
tions of most indifferent compounds ; here the imperfect correction 
for the conductivity of water makes an exact determination very 
difficult. 
For chemical purposes, the conductivity of aqueous solutions of 
inorganic and also organic salts, acids and bases is of special 
importance. 
1. The constant of molecular conductivity is, to a remarkable 
degree, a constitutive property, i. e., it depends upon the manner 
in which the atoms are linked together. Isomeric compounds 
seldom show equal conductivities. Important discriminations are 
also possible in stereochemical considerations. On the relation of 
conductivity to constitution, see Ostwald, Jour, prakt. Chem. 
N. F. 30, pp. 93 and 225, 1884 ; 31, p. 433, and 32, p. 300, 1885 ; 
* Walden, Zeit. phys. Chem. 8, p. 434, 1891. 72 
THE ELECTRIC CONDUCTIVITY OF LIQUIDS. 
33, p. 352, 1886 ; Zeit. phys. Chem. : Ostwald, 1, pp. 74 and 97, 
1887; 3, p. 170; ibid. p. 241; ibid. p. 369, 1889; Bethmann, 
5» P- 385, 1890; Bader, 6, p. 289, 1890; Walden, 8, p. 453, 
1891 ; 10, pp. 563 and 638, 1892 ; Berthelot, Compt. rend. 102, 
p. 46, 1891, and Ann. chim. phys. (6) 23, p. 5, 1891. 
2. The determination of the conductivity establishes, in most 
cases, the basicity of the acid. The difference between the values 
of p.wu and (v = 1024 and 32) amounts to: 
for monobasic acids A = about 10 
“ dibasic “ A = “ 18-20 
“ triba-ic “ A = “ 28—31 
“ tetrabasic “ A = “ 40 
“ pentubasic “ A = “ 50 
Walden, Zeit. phys. Chem. 1, p. 529, 1887, and 2, p. 19, 1888, 
and Ostwald, Zeit. phys. Chem. 2, p. 901, 1888. 
3. The remarkable degree to which this constant may be in- 
fluenced, and the large differences of the same for different com- 
pounds makes possible; 
(<2) The determination of the presence of very small quantities 
of impurities in a definite compound (example, water, p. 67) ; 
(b) a very sharp determination of the concentration, often at* 
very high dilutions (Kohlrausch, Ber. d. d. chem. Ges. 24, p. 
3560, 1891) ; 
(c) the approximate quantitative determination of small quan- 
tities of electrolytes in mixtures or solutions with large quantities 
of substances of rather low conductivity (Fock, Fresen. Zeit. 28, 
p. 1, 1889, and 29. p. 35, 1890, and Reichert, ibid. 28, p. 7, 
1889; Arrhenius, Zeitschr. phys. Chem. 9, p. 510, 1892) ; 
(r/) the determination of the solubility of sparingly soluble com- 
pounds in water. (F. Kohlrausch and Rose, Ber. Berl. Akad. 26, 
P- 453> i 893-) 
4. The conductivity is of special interest, on account of its 
close relation to many other properties; examples: the reaction 
velocity, dissociation phenomena, freezing point, vapor tension, 
diffusion, capillarity, viscosity, etc. See : 
Ostwald, Grundriss d. allgem. Chem. ir, p. 363, 1890; also Zeit. phys. Chem. 
Bd. I—x ; van ’t Hoff, ibid. I, p. 481, 1887; Anhenius, ibid. p. 631. 
Measurement of electromotive force; Kohlrausch, Prakt. Phys. vii, p, 311, CALIBRATION OF A WIRE. 
73 
1892; Wiedemann and Ebert, Phys. Prakt. I, p. 395, 1890; Ostwald, Lehrb. 
Allgem. Chem. 11, p. 808, 1893 ; Ostwald, Zeit. phys. Chem. 1, p. 403, 1887 ; 
Behrend, ibid. n, p. 469, 1893, and Brandenburg, ibid. 11, p. 552. 
Measurement of current-strength : Kohlrausch, Prakt. Phys. vn, p. 262,1892 ; 
Wiedemann and Ebert, Phys. Prakt. 1, p. 403, 1890; Glazebrook and Schaw, 
Phys. Prakt. I, p. 387, 1888. 
2. CALIBRATION OF A WIRE (Method of Strouhal 
and Barus).* 
Let E (Fig. 31) represent an element, and AMB the bridge 
with the wire to be calibrated; I, 11, 111, IV, Y are a number of 
nearly equal comparison resistances which, for a simple adjustment, 
are supported in the following manner: 
A German-silver wire of suitable thickness and length is divided 
into n, in figure = 5, nearly equal parts, which are soldered into 
Fig. 31. 
short, heavy, amalgamated copper wires. The wires are connected 
by means of the mercury cups 1, 2, 3 . . . , ; the — 1 
and B 6 are made by means of heavy copper wires. 
The one end iVof the wire M N, which passes through a sensitive 
reflecting galvanometer, is placed successively in the cups 1 and 2, 
and the two positions J/j and M 2 on the bridge, for which the 
galvanometer shows no deflection, are determined. The wires I 
and II are then exchanged, so that I is in the position of 11, after 
* Strouhal and Bams, Wied. Ann. xo, p. 326, 18S0. 
6 74 
THE ELECTRIC CONDUCTIVITY OF LIQUIDS. 
which the wire NM is placed in 2 and 3, and the positions M'„ 
and M% determined on the bridge, where the galvanometer shows 
no current. The wire lis then moved farther up, in that it is 
exchanged for 111 ; Wis immersed in 3 and 4, and the two posi- 
tions M'3 and Mi on the bridge where the galvanometer shows no 
current is determined. 
In this manner the bridge wire is divided into n, in the present 
case = 5 distances, Mx M 2; M'2 M 3; M\ .... which, with 
the above arrangement of the circuit, are all proportional to the 
same resistance I. 
If these lengths of equal resistances are represented in scale 
divisions by ax; a 2; a3 . . . an, the mean length 
a\ ~t~ a 2 ~1~ aS ~t~ • • • an 
n 
The bridge scale is 1000 mm. in length, and the number of 
resistances is so chosen that a = -°°° is a whole number; then the 
n 
values axa2a3 . . . differ from the calibration interval a only by 
the very small values i\ d 2 d 3 . . . 
We have then : 
al = a -1- 
a 9 = a + d 2 
an a -f- 6n 
and likewise the mean value of the observed resistances 
a\ + +•• • an | 
—i—l ?—! _L ~ a f a. 
n 
Then 
a ~h ~h •• • tin. 
n 
and therefore the correction table for the wire is : 
From o— a a 
“ a— 2 a a— d 2 
“ 2a 2>a a— 3, etc. 
summation we have ; 
For a the coirection a (5j 
“2 a “ 2a dj <52 
“ 3a “ 3a —(\— J2 etc. EXPANSION OF LIQUIDS. 
75 
For exact measurements," instead of five comparison resistances, 
nis taken equal to 10 or 20. By representing the corrections and 
the scale divisions graphically, it is an easy matter to determine 
the correction for any point on the scale. Instead of a constant 
current and galvanometer it is perhaps better to use an alternating 
current and telephone.* Large variations in the temperature of 
the room may occasion errors, f 
VII. THE EXPANSION OF LIQUIDS. 
The coefficient of linear expansion is the change in length per 
unit length of a body at o° for a change of i° in temperature. 
The coefficient of cubical expansion is the change of volume 
per unit volume at o° for a change of i° in temperature. 
The coefficient of cubical expansion of a body is very nearly 
equal to three times the linear expansion /?c=r 3 /?,. 
The coefficient of expansion usually increases with the tempera- 
ture. By the mean coefficient of expansion of a liquid for the 
temperature interval tx / is meant, the change per unit volume for 
i°, on the supposition that the expansion is uniform for each tem- 
perature interval. For expansion coefficients see Ostwald, Lehrb. 
Allgem. Chem., 2. Aufl., Bd. 1, p. 279, 1891. 
Expansion of solids, Kohlrausch, Prakt. Phys. vu, p. 95, 1892, 
and Wiedemann and Ebert, Phys. Prakt., p. 134, 1890. 
Expansion of gases, Wiedemann and Ebert, ibid. p. 78. 
* Ostwald, Lehrb. Allgem. Chem. n, p. 629, 1893. 
[f Closely related to the chapter on conductivities is the determination of the 
dielectric constant of liquids, which in recent years has become of considerable 
importance in chemistry. For the determination of this constant see especially 
method XI of Drude, Zeit. phys. Chem. 23, p. 282, 1897.—Tr.] 76 
EXPANSION OF GLASS AND LIQUIDS. 
DETERMINATION OF THE COEFFICIENT OF 
CUBICAL EXPANSION OF GLASS 
AND LIQUIDS. 
Let and sx represent the specific gravities, v and vx the volumes 
of a liquid at the temperatures / and /, and let a represent the 
coefficient of cubical expansion, then we have the equations; 
vx v [l -)- a (/i /)] or 
Vy V 
a= 1 , 
v to o 
and likewise 
J S-, 
a = L~. 
h {*l—*) 
Hence the coefficient of cubical expansion may be calculated from 
two determinations of the density or specific volume for the given 
temperature interval; on the other hand, the values vx and sx may 
be calculated if v and and also a are known. 
The coefficient of cubical expansion is usually calculated accord- 
ing to the following equation :* 
a= ZP A +_JL_ 
Pi h * Pi 
where p and px represent the weights of the liquid contained in 
the pyknometer (Fig. 32 or Fig. 33)f at the temperature / and the 
higher temperature tx\ 3/5 is the coefficient of cubical expansion of 
glass. If 3/? is known, then two weighings of the pyknometer at 
the temperatures / and tx are sufficient for the determination of «. 
For ordinary glass 3 /S can be placed, on an average, equal to 
0.000025 ; for Jena glass, very nearly 0.0000237. 
If 3/9 is to be determined, the pyknometer (Fig. 32 or Fig. 33) 
is filled with pure mercury and weighed at two different tempera- 
tures. If the coefficient of the cubical expansion of mercury is 
placed equal to 0.000182, then from the above formula we have : 
38— o . 000182 * tl 
P tx —l p 
* Kohlrausch, Prakt. Phys. vn, p. 97, 1892. 
•j- The pyknometer described in the chapter on Specific Gravity may also be 
used. COEFFICIENT OF CUBICAL EXPANSION. 
77 
To fill the pyknometer, the point is immersed in recently boiled 
mercury ; by carefully heating and cooling the pyknometer, whereby 
the mercury is slowly heated to boiling, the vessel is completely 
filled. 
If the pyknometer (Fig. 32) is used, it is placed in a thermostat 
(p. 65) and heated to two different temperatures. 
Fig. 32. 
Fig. 33. 
Fig. 34. 
The pyknometer (Fig. 33), on the contrary, is heated in the 
vapor of boiling ether and water in the arrangement shown in 
figure 34 (= one-half natural size). (Method of R. Schiff.*) 
The pyknometer is placed, by means of an iron spoon, in a pear- 
shaped vessel, which is heated by the vapor of the boiling liquid in 
* K. Schiff, Ber. d. d. chem. Ges. 18, p. 1539, 1885. EXPANSION OF GLASS AND LIQUIDS. 
the vessel below. The pyknometer carries a covering with a glass 
tube, the form of which is shown in the figure, and into which, 
when lowered, the liquid passes which overflows from the pyknom- 
eter. The side openings at the top of the vapor chamber are for a 
thermometer and a return condenser. 
The volume of the pyknometer at 34° is obtained from the 
weight of the mercury contained in it after heating in boiling 
ether;* and then by weighing a second time after heating in 
aqueous vapor, the coefficient of expansion 3 /9 can be calculated. 
The volume at o°, v 0 can be approximately calculated from the 
formula: 
».= V- 
I + 3^-t 
If the coefficient of expansion of the vessel is known, the coeffi- 
cient of the cubical expansion of the liquid to be investigated is 
calculated according to page 76. The filled pyknometer is heated 
in the vapors of liquids adapted to this work. 
The determination of the coefficient of the cubical expansion of 
glass can also be made by the use of the same formula with water 
free from air. The mean coefficient of expansion of water between 
the temperatures t and t1 is calculated j according to the equation ; 
Vx V S 5*2 
v(tx —t) ~sx (ifa t) 
The pyknometer and method (p. 28) are also applicable. 
On the dilatometric method see, among others, Kohlrausch, 
Prakt. Phys. vn, p. 97, 1890; Lachowitz, Ber. 21, p. 2206, 1888; 
Bremer, Zeit. phys. Chem. 3, p. 424, 1888; Knofler, Dissert., 
Erlangen, 1888, and Thorpe, Jour. Chem. Soc. 63, p. 262, 1893. 
The pyknometric methods, however, are in general to be preferred. 
General.—If the expansion of a liquid is to be established, the 
coefficients of expansion for different temperature intervals are 
determined, and the relation of a and t represented by means of 
equations of the form a. = a -j- b t and a— a -|- b t -j- c /2, in 
which the constants a, b, and c are determined by substituting the 
corresponding values of a and t. 
* Landolt-Bornstein, Phys. chem. Tabellen, pp. 36 and 37, 1883. 
f Landolt-Bornstein, ibid. pp. 33-35, 1883. MELTING POINT AND SOLIDIFYING POINT. 
79 
It is frequently the case that only the specific gravities and 
specific volumes are given, and the dependence of these two 
values upon the temperature represented by the interpolation 
formulas st (i -j- a t -f- b t2) and vt =vQ (i -f- a t -|- b t2), 
where st and vt represent the specific gravity and volume at t°, and 
j-0 and t0 the corresponding values at o°. The calculation of the 
constants is best made by the method of least squares.* The 
true coefficient of expansion then is ; 
1 d v , „, , , 
- • a 2b t -f- . 
v„ at 
Frequently the calculation is made according to the formula of 
Mendelejeff: 
v 0 
Vt = T=Tf 
in which k is a characteristic constant which can be determined by 
substituting the values of vO, vt, and t. The results, however, from 
this formula do not agree in all cases. Konowalow, Zeit. phys. 
Chem. i, p. 39, 1887, and 2, p. 1, 1888; Grimaldi, ibid. 1, p. 
550, 1887, and 2, p. 374, 1888, and Heilborn, ibid. 6, p. 578, 
1890, and 7, p. 367, 1891. Ibid., see tables of the expansion of 
organic liquids; for tables of the expansion of salt solutions see 
Gerlach, Spez. Gewichte der Salzldsungen, Freiburg, 1859, and 
Tschernai, J. russ. Ges., pp. 430 and 486, 1888 ; reference, Zeit. 
phys. Chem. 4, p. 483, 1889. 
VIII. THE MELTING POINT AND SOLIDIFYING 
POINT, f 
Method I.—For large quantities of substance use is made of 
the following arrangement: 
A cylinder about 3 cm. wide, which is provided with a carefully 
*Kohlrausch, Prakt. Phys. VII, p. 10, 1892. 
j Landolt, Zeit. phys. Chem. 4, p. 353, 1889. MELTING POINT AND SOLIDIFYING POINT. 
tested thermometer and a stirrer, and containing at least 15 to 20 
gm. of the substance, is placed in a large beaker glass which con- 
tains a suitable heated liquid (water, concentrated solutions of 
sodium chloride or calcium chloride, paraffin, oil). 
The hot liquid is heated for some time to a temperature above 
the probable melting point, estimated, if necessary, by a previous 
investigation of the substance. As soon as a portion of the sub- 
stance is melted, the stirrer, a glass rod bent into a glass ring, is 
moved constantly. If a thermostat with a stirring arrangement * 
is used instead of an ordinary water-bath, the temperature may be 
regulated still more accurately. 
The thermometer (as long as sufficient quantities of solid sub- 
stance is found with the molten material) is kept at a constant 
temperature for several minutes, or for a longer time when larger 
quantities of material are used. The necessary corrections to the 
observed melting point (due to the thread of mercury which pro- 
jects above the surface, etc., must not be neglected ; an accuracy 
of o.i° C. or less may be easily attained. 
The solidifying point which comes into question, especially with 
mixtures of substances, is determined in the same apparatus. 
After melting the substance the temperature of the surrounding 
water-bath (thermostat) is kept constant for some time at from 1 to 
20 below the melting point of the substance. By throwing a small 
crystal into the molten substance, the solidification is brought about 
and the temperature is then read off. The determination of the 
solidifying point requires that the temperature be held constant for 
a longer time, and, in general, that larger quantities of material be 
used than for the determination of the melting point. Twenty gm. 
are here scarcely sufficient. 
By using from 100 to 1000 gm. of substance, the melting point 
as well as the solidifying point can be kept constant for an hour. 
The least impurities frequently have great influence on the melt- 
ing point; the substances should therefore be carefully purified. 
Substance for investigation : Naphthalene, melting point = sol- 
idifying point = 80.03° C. 
Method II.—It frequently happens that only a small quantity 
* Page 65, and Kiister, Zeit. phys. Chem. 8, p. 578, 1891. DEPRESSION OF THE FREEZING POINT OF SOLUTIONS. 
of the substance can be, had for the investigation. In such cases 
it is better to make use of the following much used but inaccurate 
method for determining melting points : 
A vessel A (Fig. 35) is filled to the height shown in 
the figure with pure concentrated sulphuric acid, in which 
is immersed a thermometer on which is fastened, by means 
of platinum foil and platinum wire, a capillary tube 
closed at the lower end ; the two are so joined that the 
small portion of substance introduced into the bottom 
of the small tube lies in the immediate vicinity of the 
mercury bulb of the thermometer. 
The vessel is slowly and carefully heated, and the 
temperature at which the substance begins to melt away 
from the walls of the tube is taken as the melting point. 
The values observed for the melting point show varia- 
fig. 35- 
tions of from Ito 20, depending upon the width of the tube; with 
very narrow tubes the results are too high. The results are some- 
what concordant if the tubes used are always of the same diameter, 
about 1.5 mm. at the lower part. 
IX. DEPRESSION OF THE FREEZING POINT 
OF SOLUTIONS. 
Principle.—The freezing point of the solvent and the solution 
of known concentration are determined; the difference between 
these two temperatures is the depression of the freezing point, from 
which the molecular weight of the dissolved substance may be 
calculated according to page 89. 
1. METHOD OF BECKMANN.* 
Apparatus (Fig. 36).—The inner tube A, which is provided 
with a thermometer and stirrer, and also a side tube, contains the 
liquid, the freezing point of which is to be determined. 
* Beckmann, Zeit. pliys. Cliem. 2, pp. 638 and 715, 1887, and 7, p- 323> *B9l. 82 
DEPRESSION OF THE FREEZING POINT OF SOLUTIONS. 
A is fastened by means of a cork in the wider tube B, which in 
turn is supported, by means of a metallic cover, in the outer glass 
vessel C (from 2 to 3 1. capacity). 
The vessel C, which is provided with 
a stirrer, contains the freezing mixture. 
Between B and A is a layer of air which 
separates the liquid to be frozen from 
the freezing mixture, and consequently 
allows the liquid to cool uniformly and 
gradually. 
For accurate determinations the ther- 
mometer must be graduated to or yiy 
of a degree. A Beckmann thermometer 
is well adapted to this work. The mer- 
cury reservoir at the top is so large that 
the thermometer will also answer for deter- 
minations according to the boiling point 
method. The stirrer for the inner vessel 
should be made of platinum; a ring of 
platinum foil is soldered to a thick plati- 
num wire. A glass stirrer, however, may 
be used without any special disadvantage. 
If the inner vessel is to be closed at the 
top, the stirrer may be moved through a 
cork or rubber stopper. 
Method of Operation.—For accu- 
rate determinations the apparatus should 
be set up in a room, the temperature of 
which differs not more than one degree 
from the freezing point of the solvent. 
A temperature difference of io° may 
influence the depression of the freezing 
point as much as o.oi°. 
Fig. 36. 
The temperature of the freezing mix- 
ture should be from 3 to 40 below the freezing point of the liquid to 
be investigated. The result is influenced if the temperature for one 
observation is allowed to vary more than 1 to 20 from that of the 
other observations with the same solvent and solution. METHOD OF BECKMANN. 
83 
For aqueous solutions, suitable mixtures of snow or ice and salt 
water may be used for cooling; when working with benzene (melt- 
ing point about 5-4°) a mixture of water and ice is sufficient, 
regardless of the concentration of the solution ; for acetic acid 
(melting point 16.70) the temperature of the surrounding water 
may be lowered by means of small pieces of ice; for solutions in 
phenol (solidifying point 40° to 410) and naphthalene (solidifying 
point 80.o°), use is made of a thermostat (p. 65) or a beaker 
glass, by means of which the solidifying point of the molten sub- 
stance may be determined according to page 79. 
The freezing point of the solvent is determined in the following 
manner: 
Tube A is provided with a sharp-edged piece of platinum, tared, 
and supplied with about 15 gm. of the solvent, so that the upper 
part of the tube remains dry. The quantity of solvent is then 
accurately weighed to one centigram. 
After placing in the apparatus the liquid, during constant stir- 
ring, is cooled to near the freezing temperature, and the freezing 
induced by means of a crystal of the solvent. The thermometer 
falls usually several tenths of a degree below the freezing point, 
rises immediately after the beginning of the crystallization, and 
after thirty to sixty seconds—with sufficient separation of ice— 
attains a maximum which is taken as the freezing point of the 
solvent. 
The degree of over-cooling may slightly influence the accuracy 
of the result (to 0.02°); the over-cooling, therefore, for the 
parallel observations with the solution and solvent should be regu- 
lated as uniformly as possible (about o.i° below the freezing 
point). This is usually accomplished by introducing the ice 
crystal which induces the freezing, at correspondingly equal tem- 
perature intervals from the freezing point. For water and dilute 
aqueous solutions it is desirable that the over-cooling should be 
0.50, on account of the otherwise insufficient separation of ice; 
for concentrated aqueous solutions, on the other hand, the over- 
cooling must not be more than 0.20. 
If acetic acid is used, its hygroscopic properties must be taken 
into consideration for accurate determinations. Tube Ais then 
provided with a stopper. The error, however, introduced by the 84 
DEPRESSION OF THE FREEZING POINT OF SOLUTIONS 
absorption of water amounts to scarcely more than o.oi° in the 
reading of the thermometer.* 
The solvents, especially acetic acid, benzene, and others should 
be used only in a pure condition. 
After determining the freezing point of the solvent, which 
should be done before and after each series of observations, the 
substance to be dissolved is introduced through the side tube into 
the tube A. 
Solids are weighed off in small glass tubes, by means of which 
they are introduced into the solvent, or they may be introduced in 
Fig. 37. 
the form of pastilles, which are prepared by means of a pastille 
press. 
For the introduction of liquids, the pipette (Fig. 37) may be 
used. By means of this arrangement the liquid is blown into the 
freezing tube. If the capillary tube is very thin-walled and 
ground off sloping at the outlet, no drop will remain hanging; the 
pipette then needs only to be weighed before and after the removal 
of the liquid. The determination of the freezing point of the 
solution follows, just as for the pure solvent. 
*The use of the recent complicated apparatus of Beckmann (Zeit. phys. 
Chem. 7, p. 324, 1891) is unnecessary in this case. For difficultly soluble sub- 
stances the solution is prepared (if necessary with exclusion of the outer air), and 
observed according to the method of Raoult (p. 86). METHOD OF BECKMANN. 
85 
The introduction of crystals to induce the freezing is, especially 
during the warm months, attended with difficulty. Small crystals 
melt too quickly and larger crystals give rise to too great a change 
in concentration. Beckmann recommends for that purpose the 
contrivance (“ Impfstift ”) represented in figure 38. 
A portion of the liquid in A is sucked up into the narrow tube 
B, which is open at the lower end and closed at the upper end by 
means of a pinch-cock, and the whole placed 
in a freezing mixture and brought to freezing. 
B is then removed from A, and the substance 
thawed a little by slightly warming the walls of 
the tube at the bottom and afterward above. 
A momentary opening of the pinch-cock C is 
sufficient to remove the cylindrical substance 
from the open end of the tube. The small 
quantity of projecting substance may be 
brought into the freezing liquid by means of 
the stirrer. 
The method of Beckmann is used if an ap- 
proximate determination of the molecular 
weight is desired; the limit of accuracy is 
about five per cent, of the calculated value 
of the molecular weight. The change of 
concentration gives rise to errors; over-cool- 
ing of more than o.i° is, therefore, especially 
for concentrated solutions, to be avoided. 
An advantage of the method is the small 
quantity of substance required for a molecular 
weight determination. 
Inasmuch as a concentration which lowers 
the freezing point from 0.05 to o. i° can be in- 
Fig. 38. 
vestigated, per cent, solution, corresponding to one centigram 
of the dissolved substance, is sufficient for carrying out a molecular 
weight determination. 86 
DEPRESSION OF THE FREEZING POINT OF SOLUTIONS. 
This method is employed for all accurate determinations. A 
thick-walled open beaker of 120 to 150 c.c. capacity is placed in 
the vessel containing the freezing mixture.’ 
2. METHOD OF RAOULT. 
The (Beckmann) thermometer is so placed in the middle of the 
glass vessel that no ice freezes on the lower end of the mercury 
reservoir situated near the bottom of the vessel. The stirrer con- 
sists of platinum foil and heavy platinum wire soldered together. 
The quantity of liquid employed should always be the same, 
from 100 to 120 c.c. The solutions are previously prepared by 
weighing—with the greatest possible exclusion of air in the case of 
acetic acid. Each solution should be used only for one observa- 
tion ; the freezing point of the pure solvent is determined before 
and after each series of experiments. 
The temperature of the freezing mixture should always be kept 
constant to within i°; this temperature should be from 3 to 40 
below the freezing point of the liquid. The temperature of the 
room should be, at most, not more than 50 above the freezing point 
of the solvent. Especially does the temperature of the room in- 
fluence the result if, as with water, the ice separates as a solid 
cylinder on the glass. The error in such cases, for rather high 
temperatures of the room, may amount to 0.02°. 
The over-cooling should be as uniform as possible—about 0.05 
to o.i°; only for water and its dilute solutions, in order to obtain 
loose and finely divided ice, should this value amount to 0.50. 
The freezing is induced by the introduction of an ice crystal at a 
temperature very near the freezing point, or about o.i° above. 
The temperature is read off by means of a microscope accu- 
rately to 0.002°. 
The more concentrated the solution, the more rapidly the ther- 
mometer thread sinks, on account of the change of concentration 
due to the separation of ice. A small error is also introduced with 
concentrated solutions for the highest position of the mercury 
thread. The value of the necessary correction may be determined 
by observing, from minute to minute, the sinking of the mercury 
thread for solutions of different concentrations, for a period of ten 
to twenty minutes, and then calculating the time consumed from METHOD OF RAOULT. 
87 
the beginning of the Reparation of ice to the reading of the highest 
position of the mercury thread. This correction is sufficient, 
inasmuch as it is usually very small (at most o.ox to 0.02°), and 
really not so large as would be expected from the quantity of ice 
separated out. 
The liquid, during the separation of the ice and previously, 
must be well stirred. If a large number of determinations are to 
be made, the use of Raabe’s turbine (p. 65) is recommended. 
The stirrer is moved in a vertical direction. 
If aqueous solutions are to be investigated in midsummer when 
the temperature of the room is considerably above o°, sufficient 
quantities of loose ice are formed in the liquid in that the mercury 
reservoir of the thermometer is loosely surrounded by a platinum 
or silver net, and the thermometer fastened to a turbine (with the 
necessary care) is set in rapid motion. 
By exercising considerable care, the depression of the freezing 
point may be determined, by this method, accurately to from 
to yyVo of a degree; the further complications of the method 
(Raoult, Compt. rend. 114, p. 218, 1892, and Zeit. phys. Chem. 
9, p. 343, 1892, as well as Loomis, Ber. d. d. chem. Ges. 26, p. 
797, 1893) may be omitted. 
According to Jones (Zeit. phys. Chem. n, pp. no and 531, 
1893, as well as Ber. d. d. chem. Ges. 26, p. 547, 1893) it is 
advantageous, for a high degree of accuracy, to experiment with at 
least one liter of solution ; also to make use of a thermometer 
graduated to degree.* 
Choice of Concentration and Solvent for Freezing 
Point Determinations.—The determinations in general, espe- 
cially molecular weight determinations, should not be limited to a 
single concentration. After investigating various concentrations 
and noting the calculated molecular weight as well as the concen- 
trations in a system of coordinates, certain reference points regard- 
ing the molecular weight of the dissolved substance are obtained : 
especially if the investigations are to be extended to dilute solu- 
tions. By the method of Beckmann, using always the same 
* [See also the investigations of Loomis, Wied. Ann. 51, p. 500, 1894; 57, p. 
495, 1896; 60, 523, 1897, and Ber. d. d. chem. Ges. 26, p. 794.—Tr. ] 88 
DEPRESSION OF THE FREEZING POINT OF SOLUTIONS. 
quantity of solvent, the concentration of the solution to be inves- 
tigated is successively increased by the addition of small quantities 
of substances through the side tube (Fig. 36) into the thawed 
solution. 
Care should also be exercised in choosing the solvent, especially 
for molecular weight determinations. In doubtful cases the inves- 
tigation should be made with several solvents. 
Water may be used, so far as the conditions of solubility admit, 
excellent as solvent for organic compounds of an indifferent nature 
(not conductors). Considerable care is necessary for acids, bases, 
and salts; also for certain organic compounds (especially for high 
dilutions) the molecular weight found is too large. 
Acetic acid has perhaps the most general application. The con- 
stants are here much less dependent upon the concentration than 
with other solvents ; the calculated values for the molecular weights 
are usually normal. 
The following solvents may be used with similar results ; formic 
acid, lauric acid, stearic acid, thymol, phenol, etc. 
The acid character of these solvents, however, must always be 
taken into account. 
Benzene, which can be used only in the purest condition, is well 
adapted on account of the relatively large depression which is pro- 
duced, even by dissolving a minimum quantity of substance. 
However, substances dissolved in this solvent have a special 
tendency to form more complex molecules, which are broken up 
only at high dilutions; even then, values calculated for the molecu- 
lar weight are sometimes too large. 
This is especially true for compounds containing the hydroxyl 
group, particularly hydroxyl compounds of acid nature. 
Similar to benzene may be mentioned the solvents nitro-benzene, 
ethylene-dibromide, and naphthalene ; the high melting point and 
strong dissociative properties of the last-named compound must be 
taken into consideration. 
In regard to the influence of concentration and solvent on the freezing point 
and molecular weight, see, among others, Arrhenius, Zeit. phys. Chem. 2, p. 
491, 1888; Beckmann, ibid. 2, p. 715; Fabinyi, 3, p. 39, 1889; Magnanini, 
ibid. 3, p. 347, 1889; Eykman, ibid. 4, p. 487, 1889; Paterno, ibid. 5, p. 94, 
1890, abstract. CALCULATION OF MOLECULAR WEIGHTS. 
89 
On the use of Beckmann’s apparatus for solvents which do not 
solidify, see Nernst5, Zeit. phys. Chem. 6, p. 573, 1890; also F. 
Bauke, The Raoult Freezing Method and its Use for Chemical 
Investigations, Berlin, 1890. For substances suited for these in- 
vestigations, see references already cited. 
CALCULATION OF MOLECULAR WEIGHTS. 
The calculation of the molecular weight from the depression of 
the freezing point is based upon the empirical facts established by 
Raoult and the thermodynamical considerations of van ’t Hoff,* 
according to which one molecule of any substance dissolved in a 
definite quantity of a solvent lowers the freezing point of the 
solvent by a constant quantity. 
According to Raoult, the characteristic constant for each solvent 
may be calculated from the equation : 
ME _> 
M is the molecular weight of the dissolved substance, E the 
depression of the freezing point, P the number of grams of sub- 
stance contained in 100 gm. of solvent, and C is the characteristic 
constant (the molecular depression). 
According to van ’t Hoff, we have ; 
ME 0.02 T2 
= W ’’ 
M and E have the same values as above, p represents the num- 
ber of grams of dissolved substance contained in 100 gm. of 
solution (not solvent), T is the absolute melting point of the 
solvent, and W the heat of fusion of the solvent. 
O 02 
The constants C and are found to be very nearly equal. 
* van ’t Hoff, Zeit. phys. Chem. 1, p. 497, 1887. BOILING POINT AND VAPOR PRESSURE. 
O 02 'T 
The mean values calculated for C and ——- are as follows : 
w 
Solvent 
C 
0.02 T2 
Tv 
Water, 
. . - 18.5 
18.9 
Acetic Acid, 
. . - 38-6 
38.8 
Benzene, 
. . — 5°-° 
53-o 
Phenol, 
76.0 
Naphthalene, 
. . ■— 69.0 
69.4 
Formic Acid, 
. . — 27.7 
28.4 
Nitro-benzene, 
. . — 70.7 
69-5 
Ethylene-bromide, . . . 
. , — xiS.o 
117.0* 
The calculation of the molecular weight is usually made by 
o 02 T 
substituting the values of the constant in the formula of 
van ’t Hoff. 
On the relation of the freezing point to the electric conductivity, 
and the calculation of the van ’t Hoff coefficient i from the freezing 
point, see, among others, Zeit. phys. Chem. 1, pp. 497 and 633, 
1887, and 2, p. 491, 1888. Application of the freezing and 
boiling method, see page 108 of this work. 
X. THE BOILING POINT AND VAPOR 
PRESSURE. 
General.—The normal boiling point is the temperature of the 
vapor which rises from the liquid boiling under a pressure of 
760 mm. of mercury. 
In the broader sense, the boiling point is the temperature at 
which the vapor pressure of the liquid is great enough to overcome 
the external pressure. 
The boiling point, therefore, is a function of the external pres 
sure. 
* Constants for other solvents see, among others, Eykman, Zeit. phys. Chem. 
4, p. 515, 1889, and Raoult, Compt. rend. 95, pp. 188 and XO3O, 1882. ORDINARY METHOD FOR DETERMINING BOILING POINTS. 
91 
Distinction between the static and dynamic methods is made 
according as the pressure of a vapor above its liquid is measured at 
different temperatures, or the boiling temperature determined 
which corresponds to a definite pressure. 
In general, the determination of the normal boiling point is 
sufficient. 
i. ORDINARY METHOD FOR THE DETERMIN- 
ATION OF BOILING POINTS. 
The three forms of apparatus (Figs. 39-41) are especially appli 
cable for boiling-point determinations. 
Fig. 39. 
Fig. 40. 
Fig. 41. 
Figure 39 represents the arrangement of Berthelot.* An outer 
wide tube surrounds the neck of the flask in which the thermometer 
is placed. The flask is connected with a simple condenser. 
* Berthelot, Mec. chim., Bd. I, p. 288, 1879. 92 
BOILING POINT AND VAPOR PRESSURE. 
The apparatus figure 40 (O. Schumann *) has 
the advantage of being made entirely of glass. 
The flask figure 41 (L. Meyer) is provided 
with a return condenser at a and a stopper and 
thermometer at b. The narrow side tube has an 
arrangement to prevent the liquid which flows back 
in the cooler from coming in contact with the ther- 
mometer. 
The thermometer, which has been carefully tested, 
(see under 3, chap, xx), is, whenever possible, intro- 
duced into the vapor chamber so far that the correc- 
tion for the projecting thread of mercury may be 
neglected. 
The bumping of liquids should be prevented. 
This may be done by throwing in small pieces of 
platinum or some porous clay or soap-stone; also 
by means of a capillary tube in the stopper, through 
which a slow current of gas is conducted into the 
boiling liquid. Also by the arrangement on page 
98. 
The barometric pressure (4, chap, xx) must always 
be observed simultaneously with the determination 
of the boiling point. 
If the barometric pressure is b mm. of mercury, 
the boiling point at 760 mm. is obtained very 
closely by adding 0.0375 (760—b) degrees to the 
observed temperature. 
If the boiling point is to be determined accu- 
rately to the of a degree, the method should 
be carried out as described on page 97 and follow- 
ing; and the Beckmann apparatus (p. 104) should 
be employed. See also the simple apparatus of 
Glazebrook and Shaw, Physik. Prakt, p. 183, 
1888. 
Fig. 42. 
* Schumann, Ber. d. d. chem. Ges. 18, p. 2086, 1885. METHODS OF SIWOLOBOFF AND JONES-SCHLEIERMACH ER. 
93 
2. DETERMINATION OF THE BOILING POINTS 
OF LIQUIDS IN SMALL QUANTITIES. 
(a) Method of Siwoloboff.* 
The glass tube A is fastened to a thermometer as shown in figure 
42, and in it is placed one or two drops of the liquid whose boil- 
ing point is to be determined. 
In A is a capillary tube which may be prepared by drawing out 
a wider tube. The drawn-out portion is 
fused together in the middle and then (see 
figure) broken off above the place melted 
together. 
If the apparatus is placed in an outer tem- 
perature-bath (glycerin, water, sulphuric 
acid), small bubbles are produced in the 
capillary tube before the boiling begins ; 
these bubbles are quickly increased to a 
uniform chain of small vapor bubbles. The 
corresponding temperature is taken as the 
boiling point. Errors of 0.5 to i° are 
liable to occur with this method. 
Method of Jones-Schleiermacher.| 
By this—static—method, the temperature 
is determined at which the vapor pressure of 
the substance is equal to the atmospheric 
pressure. This temperature is the boiling 
point of the substance for the given pressure. 
Fig. 43. Fig. 44. 
A U-shaped barometer tube is formed from a clean, dry, glass 
tube of about 50 cm. in length and 6—B mm. in width, as shown 
in figure 44, so that the shorter limb ends in a hair-like capillary 
opening as in figure 43. 
About one decigram of the liquid or solid substance is introduced 
* Siwoloboff, Ber. d. d. chem. Ges. 19, p. 795, 1886. 
f Schleiermacher, Ber. d. d. chem. Ges. 24, p. 944, 1891, and Jones, ibid. p. 
2251. 94 
BOILING POINT AND VAPOR PRESSURE. 
into the dry tube through the opening of the longer limb. By 
inclining the tube (after heating a solid substance until liquefied) 
the substance can be conducted over into the shorter limb. Dry 
mercury is then allowed to flow in slowly until it stands, in both 
limbs, about 2 cm. below the closed end ; in this way the liquid 
or liquefied substance is collected above the mercury in the short 
limb. A portion of the substance which may remain in the longer 
limb will have no influence on the result. The liquid is then 
heated to faint boiling until the air clinging to the walls of the 
tube or absorbed by the liquid is completely removed through the 
capillary opening. Mercury is then carefully introduced until the 
liquid fills the shorter limb up to the wider portion of the capillary. 
The fine capillary tube is then melted off by means of a small 
pointed flame. Only a small gas-bubble remains then in the point of 
the capillary tube, the influence of which on the accuracy of the 
result may be neglected. 
The mercury in the open limb is then removed down to the 
upper end of the bend in the tube, by simply inclining the U-tube 
downward to a horizontal position. If the tube is narrowed some- 
what at the bend, the entrance of air-bubbles into the closed limb 
is prevented. 
The apparatus with a thermometer is then fastened in the (not 
too narrow) pear-shaped vessel of V. Meyer. The thermometer is 
placed as shown in figure 44. The liquid bath may be water, sul- 
phuric acid, paraffin, etc. 
The apparatus is slowly heated, and the use of a stirrer is advan- 
tageous. 
The temperature at which the mercury assumes the same height 
in the two limbs is the boiling point for the atmospheric pressure. 
If the thermometer is reliable, and the mean of several observa- 
tions is taken (also by cooling the hot liquid to the boiling temper- 
ature), an accuracy of from 0.2-0.3° maY be attained by this- 
method. DETERMINATION OF THE BOILING POINT. 
95 
3. DETERMINATION OF THE BOILING POINT 
AT DIFFERENT PRESSURES. 
In order to establish the relation between the vapor pressure and 
the boiling temperature, the dynamic method is preferable. 
A boiling-vessel, as represented in figure 40 or figure 41, is con- 
nected with an air-tight pressure regulator. 
A simple form of apparatus* is represented in figure 45. 
Fig. 45. 
The Beckmann boiling apparatus described on page 98 (which can 
be made air-tight by closing the boiling apparatus) is connected 
through the cooler K with the air-chamber W and the manometer 
O. At Tis a branch tube with a pinch-cock Q, which connects 
the apparatus with an air-pump or gas generator, so that the pres- 
sure in the apparatus can be increased or decreased at pleasure. 
The manometer is filled with pure, clear sweet oil, the specific 
gravity of which (for different temperatures) has been determined. 
The air-chamber W, which is interposed for the adjustment of 
♦ Roloff, Zeit. phys. Chem. ir, p. 25, 1893. 96 
BOILING POINT AND VAPOR PRESSURE. 
small pressure-fluctuations in the apparatus, has a capacity of at 
least 12 1. If the manometer still shows irregular variations, a 
capillary tube 10-20 cm. long is inserted. 
The closing of the apparatus absolutely air-tight from the outer 
air is accomplished (1) by surrounding the stoppers of the manom- 
eter and boiling apparatus L M R with rubber capsules fastened 
by means of wire; (2) by connecting the glass parts with thick- 
walled rubber tubing; and (3) by placing a layer of mercury q at 
the top of the cork in the air chamber.* 
The regulator is protected from the heat by placing a screen 
between it and the boiling apparatus. 
A cathetometer (2, chap, xx) is used in reading the manometer 
and thermometer; fluctuations in frequent readings of barometric 
pressure are to be taken into account. In order to eliminate the 
influence of the possible barometric variations, it is better to deter- 
mine the boiling point at normal pressure before and after each 
series of observations. 
Before making the experiment, the apparatus should be tested 
for its air-tightness by varying the internal pressure. Liquid for 
investigation, water, see Landolt-Bornstein’s Tabellen, p. 47, 
1883 ; also Schmidt, Zeit. phys. Chem. 7, p. 433, and 8, p. 628, 
1891 ; ibid. 7, p. 441, boiling apparatus with pressure regulator. 
Other pressure regulators, see L. Meyer, Lieb. Ann. 165, p. 303 ; 
Stadel and Hahn, Lieb. Ann. 195, p. 218, and Ber. d. d. chem. 
Ges. 13, p. 839, 1880; O. Schumann, Wied. Ann. 12, p. 44, and 
Ber. d. d. chem. Ges. 18, p. 2086, 1885; Brown, Phil. Mag. (5) 
7, p. 411, Perkin, Jour. Chem. Soc., p. 689, 1888, and Obach, 
Zeit. f. angew. Elektr. von Carl, p. 69, 1880. 
Apparatus for the static method, see Schmidt, Zeit. phys. Chem. 
8, p. 629, 1891 ; Kahlbaum, Ber. d. d. chem. Ges. 19, p. 2954, 
1886; Bremer, Rec. Pays-Bas 6, p. 121, 1887; Emden, Wied. 
Ann. 31, p. 145, 1887 ; Tammann, Akad. St. Petersburg, Mem. 
35, Nr. 9, 1887 ; Ref. Zeit. phys. Chem. 2, p. 42, 1888 ; Raoult, 
Zeit. phys. Chem. 2, p. 354, 1888 ; Beckmann, ibid. 4, p. 532, 
1889. 
The relation of pressure and temperature is represented graphi- 
* The apparatus may also be made air-tight by means of rubber stoppers. ELEVATION OF THE BOILING POINTS OF SOLUTIONS. 
97 
cally, or expressed by interpolation formulae of the form, log E 
a -(- b d and log. E= a b d -f- cft (Ostwald, Lehrb. Allgem. 
Chem., 2. Aufl., Bd. i, p. 313, 1891, and Schmidt, Zeit. phys. 
Chem. 7, p. 444, 1891). 
Relation of the boiling point to the constitution of organic com- 
pounds, see Marckwald, Verlag von Friedlander & Sohn, Berlin, 
1887. 
Tables of vapor pressures of solutions, see, among others, Tam- 
mann, Ref. Zeit. phys. Chem. 2, p. 42, 1888. 
Critical temperature and pressure. Method of determination. 
Pawlewski, Ber. d. d. chem. Ges. 15, p. 2460, 1882, and 
Schmidt, Lieb. Ann. 272, p. 273, 1891. 
Galitzine, Wied. Ann. 41, p. 614; Cailletet and Colardeau, 
Compt. Rend. 112, pp. 563 and 1170, 1891 ; Altschul, Zeit. phys. 
Chem. 11, p. 577, 1893, and Battelli, Ann. chim. phys. 29 (6), 
p. 400, 1893; Tables of critical data, Heilborn, Zeit. phys. Chem. 
7, p. 602, 1891 ; ibid, complete literature. 
XI. ELEVATION OF THE BOILING POINTS 
OF SOLUTIONS. 
Principle.—The boiling points of the solvent and the solution 
are determined in a suitable apparatus, and, from the elevation of 
the boiling point thus found, the molecular weight of the dissolved 
substance is calculated according to the formula on page 107. 
This method finds special use when the boiling point of the 
solvent is less than ioo° (at the highest 130°). 
i. METHOD I OF BECKMANN.* 
Apparatus,—The boiling-vessel consists of a three-tubed glass 
flask A, as shown in figure 46. 
* Beckmann, Zeit. phys. Chem. 4, p. 533, 1889, and 6, p. 437, 1890. 98 
ELEVATION OF THE BOILING POINTS OF SOLUTIONS. 
In the one tube is fastened a Beckmann thermometer, graduated 
to To or tot a degree, by means of a tightly fitting cork. In 
the middle tube b is introduced the reflux tube from the condenser 
Fig. 46. 
B, which can be employed, for most liquids, in the form given by 
Soxhlet; the opening at the top of this metallic cooler is provided 
with a calcium chloride tube, which is filled with not too finely METHOD I OF BECKMANN. 
99 
divided granules of perfectly anhydrous calcium chloride. The 
lower part of the' tube from the reflux condenser is provided at d 
with a vapor-hole, which is situated in the vapor chamber, and 
through which the evolved vapor rises to the condenser. The tube 
C, which is closed with a cork during the investigation, serves for 
the introduction of the substance into the boiling solvent. 
In order to protect the apparatus from side-heating, it is placed 
in an asbestos jacket m, which can be protected at the top from 
the heat influence of the surrounding air by covering over with 
clay. This jacket, with the boiling-apparatus, for further protec- 
tion against the flame, rests on two asbestos plates; in the middle 
of the upper one is a hole, the diameter of which is equal to that 
of the asbestos jacket. 
To prevent the liquid from bumping, a short piece of thick plat- 
inum wire j is fused into the bottom of the boiling-vessel; 
whereupon the boiling takes place uniformly with the formation of 
small bubbles of vapor only at the surface of this wire, owing to 
its greater conductivity of heat. 
The boiling-vessel is filled to the middle with glass-wool or glass 
pearls 3 to 4 mm. in diameter. Through the introduction of 
these, previously cleaned with con. hydrochloric acid, the temper- 
ature is regulated uniformly in the interior of the liquid, and over- 
heating is avoided. The subsequent cleaning of the pearls, in case 
the substance has adhered closely, is best accomplished in Soxhlet’s 
extraction apparatus. 
The substance to be dissolved is introduced, during the boiling, 
through the opening in the tube C, which is opened and closed as 
quickly as possible; whereby the evaporation, even for highly 
volatile solvents (as ether), is scarcely perceptible on account of 
the length of the tube. 
Substances which are easily liquefied are blown into the solvent 
by means of a pipette of the form represented in figure 47. 
The pipette is suitably graduated in cubic centimeters, and, when 
necessary, is provided with a calcium chloride tube. The pipette 
is introduced into the tube C. Before reweighing, the liquid is 
sucked back out of the capillary tube. 
Viscous liquids may be introduced into the apparatus by means- 
of the valve-tube represented in figure 48. ELEVATION OF THE BOILING POINTS OF SOLUTIONS. 
This tube, filled with the substance, is weighed and allowed to 
slide through the tube C into the solvent. At the bottom of the 
boiling-vessel the valve at the lower end of the tube opens and 
allows the liquids to mix. 
As far as possible, the introduction of glass into the boiling- 
vessel is to be avoided, inasmuch as any change in the level of the 
liquid in the boiling-vessel influences the vapor pressure and the 
boiling point of the liquid. 
The raising of the level i mm. corresponds to 0.002° in 
the elevation of the boiling point. The introduction of several 
tubes, as well as larger quantities of dissolved substance, will pro- 
duce a small error by decreasing the volume of the vapor-chamber. 
Fig. 47. 
Fig. 48. 
It is undesirable, therefore, to introduce solid substances in a 
vessel. Powdered substances are made into pastilles, the size of 
which depend upon the solubility of the substance (Pharm. Cen- 
tralhalle 30, p. 132, 1889). 
Method of Operation.—The boiling-vessel, together with its 
pearls, is tared on a balance which weighs accurately to i cgm.; 
it is then filled with the pure solvent to the height indicated in 
the figure, and the quantity of the same determined by weighing. 
Inasmuch as, for not too violent boiling, the temperature of the 
vapor and the pure solvent are the same in this arrangement, the 
thermometer is so inserted that the mercury reservoir is completely 
covered with the liquid without coming in contact with the pearls. 
The lower part of the tube from the reflux condenser is bent to METHOD I OF BECKMANN. 
one side, and is fastened in the boiling-vessel so that the lower 
portion is removed as far as possible from the thermometer, thereby 
preventing any direct influence, of the somewhat cooler liquid 
flowing back, on the reading of the thermometer. The lower end 
of each tube immersed in the liquid stands about i cm. from 
the pearls; hence the back-flow is not hindered through the evolu- 
tion of vapor-bubbles. 
The prepared boiling-vessel, after being wrapped with asbestos, 
is heated by means of a Bunsen burner. For ethereal solutions 
the point of a luminous flame is used; for alcohol, etc., the non- 
luminous flame of the burner is employed. If the asbestos pack- 
ing is properly adjusted, the difference in the highest reading of the 
thermometer for ether heated with the small point of the flame 
and the full Bunsen flame amounts to, at most, i° C. In 
general, it is important in the investigation of a solvent and 
its corresponding solution that the size of the flames should be as 
nearly as possible the same in the two cases. The use of a regu- 
lator-cock or the membrane gas pressure regulator of Elster * is 
advantageous, if not indispensable. Investigations in the evening 
should be avoided, on account of the irregular gas pressure at that 
time. 
The boiling should be so regulated that for ether and carbon- 
disulphide, one drop every two to five seconds, for alcohol, benzene, 
or acetic acid, one drop every five to ten seconds, falls from the con- 
denser at B. 
The boiling is then made somewhat more vigorous by means of 
a larger flame ; if, however, the boiling point has been reached or 
passed, the liquid is cooled to one-tenth of a degree below the 
boiling point and again heated, so that there is always a moderate 
boiling. After a time, the mercury assumes a constant position, 
which can be taken as the boiling point (of the solvent) only 
when it remains constant to 0.002° for at least five to ten minutes. 
The thermometer should always be gently tapped before reading off 
the temperature, as this frequently produces a slight change in the 
position of the mercury. The boiling point should always be 
determined by allowing the mercury thread in the thermometer to 
* Beckmann, Zeit. phys. Chem. 4, p. 546, 1889. 102 
ELEVATION OF THE BOILING POINTS OF SOLUTIONS. 
rise, as the definite positions of the mercury attained through the 
rising and falling of the thread show small variations. 
After reading off the boiling point, without removing the flame, 
a weighed quantity of substance is introduced through C into the 
boiling-vessel by means of the arrangements described on page 100. 
The thermometer sinks immediately, and after the complete solution 
of the substance the temperature again becomes constant, which 
is taken as the boiling point of the solution. A known quantity of 
substance is again added, as the investigations here should not, in 
general, be limited to a single concentration. The investigations 
of the same substance should succeed each other without loss of 
time. At the end of the experiments the quantity of solvent which 
has been vaporized during the investigations should be determined 
by repeated weighings of the apparatus. 
The accuracy of the results is influenced by the barometric pres- 
sure and the temperature of the room. 
A difference of i mm. in the barometric pressure corresponds, 
on an average, to a difference of 0.03° in the boiling point. 
If the use of the pressure regulator (p. 95) is omitted, care 
should be taken that no essential variations occur in the barometric 
pressure while the experiment is being carried out. For unsettled 
weather a second apparatus, with the pure boiling solvent, can be 
set up during the experiment. From the readings of the thermom- 
eter in the latter apparatus, the necessary corrections for the change 
of barometric pressure may be easily calculated. 
Sometimes it is recommended to work under reduced pressure to 
prevent decomposition, or under increased pressure to increase the 
solubility. In this case use may be advantageously made of the 
simple pressure regulator described on page 95. For this purpose 
the apparatus of Beckmann (Zeit. phys. Chem. 6, pp. 463 and 
464, 1890) should be used. 
The influence produced by the temperature of the room is 
greater, the higher the boiling point of the liquid. Changes in 
the temperature of the room during an experiment should be 
avoided. 
In order to insure a perfect adjustment of the temperature it is 
necessary, for boiling-point determinations of pure solvents, to 
first maintain the boiling from one to two hours before the ther- METHOD II OF BECKMANN. 
mometer is read. The second method of Beckmann, described 
below, is uninfluenced by the temperature of the room, and there- 
fore specially adapted to solvents of higher boiling points. 
Finally, it should be noticed that the recent Beckmann ther- 
mometer, graduated to of a degree, and that of F. O. R. 
Gotze, in Leipzig, adapted equally well to freezing points and 
boiling points, experience a slight change in the value of the 
degree, owing to the separation of large quantities of mercury. 
The degrees are smaller for high temperatures, thereby diminishing 
the elevation of the boiling point and increasing the molecular 
weight. The error at most for benzene amounts to 1.3 per cent.* 
2. METHOD II OF BECKMANN.f 
Apparatus and Method of Operation (Fig. 49).—The 
boiling-vessel A consists of a rather long tube about 2.5 cm. 
in width, in the side tube of which is fastened a coiled con- 
densing tube Kv and through the upper stopper of which is intro- 
duced a Beckmann thermometer. 
A platinum wire is fused in the bottom of the tube A, which 
is then filled with glass pearls to a height of 3 to 4 cm. 
This boiling-vessel, as shown in the figure, is placed in a vapor 
jacket B, which is made of glass or, for high boiling points, of 
copper. The jacket is provided with a side tube in which the 
reflux condenser is fastened. 
The boiling-vessel A is fastened in the vapor jacket by means of 
a cylinder of asbestos a, while the space above, between the tube 
and the jacket, is filled with asbestos wool. 
The boiling-tube and the vapor jacket contain the same solvent. 
The results are thereby made independent of the temperature of 
the outer room. A small piece of clay may be introduced into the 
vapor jacket to lessen the boiling. 
The vapor jacket with the boiling-tube rests on a small box C 
* Beckmann, Zeit. phys. Chem. 6, p. 443, 1890. 
f Beckmann, Zeit. phys. Chem. 8, p. 223, 1891. The Beckmann apparatus 
is furnished by the firm of F. O. R. Gotze, in Leipzig. 104 
ELEVATION OF THE BOILING POINTS OF SOLUTIONS. 
composed of asbestos board and water glass. A vertical section is 
represented in the figure. 
Where the flames fall upon the hot surface is a sickle-shaped 
opening, covered with wire gauze and asbestos board; the opening 
is arched over with the edge d of an asbestos covering. 
The boiling-vessel is pro- 
tected from the direct action 
of the flame, from the Bunsen 
burners placed to the sides, 
by means of the asbestos rings 
hx and hr A small flame un- 
der the boiling-vessel is neces- 
sary only for water (on ac- 
count of its high specific heat 
and heat of vaporization). 
For all other liquids the boil- 
ing of the outer liquid is suf- 
ficient to maintain the boiling 
of the inner liquid.* 
The arrangements j and s 
serve as outlets for the flame 
gases. 
If the apparatus is to be 
used for solvents of low boil- 
ing points (under 6o°), small 
Liebig condensers may be 
substituted for Kx and K\; 
for hygroscopic solvents a 
small calcium chloride tube 
is attached to the condenser. 
The solvent in the inner 
tube is either weighed in the 
tube or measured by means of a pipette ; the substance (p. 100) is 
Fig. 49. 
V V 
* Parizek and Sule hasten the operation by elevating the temperature of the 
vapor chamber a few tenths of a degree above the boiling point of the inner 
liquid, through the addition of a few drops of a substance of higher boiling 
point. APPLICATION OF METHODS I AND 11. 
introduced by means of a pipette or in the form of pastilles. 
Twenty gm. bf solvent is sufficient for the vapor chamber. 
A small correction should be applied, owing to the evaporation 
and condensation in the cooler. According to Beckmann, the quan- 
tity of liquid suspended in the vapor chamber amounts to, for very 
mobile liquids, from 0.15 to 0.2 gm.; for water about 0.35 gm. 
For further details of the method see the manipulations given for 
method 1. 
APPLICATION OF METHODS I AND ll.* 
Method i is applicable for solvents with boiling points up to 
about 130°. In general, the method is preferable for solvents 
with low boiling points. For solvents with high boiling points 
(anilin, phenol, etc.) method 11 is preferable; this method is also 
preferable for water. 
Besides its independence of the temperature of the room, 
method 11 has come into special prominence on account of,— 
1. The small quantity of the solvent and substance required for 
the experiment; 
2. The more rapid attainment of a constant boiling temperature 
(thirty to sixty minutes) ; 
3. The more convenient method for heating. A gas pressure 
regulator is unnecessary. 
In reason 1, however, there is also a slight disadvantage, inas- 
much as the accuracy is always influenced by the quantity of 
solvent. 
Choice of Concentration and Solvent (for the boiling-point 
method).—The investigation is begun with a concentration which 
produces an elevation of about o. lor 0.20 in the boiling point, and 
the content of the solution is gradually increased to ten or twenty 
per cent. The relations between the percentage content and the 
calculated molecular weights are represented graphically, and then, 
in most cases, definite conclusions are drawn regarding the magni- 
tude of the molecular weight. 
* [A more recent form of apparatus has been described by Orndorff and Cam- 
eron, Amer. Chem. Jour. 17, p. 507, 1895.—Tr.] ELEVATION OF THE BOILING POINTS OF SOLUTIONS. 
The choice of the solvent should always he carefully considered, 
the choice depending largely on the solubility of the substance and 
also its boiling point ; in general, only such substances are investi- 
gated* whose boiling point is at least 130 to 1400 above that of the 
solvent. 
If, for the use of a definite solvent, there is any uncertainty in 
regard to the dissociation of the complex molecules, the substance 
should be investigated with several solvents. 
Substances, especially hydroxyl compounds, dissolved in benzene, 
chloroform, and carbon disulphide, have a tendency to form com- 
plex molecules, which decompose more and more with increasing 
dilution. 
The molecular weights obtained with such solvents as acetic acid, 
formic acid, thymol, phenol, ether, alcohol, ethyl-acetate, and 
acetone at higher concentrations are more normal. 
In general, ethyl-ether is best adapted to this work. Its low 
price, its high dissolving capacity, its chemical indifference, and 
the ease with which the dissolved substance can be obtained again, 
give it preference over other solvents; also, the volatility and dis- 
sociative power are very advantageous for the convenience and 
accuracy of the determination ; in like manner, the large molecu- 
lar elevation is of special importance. Water is less suitable for 
the purpose. The number obtained for electrolytes should be care- 
fully tested ; the low solubility of non-electrolytes is objectionable. 
The high boiling point and the small molecular elevation are also 
a disadvantage. 
On the influence of concentration and solvent, see the work of 
Beckmann, Zeit. phys. Chem. 4, p. 532, 1889; 5, p. 76, 1890; 
6, p. 437, 1890; 8, p. 223, 1891. 
* Nernst, Zeit. phys. Chem. 8, p. 128, 1891; also 11, p. 1, 1893. Nernst 
shows that the boiling apparatus may be used for determining molecular weights 
of very volatile substances. CALCULATION OF MOLECULAR WEIGH TS. 
CALCULATION OF MOLECULAR WEIGHTS. 
According to van ’t Hoff,* the following formula holds good : 
M{rx-TJ) = 00277, 
/ w 
M represents the molecular weight of the dissolved substance ; 
p the number of grams of dissolved substances in 100 gm. of solvent; 
Tx and T0 are the absolute boiling points of the solution and sol- 
vent = the observed 273.20. Tx T0 is therefore the elevation 
of the boiling point ; Wis the heat of vaporization of the solvent. 
o 02 T 
The constant —(the molecular elevation of the boiling 
point) may be determined from the known molecular weight of the 
dissolved substance, or calculated from the heat of vaporization 
and the boiling point of the solvent. 
The following table (according to Beckmann) f contains the 
values of this constant for a number of solvents ; 
o mux Boiling Molkcular Elkvation 
solvk t. Point. of the Boiling Point. 
Ethyl-ether, .... 
. • 34-97 
21.1 
Carbon disulphide, 
. . 46.2 
23-7 
Acetone, 
• • 56.3 
16.7 
Chloroform, .... 
. . 61.2 
36.6 
Ethyl-acetate, . . . 
- - 74-6 
26.1 
Ethyl-alcohol, . . . 
• - 78.3 
ir-5 
Benzene, 
. ■ 80.3 
26.7 
Water, 
. . 100. 
5-2 
Acetic acid, .... 
. . x 18.1 
25-3 
Ethylene-bromide, . . 
. . 131.6 
63.2 
Phenol, 
. . 182.3 
30.4 
Anilin, 
. . 183.7 
32.2 + 
If a solvent is to be used, the constant of which is unknown, 
the same may be determined by dissolving in the solvent a sub- 
* Beckmann, Zeit. phys. Chem. 4, p. 533, 1889. 
V V 
f According to Parizek and Sule (Ber. d. d. chem. Ges. 26, p. 1410, 1893) 
this constant for methyl-alcohol = 9.20, and for iso-propyl-alcohol = 12.9. 
J In regard to the change of these constants with the bo ling point of the sol- 
vent for diminished pressure, see Beckmann, Zeit. phys. Chem. 6, p. 463, 1889. ELEVATION OF THE BOILING POINTS OF SOLUTIONS. 
stance of known molecular weight (ligroin, petroleum, ether, 
aqueous alcohol, etc.). 
APPLICATION OF THE BOILING-POINT AND 
FREEZING-POINT METHODS. 
In general, the chemical nature of the substance to be investi- 
gated, especially its solubility and volatility, determines which of 
the two methods is preferable. 
The freezing-point method, it is true, is no more convenient to 
operate than the boiling-point method; but it requires less time, 
and is also (not considering the investigation of concentrated solu- 
tions) capable of greater accuracy. The constants of the molecu- 
lar depression of the freezing point are greater than the correspond- 
ing constants of the molecular elevation of the boiling point. The 
freezing-point method is preferable for substances which have a 
tendency to decompose at high temperatures, although the boiling 
point can be lowered by the use of a pressure-regulator. 
The freezing-point method is independent of the barometric 
pressure, and may be used for the investigation of volatile sub- 
stances, while the simple boiling-point method has hitherto been 
limited to substances whose boiling points were at least 130° above 
that of the solvent (p. 106). 
On the other hand, the boiling-point method admits of a larger 
number of excellent solvents, as ether, alcohol, carbon disulphide, 
etc. An important advantage is the greater solubility of sub- 
stances at higher temperatures, and the greater tendency toward 
the decomposition of the complex molecular groups. For the 
investigation of concentrated solutions the temperature-reading is 
more accurate, for no essential change of concentration occurs, as 
in the freezing method. SPECIFIC HEAT. 
109 
XII. SPECIFIC HEAT. 
General.—The unit of heat is the calorie. 
The calorie is that quantity of heat required to raise the temper- 
ature of 1 gm. of water from o to i° (gram-calorie). 
If 1 gm. of water is heated to i° above the temperature of the 
room, the quantity of heat required is not equal to 1 calorie, but 
probably somewhat less (a fraction of a per cent.). 
Inasmuch as the specific heat of water depends upon the tempera- 
ture, and as experiments on heat capacity are frequently made at 
the temperature of the room t° (usually 180), the calorie at t° 
(180) is selected as the unit, so far as the method of mixtures 
(p. no) is concerned. It is the quantity of heat required to 
raise the temperature of 1 gm. of water at t° (180) i°. 
For the method of melting ice (p. 121) the mean calorie—i. e., the 
hundredth part of the heat required to raise the temperature of 
water at o° to ioo°—is usually taken as the unit. 
The mean calorie and the calorie at 180 differ, at most, not 
more than one per cent. The exact relation, at present, is not 
known with sufficient certainty. 
In regard to the large calories for thermo-chemical measure- 
ments, see page 132. 
The specific heat of a body is the quantity of heat, measured in 
calories, required to raise the temperature of the unit-mass = 1 gm. 
of the substance i°. As the specific heat in general varies some- 
what with the temperature, the temperature at which the specific 
heat is determined should always be specified. 
By the method of mixtures, and also the method of melting ice, 
only the mean specific heat is obtained—i. e., the mean value of 
the quantity of heat required to raise 1 gm. of the substance i° in 
temperature for a given temperature interval t—tx. 
If Q is the quantity of heat necessary to raise the temperature 
of 1 gm. of substance from tx to t°, then is the average 
specific heat for that temperature-interval. 
The mean specific heat increases, in most cases, proportionally SPECIFIC HEAT. 
with the temperature, and can be represented by the equation 
Ct tl = a -f- b (/-f- /j) ; ci and b are constants which can be cal- 
culated from two determinations of the mean specific heat for 
different temperature-intervals. Then the quantity of heat sup- 
plied from o to t° is Qt = atJrbt'1, from which it follows that 
—i. e., the true specific heat at t°isKt = a 2b t. 
Usually, a determination of the average specific heat is sufficient. 
The product of the specific heat and the atomic or molecular 
weight is called the atomic or molecular heat. 
1. THE METHOD OF MIXTURES. 
Principle and Calculation.—A liquid or solid heated to a 
definite temperature is intimately mixed with a liquid of known 
specific gravity at a lower temperature. Mixtures involving chem- 
ical action must always be excluded. Then the quantity of heat 
given up by the first body in cooling is placed equal to that taken 
up by the liquid in the calorimeter on heating, as the heat given 
out by the system through radiation and conduction is inappre- 
ciable. 
If P represents the weight (in grams) of the liquid or solid 
heated to the temperature T, C the unknown specific heat of the 
same, p the weight of the liquid in the calorimeter at the lower 
temperature t and of unknown specific heat c, and r the final tem- 
perature assumed by the mixture, then the quantity of heat given 
up by the heated body is P C ( T—r), and the quantity taken up 
by the liquid in the calorimeter is pc (r t). Therefore P C 
(T—r)=pc (t —/). 
Inasmuch as the parts of the calorimeter (vessel, stirrer, ther- 
mometer) take up a portion of the heat, a correction must be 
applied to the above equation. 
The quantity of heat c (r —t) must be multiplied hyp-\-w 
instead of p, where w represents the heat capacity of all the parts 
of the calorimeter. It is the number of grams of water which 
corresponds in thermal value to the parts of the apparatus—i. e., 
the quantity of heat required to raise the temperature of the ap- 
paratus i°. If the specific heat of the metallic portion 
of the apparatus, the weight of which is k gm., then the product it y METHOD Of' MIXTURES. 
is the water-equivalent and zy (r t~) the quantity of heat neces- 
sary to raise the temperature from tto r°. The specific heat of the 
substance, therefore, is,— 
_f/ + w)c (t t) . 
P{T-t) ’ 
or if, as is usually the case, water is employed in the calorimeter, 
then 
r__(P + w) (r t) 
’ 
since c may be placed approximately equal to unity (p. 109). 
(a) Specific Heat of Solids. 
Heating Vessel.—A vessel of the form of figure 50 may be 
employed. The substance is heated by means of the vapor of 
Fig. 50. 
Fig. 51. 
boiling water (and other liquids) until the temperature of the ther- 
mometer is constant. If no thermometer is at hand, the boiling 
temperature is calculated from the barometric pressure.* 
Very advantageous also is the short-necked retort A (Fig. 51) 
composed of copper or glass, in which water, nitrobenzene, di- 
phenylamine, etc., may be kept vigorously boiling. 
Not too small a quantity of the substance is placed in the small 
tube C. The heating of the retort is so adjusted that the vapor of 
the liquid condenses, for most part, at D. At a given moment the 
* Landolt-Bornstein, Physik. Chem. Tab., pp. 48 and 49, 1883. SPECIFIC HEAT. 
substance in the calorimeter is introduced into the retort, so that 
none of the heating liquid flows out. 
The substance, especially if it is a poor conductor of heat, is 
used in small pieces and weighed in the tube. As a portion of the 
substance frequently clings to the tube, the tube is reweighed after 
the experiment. 
Pulverized substances or small granules, as well as substances 
which act chemically on the liquid in the 
calorimeter, are enclosed in a small metallic 
vessel made of platinum gauze, or in a plati- 
num shell soldered with gold. The weight 
of the platinum, multiplied by the specific 
heat = 0.0324, is the water-equivalent of the 
small vessel. 
The Calorimeter (Fig. 52).—The calo- 
rimeter consists of a cylindrical, thin-walled 
vessel, made of platinum, silver, or brass. 
Glass vessels * are used only for very rough 
determinations. 
The outer surface of the vessel is polished 
to prevent radiation. The length of the 
cylinder is somewhat greater than the diam- 
eter ; the capacity should be at least 200 c.c., 
and, better, 500 c.c. 
To prevent a considerable loss of heat to 
surrounding bodies, the calorimeter, resting 
on three pieces of cork, is placed in a larger 
double-walled brass vessel. The space be- 
tween the walls is filled with water, and the 
size of the vessels so adjusted that the dis- 
tance between the inner and outer vessel is about 5 cm. at all points. 
During the investigation the vessel is provided with a cover. 
For accurate determinations the inner calorimeter vessel, resting on 
pieces of cork, is placed in one or two larger brass vessels, and 
these in turn placed in the outer double-walled vessel. 
Fig. 52. 
* Nernst, Zeit. phys. Chem. 2, p. 24, 1888; Bersch, Zeit. phys. Chem. 8, p. 
388, 1891; and Kohlrausch, Prakt. Phys. vil, p. 119, 1892. METHOD OF MIXTURES. 
The calorimeter is provided further with a small, suitable stirrer 
(platinum, brass, etc.) and a carefully tested thermometer (see under 
3, chap. xx). 
The stirrer may have the form represented in figure 52. A me- 
tallic wire, movable in a vertical direction, is soldered to a metallic 
gauze, which is provided with a slit for the thermometer; or a 
metal ring is soldered to a metallic wire at an angle of 90°. The 
stirrer may also have the form of a screw (Fig. 58, p. 131). 
The thermometer, for accurate observations, is graduated to 
°r tet of a degree, and is read by means of a microscope accu- 
rately to -g-Jj-g- of a degree. 
The heating vessel and calorimeter should be separated by means 
of a cardboard screen. 
Method of Operation.—When the substance has been heated 
to the desired temperature, and the temperature of the water in 
the calorimeter has been accurately determined, the substance is 
allowed to fall into the calorimeter with the necessary precaution, 
and, during constant stirring, the maximum temperature ris read off. 
The stirring must be carefully done. In using the stirrer repre- 
sented in figure 52, care should be taken not to remove any portion 
of the substance above the liquid. 
If water can not be employed, use may be made of such liquids 
as turpentine (sp. H. = 0.43), toluene (sp. H. = 0.40), and ani- 
lin (sp. H. = 0.49). 
The corrections to be applied are: (x) That for the water- 
equivalent of the calorimeter, stirrer, and thermometer; (2) for 
the loss of heat by radiation. 
The water-equivalent of the metallic portions is obtained by 
weighing the calorimeter vessel, together with the stirrer. Only 
the portion of the stirrer, however, which is immersed in the liquid 
is to be taken into account. Let the combined weights =tt and 
the specific heat of the metal =y, then tt y is the water-equivalent 
(y for platinum = 0.032, for silver = 0.057, and for brass, with 
sufficient accuracy = 0.094). If the combined weights are not 
more than 20 gm., the wTater-equivalent Try for platinum is only 
0.64, and for brass 1.88 gm. 
The water-equivalent of the portion of the thermometer im- 
mersed in the liquid is determined most simply by estimating the SPECIFIC HEAT. 
volume of the same by sinking into a graduated vessel. Inasmuch 
as i c.c. of glass has the same water-equivalent, 2.5 X 0.19 = 0.47, 
as 1 c.c. of mercury = 13.6 X 0.034 = 0.46, it is only necessary 
to multiply the volume v in cubic centimeters, of the portion of the 
thermometer immersed, by 0.46 to obtain the water-equivalent. 
The total water-equivalent of the apparatus, then, is w r. y -)- 
0.46 v. 
The water-equivalent of the thermometer may be determined 
somewhat more accurately by heating the same in a flame or in a 
mercury bath to 40-50° and then immersing it in the water in a 
calorimeter. If mis the weight of the water in grams, /2— tY the 
increase of temperature, and tz—12 the decrease in the temperature 
of the thermometer, then,— 
m ( 
\k~tJ 
is the water-equivalent of the thermometer. 
The loss of heat through radiation is easily understood, for it is 
evident that, when the calorimeter is heated above the temperature 
of the surroundings, a continual loss of heat takes place, which 
increases with the difference in the temperatures of the calorimeter 
and the surroundings. The final temperature, then, is too small by 
an amount J. 
The influence of the radiation can be neglected as inappreciable 
only when the adjustment of the temperature takes place quickly, 
and the maximum temperature is not more than 2-30 above that 
of the surroundings. It is also necessary that the capacity of the 
calorimeter should be at least 500 c.c. The larger the calorimeter, 
the less the influence of radiation. 
Before the investigation is begun, the calorimeter, etc., should 
be left in the observation room for some time, until the calorimeter, 
the water content of the surrounding jacket, and the liquid to be 
employed have assumed the temperature of the room. 
The method of Rumford, in which the initial temperature of 
the calorimeter is adjusted (from a previous experiment) so as to 
be as much below the temperature of the surroundings as the final 
temperature is above, can lead, in some measure, to accurate 
results only when the temperature adjustment takes place quickly METHOD OF MIXTURES. 
and the temperature change amounts to not more than 4 to 50. 
To preveqt the condensation of moisture on the outer wall of the 
colorimeter, the same should be cooled, before the experiment, to 
at least 20 below the temperature of the room. 
If the investigation requires considerable time, or if there is a 
considerable increase or decrease in temperature, then the influ- 
ence of the radiation must be fully taken into account. For 
determining this correction, the method of Regnault-Pfaundler * 
is, perhaps, most free from objection. 
1. The Fore-period.—Before the investigation is begun, the 
temperature of the calorimeter is observed at equal intervals of 
time, from minute to minute, for a period of ten minutes. 
Let these temperatures be &0 .. . #lO. If the ex- 
periment is begun at the moment when # must be read off, then 
#lO can not be determined directly, but it is ; 
// 
10 9 ' g 
$ 
—s is the average temperature change per minute for the first 
nine minutes of the fore-period. 
2. The Principal Period.—The principal period begins at the 
moment when the experiment is begun. An increase of tempera- 
ture follows, which is observed to a maximum temperature; after 
which the temperature decreases, on account of the radiation. The 
decrease at first is not uniform, as would be the case if the substance 
had given up all its excess of heat to the calorimeter immediately 
after reading off the maximum temperature. 
It is assumed that the principal period continues through ten 
minutes—i. e., after ten minutes the decrease of temperature from 
minute to minute is uniform. 
Then /0 is the temperature at the beginning of the investi- 
gation, and /4 . . . /10 the temperatures observed from minute 
to minute during the principal period. 
3. The After-period.—Finally, /10 = rO, and r1r2rsri . . . tlO 
are the temperatures observed from minute to minute during the 
after-period—i. e., the period in which the temperature change, due 
* Other corrections, Berthelot, Mec. chim. I, p. 208, 1879; Wiedemann and 
Ebert, Phys. Prakt., pp. 187 and 2x5, 1890. SPECIFIC HEAT. 
to radiation, has become uniform. Let the temperature changes 
during the fore-, principal, and after-periods be represented by 
A&, Al, At, then the mean temperature changes of the fore- and 
after-periods correspond to the mean temperatutes and r5 of the 
two periods ; that is,— 
and jr 
5 XO 6 IO 
It can be assumed, then, that the differences in the temperature 
changes A stand in the same ratio as the differences in the corre- 
sponding temperatures; if, therefore, tn and A* represent any given 
values for the principal period, we have the following proportion : 
(4-4) :0»'-jf) = (z.-».) 
or, 
At=(t -,<> ) + j*. 
5 5 
If for 4 is substituted the mean value of the temperature read off 
at the beginning and end of the nth minute, and for n all values 
from n= o to n= xo, the loss by radiation for each of the ten 
minutes of the principal period is obtained. If the sum of these A’s 
is added to the final temperature tw, we obtain /10+ as the cor- 
rected final temperature free from the influence of radiation. 
It is calculated in the following manner: 
SA =U,+ A\ + A[+ . ■ • zf') 
The following example* will serve to illustrate the method. 
The temperature of the room is 23.5, and the temperature of the 
calorimeter is read off every twenty seconds. The observed tem- 
peratures of the calorimeter are as follows : 
Time. 
Temperature. 
Time. 
Temperature. 
O. 20" 
19.78° 
9.2o// 
24.22° 
1.20// 
19.80° 
I0.20// 
24.22° 
2.20" 
19.82° 
IX.20// 
24.22° 
3.20// 
19.84° 
I2.20// 
24-215° 
4. 20// 
(Beginning of Experiment.) 
13. 20" 
24.2x5° 
5-2o// 
23-54° 
I4.20" 
24.2X0° 
6.20" 
24. IO° 
15.20" 
24.207° 
7.20// 
24.I90 
16.20" 
24.204° 
8.20" 
24.21° 
1J.20// 
24. 200° 
*Wiillner, Physik. 3, p. 407, 1875. METHOD OF MIXTURES. 
117 
From the 14th interval the temperature decreases uniformly, 
o.oi° in 3.20". The value 0.003° corresponds here to Ars in the 
formula, and the temperature 24.2050 corresponds to the value r5. 
In the fore-period the temperature increases by 0.02° each in- 
terval. The temperature immediately before the experiment, 
therefore, is 19.86°; the temperature 19.82° corresponds to the 
value $5, and 0.02° corresponds to A'K The negative sign must 
be taken into consideration. If the calorimeter before the investi- 
gation, as in this case, is at a lower temperature than that of the 
surroundings, the value is negative, otherwise positive. Hence : 
IA = 24.10-j- 24.194- 24.21 4- 24.22 4- 24.22 
. , , , 19.86 + 24.21 \ 
+ 24.22 + 24.215 + 24.215 4 10 X 19-02 j 
(0.003 + 0.02 \ 
——) 10 X 0.02; 
24.205 —19.82/ ’ 
or, 
SA = 0.015, 
and the corrected temperature,— 
= 2 4-210° -f- 0.015 = 24.225°. 
(b') Specific Heat of Liquids. 
Method of Kopp and Schiff.—The specific heat of a liquid 
may be determined in the manner already described, except that 
the liquid must be enclosed in a suitable vessel, which, after heat- 
ing, is immersed in the water of the calorimeter. The form and 
size of the calorimeter, as well as the stirrer, should conform, as far 
as possible, with the heating vessel. A ring-shaped stirrer is best 
adapted to this work. If wx is the water equivalent of the heating 
vessel, the calculation may be made from the following formula: 
(PC+a/j) {T— t) =(/ + «/) (j f), 
in which w has the same meaning as on page no. 
According to the method of Kopp, small, thin-walled, glass 
vessels, about 6 cm. high and 1.5 cm. wide, and provided with a 
narrow neck about 10 cm. in length, are used as the heating 
vessels. The filling is accomplished by means of the arrangement 118 
SPECIFIC HEAT. 
described on page 30 (Fig. 11). The vessel is heated in a mercury 
bath. The mercury during constant stirring is heated uniformly 
on a water-bath or, better, in an oil-bath, which-, in turn, is 
placed in a sand-bath covered with cotton. Simple beaker glasses 
may be used to contain the mercury and oil. The wide portion of 
the heating vessel is completely immersed in the mercury, and the 
thermometer, which has been previously adjusted, is placed in the 
immediate vicinity of the vessel. By regulating the flame, the tem- 
perature of the bath may be kept constant to within o. 1 to o. 2 of 
a degree. 
The water-equivalent wx of the heating vessel of the weight tt gm. 
is approximately equal to 0.19 tt. 
The method leads to more accurate results if the calorimeter 
and heating vessel are of the form proposed by R. Schiff.* 
The inner-vessel of the calorimeter, which is best constructed of 
platinum, has a capacity of about 600 gm., and contains 500 gm. 
of water. The total water-equivalent (including thermometer) 
may amount to about 5 gm. (sp. H. of platinum = 0.0324). 
A platinum vessel of the form represented in figure 53 with the 
cross-shaped outline may be used as a heating vessel. Its capacity 
is about 70 c.c., the inner width of an arm is about 1 cm., and the 
water-equivalent about 4 gm.; the vessel is filled to five-sixths of its 
capacity with water. Of special advantage is its large, good- 
conducting, cooling surface; for an elevation of 50 in the tempera- 
ture of the calorimeter, the maximum temperature is attained in 
from one and one-half to two minutes. Another advantage lies in 
the fact that the vessel itself serves as stirrer. 
The vessel is heated in the vapor of a suitable liquid (acetone, 
methyl-alcohol, benzene, water, toluene, xylene, and mixtures) in 
the apparatus represented in figure 54. 
A funnel-shaped copper vessel is heated in the vapor of a boiling 
liquid in the heating flask, and is connected above with a reflux 
condenser by means of two symmetrical tubes joined together in the 
form of aY. In the upper portion of the vessel is soldered a 
cross-shaped copper shell, about 10-12 cm. in length, and closed 
at the lower end; the platinum vessel of corresponding shape can 
* R. Schiff, Ann. Chem. Pharm. 234, p. 302, 1886. METHOD OF MIXTURES. 
be easily introduced into this shell. The vessel, after heating with 
a spirit-lamp, is provided with a thermometer, placed in a copper 
shell, covered with a perforated copper plate, which in turn is cov- 
ered with flannel, and heated for about twenty to thirty minutes, 
until the temperature has become constant for some time, and then 
quickly introduced into the calorimeter, which is protected by 
means of a wood or cardboard screen. 
The thermometer is removed, however, before introducing into 
Fig. 53. 
Fig. 54. 
the calorimeter, and can be replaced by a small calcium chloride 
tube. In order to remove the thermometer easily, and have a con- 
venient handle for introducing the vessel into the calorimeter, a 
thin-walled glass tube, as wide as possible and about 6-8 cm. in 
length, is fastened in the neck of the vessel by means of a cork 
ring, so that the tube does not project below the cork into the 
vessel. The thermometer is then loosely placed in, and when it is 
read, the projecting thread must be taken into consideration. 120 
SPECIFIC HEAT. 
The observation error of the method influences the result only 
from 0.5 to, at most, 1 per cent. 
Method of Andrews.—When somewhat larger quantities of 
a liquid are at hand, this method may be advantageously used. 
A heating substance, heated to a definite temperature, is im- 
mersed (1) in the liquid to be investigated, (2) in water; then, as 
the substance gives up equal quantities of heat to the two liquids, 
we have the following equation : 
{fc+w) (T-o = (A+ tv) (7;-o, 
in which P, C, and T t represent the weight, specific heat, and 
temperature elevation of the liquid, Pv Tx tx the weight and tem- 
perature elevation of the water, and w the water-equivalent of the 
calorimeter (pp. no and 113). 
The heating substance consists of a thin-walled glass globe of 
sto 10 c.c. capacity filled with mercury. Onto the globe is fused 
a capillary tube (50 cm. in length and from 0.6 to 1 mm. in 
diameter) provided with two marks and supplied with a funnel at 
the top. The distance between the marks is such that the mercury 
thread reaches the two marks when heated to about 30 and Bo°. 
In regard to the filling of the glass globe, and its heating in a 
mercury bath, see pages 77 and 118. The globe is introduced into 
the calorimeter at the moment when the cooling mercury passes 
the upper mark, and as soon (with constant stirring) as the lower 
mark is reached the vessel is removed from the calorimeter, the 
temperature of which is then read off. 
Tables of specific heats, see Berthelot, Mec. chim. I, pp. 434, 456, 467, and 
495, 1879; Thomsen, Therm. Unters. I, p. 46, 1882; Landolt-Bornstein, 
Tabellen, pp. 174 to xB6, 1883. Specific heats of organic compounds, R. 
Schiff, Lieb. Ann. 234, p. 300, 1886. Specific heats of gases, Wiillner, Exper. 
Physik. 111, p. 423, 1875; E. Wiedemann, Pogg. Ann. 157, p. I, 1876, and Wied. 
Ann. 2, p. 195, 1877. THE ICE-CALORIMETER. 
DETERMINATION OF SPECIFIC HEAT WITH 
THE ICE-CALORIMETER. 
Method of Bunsen. 
Apparatus and Method in General.—A heated substance 
is introduced into the calorimeter (Fig. 55) where a definite 
quantity of ice is melted. The quantity of ice melted is calcu- 
lated from the change of volume, and from this the quantity ot 
heat given up by the substance can be calculated. 
The calorimeter, which is made of glass, consists of an inner 
tube fused to an outer cylin- 
drical or oval glass mantle V. 
This glass mantle is nar- 
rowed at the bottom into a 
smaller tube, which is bent 
upward and provided, at the 
upper end, with a small fun- 
nel, and connected, by means 
of a forking arrangement, 
with the capillary tube A. 
The wider portion of the 
glass mantle V is filled with 
water and the lower part with 
mercury. The mercury also 
completely fills the tube S, 
the outlet of which is immersed in a small vessel filled with mercury. 
The water in Vis in part brought to freezing, and the apparatus 
i and J filled with ice and ice-water, so that the whole system 
assumes the temperature o°. The introduction then of a heated 
substance into the inner tube will convert a definite quantity of ice 
at o° to water at o°. This melting process is accompanied by a 
decrease in volume, which is evident from the fact that the capillary- 
tube sucks in a definite quantity of mercury from the small vessel. 
Dig. 55. 
Calculation.—If this quantity of mercury, obtained by weigh- 
ings of the mercury basin, is a gm., then the corresponding vol- 
ume at o° is 
13-596 C-°- 122 
SPECIFIC HEAT. 
This represents the decrease in volume due to the melting of the 
ice. According to Bunsen, i gm. of ice at o° has the volume of 
1.09082 c.c., and 1 gm. of water at o° the volume of 1.00012 c.c. 
The melting, therefore, of x gm. of ice produces a decrease of 
0.0907 c.c. in the volume. 
As the volume has been decreased by 
the quantity of ice melted is 
13-596 °-c-’ 
a 
i3-596X°-°9°7 gm' 
The melting of one gm. of ice requires 79.9 calories (heat of 
fusion). 
The melting of 
a 
13-596X0-0907 gm‘ 
of ice is equivalent, therefore, to 
—— = a mean calories (p. 109) of heat. 
*3-596 x 0.0907 0.01544 
This quantity of heat has been added to the calorimeter by the 
heated substance. If the quantity of substance = p gm., its 
temperature in Celsius degrees = t, then the mean specific heat of 
the substance between o and t° is 
a * 
0.01544/ t ■ 
Apparatus and Method in Detail.—The filling of the 
glass mantle V with previously boiled water and mercury may be 
accomplished in the following manner : 
The upper end of the tube, which extends from the bottom of 
the apparatus, is immersed in recently boiled water, whence the 
glass mantle, by careful heating, is filled to about one-third of its 
length with water. The liquid which has been sucked in is heated 
to boiling, and the open end of the tube immersed in boiling 
* The quantity of mercury corresponding to a mean calorie can be determined 
directly by introducing known quantities of water at t° in small glass bulbs into 
the calorimeter. (Schuller and Wartha, Wied. Ann. 2, p. 359, 1877.) THE ICE-CALORIMETER. 
water. When the water in the glass mantle is for the most part 
evaporated, the liquid is allowed to rise again, and the vessel is 
in that way completely filled with water free from air. Previously 
boiled mercury is then poured in until it has the same height in 
the two limbs of the tube (see the wider tube in figure). The 
water in the narrower tube is then removed by means of a pipette, 
the walls are dried, and it is then filled with mercury by means of 
a capillary-tube, so that no air-bubbles adhere to the sides. 
The funnel and the capillary suction-tube £ must be fastened in 
the mantle-tube mercury-tight.* The latter is a bent tube (Fig. 
56), which widens into a pear-shaped opening at the end which is 
immersed in the small basin. This widening is necessary to main- 
tain a perfect contact between the inner and outer mercury, which 
might otherwise be disturbed by the influence of capillarity. 
The tube may be prepared in the fol- 
lowing manner : The tube is filled with 
colored liquid and fused together at one 
end, which is then ground off with gly- 
cerine and a fine oil-stone, until the 
opening is about 0.5 mm. in diameter. 
The well-cleansed suction-tube is fast- 
ened to the glass mantle, when the ice- 
formation in the same has taken place. 
A beautiful cylinder of ice can be produced in V (see the shading 
in the figure) in the following manner: 
Two flasks from one-half to one liter capacity, one of which 
contains a large quantity of alcohol, are surrounded by a freezing 
mixture (salt and snow) at about 150 to —2o°. The flasks are 
then connected, by means of doubly perforated corks, with the 
inner tube of the calorimeter, so that the strongly cooled alcohol, 
by means of a pump, can be sucked through the tube a number of 
times, changing from one flask to the other. The calorimeter is 
placed at the same time in snow or ice-water (better, not in freez- 
ing mixtiire). 
Fig. 56. 
There is formed then, after two to three hours, from the interior 
* The funnel is not necessary. The tube may be closed with a stopper; the 
apparatus is then less liable to be broken. 124 
SPECIFIC HEAT. 
outward, a clear ice-mantle, which may easily be obtained from 
5-10 mm. in thickness, and which will suffice for a large number 
of investigations. The ice-mantle should not adhere too tightly 
to the inner wall. The ice, therefore, in immediate contact is 
thawed by repeatedly filling the tube with water some degrees 
above o°. 
After obtaining the ice-mantle, the apparatus is packed. If per- 
fectly clean, frdshly fallen snow is at hand (kept in a clean box), 
the calorimeter is packed as completely as possible in a larger ves- 
sel, which is provided with an outflow-cock for the molten ice. 
When snow is lacking, use is made of the arrangement repre- 
sented in the figure. 
The two vessels J and i are made of zinc-plate. An ice-mantle 
is formed in the inner vessel from pure distilled water. This man- 
tle surrounds the walls of the vessel to a thickness of 2 to 3 cm. 
The surface of the water in J is covered with a finely pulverized 
ice, and the vessel then provided with a well-closed metallic cover. 
The outer vessel is filled with pieces of ordinary ice, provision 
being made for the water which is formed to escape. 
If the apparatus is so packed and placed in an ice-chest or a 
specially cold room, a large number of determinations can be 
carried out at long intervals without difficulty. 
If the snow or ice-water in the vessel J is not perfectly pure, 
the thickness of the ice-mantle in V changes continually. The 
accompanying volume change will influence the results more or less. 
For the use of pure snow and ice-water a continual decrease in 
the melting of the ice-cylinder in V takes place. This is stirred, 
therefore; for, on account of the mercury pressure, the melting 
temperature in V is a little below o°, and hence a continually less 
supply of heat from without takes place. 
The investigation is made by connecting the calorimeter with a 
suitable pressure apparatus, extension of the suction-tube from 
below, or by occasioning an increase or decrease in the ice-cylinder 
through the introduction of traces of common salt into the ves- 
sel/. 
The thawing of the ice-mantle can usually be regulated by raising 
or lowering the point of the suction-tube in the mercury basin, so 
that the amount of mercury in the basin decreases only a few railli- THE ICE-CALORIMETER. 
1 25 
grams per hour. This change of weight for the period of the inves- 
tigation—usually twenty to thirty minutes—must be taken into 
account. Two mercury basins are necessary, which, changing 
every half hour, are weighed and connected with the calorimeter 
(gently tapping the suction-tube). If the thawing of the ice- 
mantle in equal intervals of time is uniform, the investigation may 
be commenced. The small corrections are then calculated from 
weighings before and after the time of the investigation. 
The investigations are carried out in a room the temperature of 
which, at most, should not be more than 5 to xo° above o°. 
The inner tube of the calorimeter contains some glass-wool on 
the bottom, and is partially filled with water (or some other suitable 
liquid). Its cork is removed only for the introduction of the sub- 
stance. The latter is heated to a constant temperature in a heating 
vessel (p. m). The heating vessel and calorimeter are separated 
by means of a cardboard screen, and set up so that an easy and 
quick transfer is possible. 
Pulverized solids are introduced in platinum shells (specific heat 
= 0.0324) ; liquids are introduced in small glass globes, which are 
filled, almost completely, at the temperature of the heating vessel, 
and then fused together. The specific heat of the glass (on an aver- 
age 0.19) should be determined by a previous investigation, and the 
water-equivalent (pp. no and 113) taken into consideration. Three- 
tenths to one gm. of substance is sufficient for most determinations. 
calorimetric method has the advantage over the mixture-calorimeter 
of a greater and even extraordinary accuracy for the use of small 
quantities of substances ; the substantially lower cost of the appa- 
ratus, in comparison with the better mixture-calorimeter, should 
also be mentioned. On the other hand, extreme care is required 
in working with the ice-calorimeter. 
Ice-calorimeter and Mixture-calorimeter.—The ice- 
In regard to the ice-calorimeter, see: Bunsen, Pogg. Ann. 141, p. I, 1870 ; * 
Schuller and Wartha, Wied. Ann. 2, p. 359, 1877; Bliimcke, ibid. 25, p. 154, 
1885; Dieterici, ibid. 33, p. 425, 1888, and 38, 1889. Literature on the use of 
the ice-calorimeter for measuring the heats of solution, neutralization, vaporiza- 
tion, and combustion, see the following chapters. 
* This method of measuring the mercury in a graduated tube is less accurate 
than the modified method of Schuller and Wartha. 126 
HEAT OF FUSION. 
XIII. HEAT OF FUSION. 
By the heat of fusion is meant that quantity of heat, measured in 
calories, which is required to melt i gm. of a substance. 
The heat of solidification is the quantity of heat set free when 
i gm. of a substance is changed to a solid state. 
The molecular heat of fusion or solidification is the product 
of molecular weight and the heat of fusion or solidification, there- 
fore the heat of fusion or solidification referred to one molecular 
weight in grams. 
Principle and Calculation.—The method of mixtures is 
usually employed. 
i. If the melting point of the substance is below the tempera- 
ture of the room (benzene, etc.), the substance is allowed to 
solidify and is introduced, in a suitable vessel, into the calorimeter, 
which contains at least enough liquid, so that the final temperature 
is above the melting temperature of the substance. 
The quantity of heat which the introduced substance takes up is 
the sum of three values : 
(a) The quantity of heat taken up in heating from the tempera- 
ture /, the temperature of the solid substance when introduced into 
the calorimeter, to the melting temperature /0. A knowledge, 
therefore, of the specific heat cx of the solid is necessary. 
(b) The quantity of heat taken up in changing from the solid to 
the liquid state at the temperature /0 (heat of fusion). 
(c) The quantity of heat required to heat the liquid from the 
temperature /0 to the final temperature of the calorimeter r. The 
specific heat c 2 of the liquid substance must therefore be known. 
Let L represent the heat of fusion of the substance, px the weight 
in grams of the substance used, p2 the weight of the water in the 
calorimeter, the initial temperature of which is T; wx the water- 
equivalent of the vessel containing the substance, w2 the water- 
equivalent of the different parts of the calorimeter ; then the 
quantity of heat given up by the calorimeter and contents HEAT OF FUSION. 
127 
= (/2+ w2) (T —r), and the quantity of heat taken up by the 
substance and vessel 
—P\ l>i (4) —O+P' + ci (T —Ol "t" w\ (r 
equating these two values we obtain 
(A + T~ T) iT Q —P\ Ol — *1) + C‘l iT —Q] 
A 
2. If the melting point of the substance is below the tempera- 
ture of the room in general, the heat of solidification is determined. 
The procedure is the reverse of that just described. 
The substance is heated above the melting point f0 to the tem- 
perature tv and introduced into the calorimeter, the temperature r 
of which lies below the temperature /0. Then, if Eis the heat of 
solidification of the substance, and the remaining letters have the 
meaning given above, the quantity of heat given up by the intro- 
duced substance (-(- vessel) is 
—P\ (A —O + +A(A T)1 + (A —T) 
and the quantity of heat taken up by the calorimeter 
= (A + w2)(r— T)- 
Therefore 
„ _ (A + w2)(r —T) —r)— A 02 (/i —V+ <i (/0 t)] 
A T 
A 
Method of Operation,—The chapter on Specific Heat may be 
referred to here. The solid or liquid substance is usually introduced 
in a small, thin-walled flask (p. 118). The specific heats of the 
solid and liquid substances are determined for the temperature-inter- 
val of the experiment. The influence of radiation is to be taken 
into consideration, as described on page 115. 
The determination of the heat of solidification according to the 
above method is sometimes very uncertain. Very different values 
are frequently obtained for the heat of fusion and solidification. 
This indicates that substances, after solidifying, are not always in the 
same condition. The determination of the heat of solidification, 
therefore, is avoided in many cases. 
Assuming the substance to be soluble in the liquid in the calor- 128 
HEAT OF FUSION. 
imeter, and its melting point to be e.g. 6o°, then the following 
values must be determined : 
(a) The heat of solution of the solid substance at the tempera- 
ture of the room (iB°) according to page 137. 
(' b) The specific heat of the solid for the temperature interval, 
from the temperature of the room to a little below the melting 
temperature. This specific heat may be easily calculated if the 
quantity of heat, apart from the heat of solution of the sub- 
stance dissolved at the temperature of the room, is known, which is 
given up by the substance, previously heated to about 5 50, when 
dissolved in the liquid in the calorimeter. 
(c) The specific heat of the liquid substance for the temperature 
interval 65°-ioo°. This value is calculated from the difference 
between the quantity of heat given up when the liquid substance, 
heated to 65°, is dissolved in the calorimeter at the temperature of 
the room, and that given up when the substance at ioo° is dis- 
solved at the temperature of the room. 
If these three values are known, the heat of fusion may be 
easily calculated; for the total quantity of heat which 1 gm. of 
the molten substance heated to 65° gives up in the calorimeter, is 
the sum of; (a) The specific heat of the liquid substance multi- 
plied by the temperature interval 6s°-6o° ; (b) the heat of fusion 
at 6o° ; (c) the specific heat of the solid substance multiplied by 
the temperature interval 6o°-iB° ; and (d) the heat of solution 
of 1 gm. of the substance at 180. 
CALCULATION OF THE HEAT OF FUSION 
FROM THE DEPRESSION OF THE 
FREEZING POINT. 
This indirect method can be used only for approximate deter- 
minations. 
According to van ’t Hoff we have : 
T 0.02 T2 
X== A 
L represents the heat of fusion of the solvent, T the absolute 
freezing point of the same, and A the molecular depression of the 
freezing point for the given solvent. The variations between the HEAT OF VAPORIZATION. 
observed and calculated values amount to usually less than 5 per 
cent. 
See p. 90 and van ’t Hoff, Zeit. phys. Chem. I, p. 497, 1887 ; Eykmann, 
ibid. 3, p. 208, 1889. 
Tables of heats of fusion, Berthelot, Mec. chim. I, p. 423, 1879, an(i Eandolt- 
Bornstein, Tabellen, p. 188, 1883. 
XIV. HEAT OF VAPORIZATION. 
By the heat of vaporization is meant the quantity of heat, 
measured in calories, which is required to change i gm. of a 
liquid at its boiling point to a vapor at the same temperature. The 
heat of vaporization is equal to the heat of condensation. 
The molecular heat of vaporization is the product of the molec- 
ular weight and the heat of vaporization. 
METHOD OF R. SCHIFF. 
Principle and Calculation.—The heat of condensation is 
here determined. A definite quantity of liquid is vaporized and 
the vapor, freed from all previous condensations, is condensed to a 
liquid in a calorimeter. 
If p is the weight in grams of the liquid changed to vapor, T 
the boiling point, r the final temperature in the calorimeter, c the 
mean specific heat of the liquid between T and r°, and V the heat 
of vaporization, then the quantity of heat in calories, which the con- 
densed vapor gives up to the calorimeter is,p\c(T—r) -f- TJ, 
and the quantity of heat taken up by the calorimeter and contents, 
if P is the quantity of water in grams, w the water-equivalent of 
the parts of the calorimeter and t the initial temperature, is 
(P -f- w) (r f). By equating these two values we obtain ; 
y_ iF +w)(r—t)—p c ( T— r) 
P 
Apparatus and Method of Operation.—The calorimeter has 
the usual form (see chapter on Specific Heats). It is made of brass HEAT OF VAPORIZATION. 
surrounded by a water mantle, and contains about one liter of 
water. 
The liquid is vaporized in a small round flask, which is placed at 
some distance from the calorimeter, and is connected by means of 
a stopper with a wide glass tube, about 30 cm. long, which is bent 
upward at an angle of 120°. This tube is wrapped with wadding 
as far as possible, and is surrounded by an outer tube. The vapor 
passes from the inner tube into the arrangement represented in figure 
Fig. 57. 
Fig. 58. 
57, which is best made of silver. The inflowing vapor moves first 
in the direction of the arrow, then into the inner silver tube ad- 
justed almost to the upper opening, then downward, when the tem- 
perature of the tube will become the same as that of the vapor. A 
previous condensation is in this way avoided. The vapor then 
passes into the (silver) coiled tube (Fig. 58) connected by means 
of a cork. This tube projects at most from 2to 3 mm. out of the 
water in the calorimeter. The coiled tube terminates below in a HEAT OF VAPORIZATION. 
131 
vessel of about 70 c.c. capacity, in which the condensed liquid is 
collected. 
The thermometer is introduced into the middle of the calorimeter, 
or between the metallic coil and the wall of the calorimeter, after 
which a ring-shaped stirrer or the specially adapted stirrer (Fig. 58) 
of brass with an ivory handle is arranged. 
On the determination of the water-equivalent (calorimeter, stirrer, 
thermometer), see pp. no and Ix 3 ; the same is about 15 to 20 gm. 
During the investigation the calorimeter and thermometer are 
carefully protected from the influence of the radiation at the sides 
of the heated vessel and the hot conducting tube by means of card- 
board screens. 
For estimating the temperature, the loss of heat by radiation must 
be taken into account according to p. 115, as the time of the experi- 
ment amounts to at least five minutes. 
The weight of the liquid vaporized is determined by weighing in 
the coiled tube. Sufficient liquid (20 to 30 gm.) is vaporized, so 
that the increase in the temperature of the water in the calorimeter 
amounts to 4 to s°. 
At the end of the investigation, after removing the flame, the 
small stopper (Fig. 57) should be loosened, otherwise the rapid 
rushing in of air may remove a portion of the liquid from the coiled 
tube. Substance for investigation: water, heat of vaporization 
= 537-3 calories. 
HEAT OF VAPORIZATION AND ELEVATION OF 
THE BOILING POINT. 
The heat of vaporization can be approximately calculated from 
the elevation of the boiling point, just as the heat of fusion can be 
calculated from the depression of the freezing point. The formula 
is as follows : 
W— _ 0-02 A 
See p. 107. Tables of heats of vaporization, see Berthelot, Mec. chim. I, p. 418, 
1879, and Landolt-Bornstein, Tabellen pp. 189 and 190, 1883. 
Heat of vaporization of organic compounds, R. Schiff, Lieb. Ann. 234, p. 338, 
1886, and H. Jahn, Zeit. phys. Chem. 11, p. 790, 1893. 
Determination of the heat of vaporization with the ice-calorimeter, Dieterici, 
Wied. Ann. 38, p. X, 1889, and H. Jahn, Zeit. phys. Chem. 11, p. 788, 1893. 
For the special advantages of the ice-calorimetric method see p. 125. 132 
THERMOCHEMICAL CONSTANTS. 
XV. THERMOCHEMICAL CONSTANTS. 
General.—So far, the method of mixtures has been usually 
employed in determining thermochemical values. The unit of 
heat, therefore, is the calorie at 180 (p. 109). 
Inasmuch as the value of the thermal effect measured in small 
calories (cal.) is usually too large, and the last figure uncertain, it 
is better to employ as unit a value equal to 100 times that calorie. 
This large calorie is represented by K, and is approximately equal 
to the quantity of heat which is necessary to heat 1 gm. of water 
from o° to ioo°. 
Besides that, the calorie of Berthelot should be mentioned, 
which is equal to 1000 small calories, and is represented by Cal., 
to distinguish it from cal. 
The thermal effect is always referred to gram-formula-weight. 
This is mentioned on account of its dependence upon the temper- 
ature. As far as the method of mixtures is concerned, the tem- 
perature of the room (180) comes into consideration. 
Of the different methods of notation in use, that of J. Thomsen 
is preferable on account of its brevity. 
The thermal equation, 
K, Cl, 03= 959 K, 
means that in the formation of one gram-molecule of potassium 
chlorate from the elements, 959 large calories of heat are set free 
(heat of formation) ; KCI, 03 is the thermal effect of the salt when 
formed from potassium chloride and oxygen, K, Cl, 03, aq the 
thermal effect in forming one gram-molecule of potassium chlorate 
in aqueous solution from the elements, KCI03, aq the thermal 
effect of dissolving one gram-molecule of potassium chlorate in a 
definite quantity of water (heat of solution). KOHaq, HClaq, 
is the quantity of heat set free in the neutralization of one gram- 
molecule of potassium hydrate and hydrochloric acid in dilute 
aqueous solutions (heat of neutralization). The state of aggre- 
gation, in case of doubt, is represented by means of indices 
(HsO„„ H,O„ H,0.). HEAT OF NEUTRALIZATION. 
133 
If several reactions are possible between two substances, combi- 
nations, apd decompositions, the latter are represented by a colon 
(HgO : Cl2; SbCl3; aq). 
The most important law of thermochemistry is the law of Hess, 
according to which the thermal effect of any chemical change is 
the same whether the change consists of one phase or any number 
of separate phases,—e.g. ; 
or,— 
K, Cl =H, Cl, aq +K,O,H, aq + HCI aq, KOH aq H2, O KCI, aq. 
C, O + CO,O = C,02 ; 
i. THE HEAT OF NEUTRALIZATION. 
By the heat of neutralization of a monobasic acid and a base is 
meant the amount of heat evolved when one gram-molecule of the 
acid and one gram-molecule of the base dissolved in water are 
mixed. For polybasic acids, as many heats of neutralization are 
distinguished as there are basicities (H3PO4 aq,KOH aq; H3P04aq, 
2KOH aq ; H3P04aq, 3KOH aq). 
Apparatus.—The use of a mixture calorimeter (Fig. 59) is 
advantageous. A and B are two cylindrical vessels, somewhat 
higher than wide, with a capacity of 1000 c.c. (A), and 500 c.c. (i?) 
or at least 500 to 250 c.c. As material, platinum and pure or gold- 
plated silver are to be recommended; for weak acids and bases, 
nickel-plated brass may be used ; glass vessels (p. 112) can be used 
only for very rough measurements. The outer cylinders C and D, 
in which A, supported by means of three cork-points, is placed, 
consist of brass (polished on the interior surface). CorD is 
double-walled, and contains air or is filled with water. During the 
investigation both vessels are provided with covers with suitable 
openings. The vessel Bis narrowed below into the tube r, which 
discharges below the upper edge of A and can be opened and closed 
by means of the valve v. 
As stirring arrangement for A and B, the stirrer on page 113 is 
to be recommended, which, for a large number of experiments, can 
be connected with a turbine (p. 65). 
The thermometers in A and B are graduated to Ag- of a degree, 
and are read by means of a microscope or telescope (after previous THERMOCHEMICAL CONSTANTS. 
tapping) to 0.0020. From time to time these thermometers should 
be compared by immersing the two simultaneously in a liquid; the 
necessary correction is to be applied.* 
On the determination of the water-equivalent of the vessel A, 
stirrer and thermometer, see pages no and 113. The total water- 
equivalent amounts to about 5 to 10 gm. 
Fig. 59. 
A card-board or asbestos screen should be placed between the 
observer and the calorimeter. 
Method of Operation and Calculation.—The observations 
should be made in a room the temperature of which is as constant 
as possible. The temperature best adapted is iß° to, at most, 20°. 
The solutions for investigation are usually, very dilute : ordinarily 
* See also J. Thomsen, Therm. Unters. in, p. 341, 1883. HEAT OF NEUTRALIZATION. 
one gram-equivalent of the acid and base in 100 or 200 gram- 
molecules of water (NaOH -j- 100 or 200 H2O ; H2S04 -f- 200 or 
400 H2O). 
Sometimes still higher dilutions are used, e.g., to prevent pre- 
cipitation. The use of concentrated solutions should be avoided 
as much as possible. 
It is advantageous to have a simple fractional part of the molec- 
ular weight of the solution in the calorimeter. For a solution 
then, of NaOH -j- 100 H2O (molecular weight 1840 gm.) %or 
yk of a gram-molecule is used ; the solution would then contain 
450 or 300 gm. of water. Likewise for a solution of 2504 
-(- iooH20, or yfc equivalent should be placed in the calor- 
imeter. 
The solutions are best weighed off in the calorimeter vessels. 
It is immaterial which of the two vessels A and B contain the acid 
or base. 
At the beginning of the investigation, the two solutions are 
constantly stirred until their temperature change amounts only to a 
few thousandths of a degree in several minutes. Then, after read- 
ing the temperature, the valve v is opened. The adjustment of 
the temperature usually takes place within one minute (especially 
if the temperature is not lowered). If the temperature differs not 
more than i° from the temperature of the surroundings, it will 
remain constant for several minutes. 
A correction for the loss of heat by radiation, then, is unnecessary; 
otherwise see page 115. 
If a and b are the weights in grams of the water in the solutions 
(usually a= b) contained in A and B, and 4 and tb the tempera- 
tures at the time of the mixing, r the final temperature of the 
system, w the water-equivalent of the parts of the apparatus which 
come into consideration, and —■ the fraction of a gram-molecule 
which was dissolved in the solutions contained in A and B, then 
the heat of neutralization A 7" for 1 gram-molecule of acid and base, 
in large calories (p. 132) =A" is given by the expression : 
N= WO (r~ *») +(a+W) (T M]- 
The specific heat of the solution is here taken equal to unity, THKRMOCHEMICAL CONSTANTS. 
which can be done for the dilution under consideration. The error 
amounts to less than one per cent. See Tables of Specific Heats : 
Thomsen, Therm. Unters. i, p. 46, 1882. 
Special Rules for Determining Heats of Neutralization, 
—When it is required to determine the heat of neutralization of a 
polybasic acid with a monovalent base, or a polyvalent base with a 
monobasic acid, the thermal effect is calculated for the neutraliza- 
tion of each of the basicities separately. 
Precipitations should be avoided if possible; in case a precipi- 
tate is formed, the heat of precipitation (p. 138) must be subtracted 
from the heat of neutralization. For incomplete precipitates, the 
necessary correction is calculated. 
The state of aggregation of the substance acting on another 
should be specified in cases where doubt is possible ; if the acid or 
base is a solid or gas, the correction for the heat of fusion and solu- 
tion or the heat of absorption (p. 138) must be applied as far as 
possible ; e.g., from the thermal effect (2NaOH aq,C02), which refers 
to the neutralization of aqueous sodium hydrate with gaseous car- 
bonic acid, must be subtracted the thermal effect (CO2, aq); i.e., 
the heat of absorption of carbonic acid, thereby the true heat of 
neutralization (2NaOH aq,C02 aq) is obtained. 
If for any reason the direct mixture of an acid and a base is not 
possible, or a control determination is desired, an indirect deter- 
mination is made either by the decomposition of a salt with an acid 
or base or by the interaction of two salts (see p. 133, law of Hess). 
The heat of neutralization of barium hydrate with chloric acid 
can be calculated from the equation : 
BaCl206 aq,H2S04 aq = Ba02H2 aq,H2S04 aq Ba02H2 aq, 2HC103 a<B 
Likewise we have the equation : 
BaCl2 aq, K2S04 aq = Ba02H2 aq,H2S04aq Ba02H2 aq. 2HCI aq 2KOII aq, 
H2S04 aq -f- 2KOH aq, 2HCI aq. 
When four values are known the fifth can be calculated. 
Tables of heats of neutralization, see Thomsen, Therm. Unters. I, pp. 295 and 
418, 1882; and Berthelot, Mec. chim. I, p. 384, 1879. Influences of tempera- 
ture, Thomsen, Therm. Unters. I, p. 68, 1882. 
Measurement of the heat of neutralization with the ice-calorimeter, Jahn,Wied. 
Ann. 43, p. 307, 1891. HEAT OF SOLUTION. 
137 
2. HEAT OF SOLUTION. 
By the heat of solution is meant the thermal effect produced by 
dissolving one molecular weight of a substance in a given number 
of molecules of water (or other solvents). 
The heat of solution is sometimes positive and sometimes nega- 
tive. It varies with the quantity of water used, and likewise with 
the temperature. Both must therefore be specified. 
Apparatus and Method of Operation.—The mixture calor- 
imeter described on page 112 may be employed. The same can be 
provided with a Beckmann thermometer. Glass apparatus (p. 112) 
is sometimes used for rough determinations. 
In regard to the quantity of substance to be dissolved, see re- 
marks on page 135. Here also a rational fraction of a gram- 
molecule = -I- is dissolved in a quantity of water, so that the solu- 
tion contains 200 or 400 gram-molecules of water to one equivalent 
of the substance. 
-b. gram-molecule of the substance to be dissolved and the cor- 
responding quantity of water = a gm. is weighed off in the 
calorimeter. 
If w is the water-equivalent (pp. no and 113), r the final tem- 
perature of the system, and t the initial temperature, then the heat 
of solution Z, measured in large calories, is : 
L -2 (a 4- w) (r—/). 
100v v ' 
The specific heat of the solution is here placed equal to unity. 
This can be done only for dilute solutions, not for concentrated. 
For such cases, see Tables of Specific Heats, Thomsen, Therm. 
Unters. 1, p. 46, 1882, and Berthelot, Mec. chim. 1, p. 495, 1879. 
In regard to the method of operation, it is only necessary to add 
to what was said on the method of mixtures (p. 112) that the 
investigation is commenced when the substance to be dissolved has 
assumed the temperature tof the water in the calorimeter. To 
accomplish this, the substance is introduced into the water of the 
calorimeter, in a weighed quantity, in a small, thin-walled glass 
bulb. After the temperature has become settled, the glass bulb is 138 
THERMOCHEMICAL CONSTANTS. 
broken by means of the stirrer or two pieces of glass introduced 
into the calorimeter. 
The accuracy of the results depends upon the rapidity with 
which the substance dissolves. If the investigation continues for 
several minutes, or if the increase or decrease of temperature 
amounts to several degrees, the loss of heat by radiation must be 
taken into account according to page 115. 
Substances for investigation; iNaCI -f- io°H20, heat of solu- 
tion 11.8 K \ [MgS04 -)- yH20] heat of solu- 
tion = 38 K (according to Thomsen). 
For difficultly soluble substances, compare the special methods 
of Thomsen, Therm. Unters. 11, p. 232, 1882 ; hi, pp. 328 and 
341, 1883. 
Sometimes the heat of precipitation, numerically equal to the 
heat of solution, is determined ; i. e., the quantity of heat which is 
set free in the separation of a gram-molecule of a substance from a 
solution. By a suitable reaction, a substance is formed in a solution 
(1) at such a dilution that no precipitate is formed, (2) so that the 
substance is precipitated as completely as possible. The heat of solu- 
tion is calculated from the difference of these two thermal effects. 
If the heat of solution of a substance containing water of 
crystallization is determined, care should be taken that the water 
content slightly exceeds the normal water of crystallization, rather 
than that a loss of the water of crystallization takes place. The 
quantity of solvent is then chosen so that, if the substance con- 
tains n molecules of water of crystallization, 200 n or 400 n 
molecules of water are used for each equivalent of the substance 
(Na2SO4 -j- ioH20, 390H20). See Heat of Hydration, page 140. 
The state of aggregation of the substance to be dissolved must 
be taken into consideration, and if necessary should be specified. 
For gases, the heat of absorption is to be considered ; i. e., the 
quantity of heat set free when one molecular weight of a gas is 
dissolved in a constant quantity of water. 
Thomsen, Therm. Unters. T, p. 257, 1882. Tables of heats of solution and 
absorption, Thomsen, Therm. Unters. ixi,p. 195,1883, and Berthelot, Mec. chim. 
1, p. 394; p. 511,1879. Influence of temperature on the heat of solution, Thomsen, 
Therm. Unters. 1, p. 70, 1882. 
Use of the ice-calorimeter for determining the heat of solution, Scholz, Wied. 
Ann. 45, p. 195, 1892. HEAT OF DILUTION. 
3. HEAT OF DILUTION. 
By the heat of dilution is meant the quantity of heat which is set 
free or absorbed when a solution is further diluted with the solvent. 
The heat of dilution is referred to as HCI 50 aq, 50 aq ; HCI 
25 aq, 75 aq ; HCI 40 aq, 60 aq, etc., and the quantity of water 
is chosen usually so that the quantity of water of the solution and 
the final quantity of water make a constant whole number, as HCI 
n aq, 100 n aq. 
The heat of dilution may be determined in a manner similar to 
that for the heat of solution, In that the solution to be diluted is 
introduced in a small closed tube, which is broken as soon as the 
temperature becomes constant. 
The calorimeter (Fig. 59, p. 134) is also frequently used. The 
water is usually placed in A and the solution in B. For higher 
concentrations a special arrangement is sometimes necessary. .The 
quantity of solution used is so measured that it contains a simple 
fractional part = -F. of a gram-molecule (see p. 135). 
For the method of operation see the same page; the loss of heat 
by radiation, however, is generally taken into consideration accord- 
ing to page 115. 
If ta is the temperature of the water, th the temperature of the 
solution, r the corrected final temperature of the mixture (the 
specific heat of which is c), w the water-equivalent (pp. no and 
1:13) of the lower vessel A (with the stirrer and thermometer), a 
the weight of the water, b the weight of the solution to be diluted, 
and the fraction of a gram-molecule of dissolved substance 
P 
contained in the solution, then the heat of dilution V, measured in 
large calories (JT), is; 
Vz= -^-[(r —4) (O +£)C+ w) (/„ —4) O + «01 
100 v 7 
For accurate determinations, therefore, of the heat of dilution, 
the specific heat of the resulting solution must be known. See 
Tables of Specific Heats, Thomsen, Therm. Unters. 1, p. 46, 1882 ; 
Berthelot, Mec. chim. 1, p. 495, 1879 ; and Landolt-Bornstein’s 
Tabellen, p. 185, 1883. 140 
THERMOCHEiMICAL CONSTANTS. 
The heat of dilution can, however, be accurately determined 
for a solution the specific heat of which is unknown. It is then 
only necessary that the temperature of the water in A be such that 
the temperature of the solution after dilution is the same as that of 
the original solution in B. See Thomsen, Therm. Unters. m, 
p. 43, 1883. Substances for investigation : [NaCI -f- ioH20] 
+ 4oH20; V=~ 5.3 K [MgSO, + 2oH20] + 30H20, 
V = -\- 2.8 K (according to Thomsen). Tables of heats of 
dilution: Thomsen, Therm. Unters. in, p. 37, 1883; influence of 
temperature on the heat of dilution, ibid. 1, p. 80, 1882. 
4. HEAT OF HYDRATION. 
The heat of hydration is the quantity of heat set free when one 
gram-molecule of a substance combines with a definite number of 
molecules of water to form a hydrate. 
The heat of hydration is obtained by subtracting the heat of 
solution of the substance containing water of crystallization 
from the heat of solution of the anhydrous substance,—e.g., 
MgS04, 7H20 = MgS0i, aq—MgS04, 7H20, aq. The method, 
therefore, is that for determining the heat of solution (p. 137). 
The thermal effects for the taking up of the first, second, third, 
etc., molecule of water of crystallization are often very different. 
The thermal effect, therefore, is frequently determined for each 
molecule of water separately. 
If L 0 is the heat of solution of the anhydrous substance, Lw the 
heat of solution of the compound with the maximum water of 
crystallization, Ln the heat of solution of the substance with n 
molecules of water, and m the maximum number of molecules of 
water, then 
and 
m n 
are the average thermal effects corresponding to the total number 
in and the first n molecules of water. If the two values are equal, 
it is evident that all the molecules of water are combined with 
equal quantities of heat. 
The partial and complete dehydrations are accomplished in a 
drying oven. It is better that the substance with the maximum HEAT OF COMBUSTION. 
141 
water of crystallization should contain a slight excess rather than a 
deficiency of water. In regard to the quantity of water used for 
the solution, see page 138. 
The following example will serve as an illustration : 
Thomsen found for the solution of iNa4P207 in 800 mol. H2O : 
Molrcui.es op Heat of Mean Thermal 
Water of Sol.ution of the Effect for the 
Crystallization Salt Na4P2O7, Taking up of n Mole- 
= n. nHoO. cules of Water. 
lNa4P207, . . o. H2O 1x8.50 K 
iNa4P2Q7, . , . 1.480 PI20 82.49 K 36.01: 1.480 = 24.3 K 
iNa4P207, .. . 5 °74 H2O i 23 K 119.73:5.074 = 23.6^ 
iNa4P207, . . . 5.962 H2O 21.39 K 139-89= 5-962 = 23-5 K 
iNa4P207, . . . 10.0 H2O 235.20:10.0 =23.5 K 
The thermal effects, therefore, for the separate molecules of 
water for sodium pyrophosphate are approximately equal; this is 
not the case with most salts. 
Tables of heats of hydration : Thomsen, Therm. Unters. hi, 
p. 187, 1883, and Berthelot, Mec. chim. 1, pp. 359 and 392, 1879. 
5. HEAT OF COMBUSTION. 
The heat of combustion is the quantity of heat set free in the 
complete combustion of one gram-molecule of a substance. 
The Calorimetric Bomb (Method of Berthelot).* 
Principle and Calculation.—The substance is placed in a 
suitable vessel a calorimetric bomb and surrounded by an 
atmosphere of oxygen at a suitable pressure. After introducing 
the bomb into the calorimeter, the substance is burned in the 
nature of an explosion induced by electrical means. 
If /is the initial temperature in the calorimeter, r the final tempera- 
ture of the same, P the weight of the water in the calorimeter, w 
the total water-equivalent of the calorimeter, stirrer, thermometer, 
and bomb, p the weight of the substance burned in the bomb, and 
* Berthelot, Ann. chim. phys. (5) 23, p. 160, 1881 ; Compt. rend. 115* p. 201, 
1892 ; and Stohmann, Jour, prakt. Chem. N. F. 39, p 503,1889. 142 
THERMOCHEMICAL CONSTANTS. 
m the molecular weight of the substance, then the quantity of heat 
evolved, measured in large calories (X), 
= + w) (r-0> 
and the heat of combustion for constant volume is 
Qv = (p + w'> 
The heat of combustion is usually referred to constant pressure. 
This reduction of the heat at constant volume to constant pres- 
sure at 180 can be made, for solids and liquids of the formula 
CmHreOr, according to the formula: 
QP =Qv + 0.291 ( r), 
where Qp and Q„ are the heats of combustion at constant pressure 
and constant volume, and n and r the number of hydrogen and 
oxygen atoms. 
The following formula is of general application : 
Qp : Qv 0.02 (j T, 
q represents the number of gram-molecules of gas which dis- 
appear in the reaction, and T the absolute temperature; 
0.02 X 291 K— 5.82 K must therefore be added to the observed 
heat of combustion at 180 for each gram-molecule of gas which 
disappears, and the same number of calories subtracted for each 
gram-molecule of gas formed.* 
Apparatus.— i. The Calorimeter.—The calorimeter is placed 
in the experimental-room, the temperature of which must be care- 
fully regulated. 
The inner cylindrical brass vessel (20 cm. high and 15 cm. wide 
and 500-600 gm. in weight) rests in a larger double-walled vessel 
of the same material, which is filled to a height of 10 to 15 cm. 
with water. The two vessels are isolated by means of pieces of 
ebonite, which are fastened together by means of glass rods. The 
stirring arrangement (about 200 gm. in weight) may be made of 
*Ostwald, Allgem. Chem., 2. Aufl., Bd. 11, pp. 81 and 370, 1892; Berthelot, 
Mec. chim. I, p. 116, 1879; and Ann. chim. phys. (5) 23, p. 168, 1881. HEAT OF COMBUSTION. 
143 
three ring-shaped brass plates, which are firmly fastened together 
by means,of wires, so that the cylindrical discs lie one above the 
other, and so that the wires are united at the top of, and in the axis 
of the cylinder. 
The stirrer should take up the entire space between the outer 
wall of the bomb and the inner wall of the calorimeter vessel. For 
a bomb, therefore, of 10 cm. and a calorimeter of 15 cm. in diam- 
eter, the discs should be 10.5 cm. and 14.5 cm. in diameter. The 
stirrer must be moved uniformly and in a vertical direction. The 
wires, therefore, at the point where they are joined together, are 
fastened to a slide which moves in a vertical direction, owing to its 
being fastened eccentrically on a disc which is rotated by means 
of a turbine. 
This movement must take place so that, for the deepest position 
of the stirrer, the lower plate must come almost in contact with the 
bottom, and for the highest position the upper plate must come 
almost to the surface of the water. 
The upper discs of the stirrer are provided with two openings for 
the introduction of the thermometer. 
The (Beckmann) thermometer must be carefully tested. It is 
graduated to or yTy of a degree, so that, by means of a micro- 
scope, it may be read accurately to 0.002°. (The tapping of the 
thermometer must not be forgotten.) The contrivance which sup- 
ports the stirring apparatus is fastened to the outer calorimeter 
mantle. 
2. The Bomb (Fig. 60).—The bomb consists essentially of a 
cast-steel vessel A, which is closed air-tight by means of the steel 
cover B. The interior of the vessel and cover is lined with plat- 
inum. For a bomb with a capacity of 300 cm., about 1200 gm. 
of platinum and 2700 gm. of steel* should be used, so that, with 
the addition of the brass contrivance which supports the bomb in 
the calorimeter, the combined weight amounts to about 4 kgm. 
The manner in which the bomb is closed by the cover is evident 
from the figure. 
* These are the approximate weights for the bomb of Stohmann ; Berthelot’s 
bomb of 200-250 cm. capacity requires not more than half this quantity of platinum. 
The calorimeter is correspondingly smaller. 144 
THERMOCHEMICAL CONSTANTS. 
Fig. 60. HEAT OF COMBUSTION. 
The platinum edge of the cover is carefully slipped into the con- 
ical opening of the vessel A. The cover is pressed down firmly 
by means of a large screw, which surrounds and screws tightly to 
the outside of the vessel. In the upper surface of the screw are 
two holes, in which are placed two iron pegs (not shown in the 
figure). By means of these the screw C can be tightly turned. 
The bomb, after filling with oxygen and the substance, is firmly 
fastened in a steel ring consisting of two halves covered with white 
lead, and tightly closed by means of the steel pegs. Previously, 
however, the upper portion of the conical part of the cover should 
be carefully covered with grease. 
The contrivance a in figure 60 is used for filling the bomb with 
oxygen and the gases to be combusted ; likewise for the subsequent 
removal of the gases resulting from the combustion. 
It consists of a hollow, thick-walled, steel cylinder, which can be 
so adjusted by means of the screw arrangement, which is from 3 
to 4 cm. long, that the conical valve below is either tightly closed, 
or that the opening for the outflow and inflow of gases is in direct 
communication with the short platinum tube, bent at a right angle, 
which extends from the lower end of the screw arrangement into 
the interior of the bomb. 
When the screw is turned down as far as possible, the bomb is 
closed air-tight; half a turn upward then is sufficient to allow the 
gases to enter. 
For solid and liquid substances there is situated in the interior 
of the bomb a small platinum vessel b resting in a platinum ring, 
which can be raised or lowered on a heavy platinum wire, which is 
fastened to the cover. This arrangement is necessary so that the 
substance can be placed just below the wires c c', by means of 
which the combustion is induced. 
Inasmuch as the wire c, which is firmly soldered to the plati- 
num support of the vessel, is connected with the bomb, thus forming 
a conductor, c' must be carefully insulated. This can be accom- 
plished by means of a small platinum cone which is connected 
with c' and inserted, air-tight, in the cover. The cone is covered 
with thin black rubber. (A shellac covering is less durable). A 
small ivory ring, at the outlet through the cover, is shoved over 
the platinum rod which supports the cone; the ring is made air- 146 
THERMOCHEMICAL CONSTANTS. 
tight by means of a screw, which simultaneously exerts a pressure 
on the rubber, thus forming a very thin membrane. Care should 
be taken (especially before the first combustion) that small pieces 
of rubber do not fall into the interior of the bomb during the 
tightening of the screw; otherwise the pieces must be removed. 
The danger from the burning of rubber can be prevented by 
placing a piece of mica, through which a hole has been bored, 
between the cover and the rod of the cone. 
The burning of the substance is brought about by means of fine 
iron wire (Blumendraht) which is melted off at a glowing heat. 
The wire is rolled spirally on a strong needle and is fastened to c 
and c' by means of fine platinum wires. In order to remove the 
thin coatings of non-conducting iron oxide which may be formed 
on c and c' during the combustion, the ends of the wires are 
immersed from time to time in molten potassium bisulphate. 
As equal lengths of the iron wire have approximately equal 
weights, a correction may be easily calculated for the iron which 
burns to iron oxide; equal lengths of wire = 5 cm. are always 
taken so that the weight (about 0.006 gm.) need be determined 
only once. 
The wire is heated by means of three Bunsen chromic-acid 
elements; the glowing particles of oxide from the burning wire 
fall upon the substance immediately under the wire and start the 
combustion. 
3. Contrivance for the Introduction of Oxygen.—The oxygen to 
be used should be free from chlorine and carbon monoxide. Any 
chlorine present may be removed by passing the gas through 
potassium hydrate, while the carbon monoxide can be best removed 
by means of palladium chloride. Combustible gases and small 
particles of oil from the pump are rendered harmless, in that the 
oxygen is first passed through a copper tube heated in a com- 
bustion furnace, and after cooling is introduced through a narrow 
spiral tube into the bomb. The main portion of the oil from the 
pump is held back mechanically, in that a large number of fine 
wire gauzes are placed at very small distances from each other in a 
metallic cylinder immediately behind the pressure-valve of the 
pump. The presence of carbonic acid causes no inconvenience. 
To avoid corrections, the oxygen should not be dried, but should 
be saturated with water vapor. HEAT OF COMBUSTION. 
147 
It is very convenient to make use of the commercial oxygen 
tanks, in which the oxygen exists under a pressure of about 120 
atmospheres. The gas can best be pumped from an ordinary 
gasometer into the calorimetric bomb by means of a good suction- 
or pressure-pump; the tube of the pump should be surrounded 
by a mantle of flowing cold water; otherwise the heat from 
friction may occasion explosions between oil and compressed 
oxygen. 
The pump should be provided with a manometer which indicates 
Jg- atmospheres. 
Details of the Method of Operation.—The water-equiva- 
lent of the calorimeter and stirrer (pp. no and 113) can be 
determined simply by multiplying the weight in grams by the 
specific heat of brass = 0.094. However, it is perhaps better to 
determine the specific heat of the particular kind of brass used in 
the calorimeter. The weight of only that portion of the stirrer 
which is immersed for the highest position in the water of the 
calorimeter can be taken into account.* A further determination 
of the water-equivalent of the calorimeter and stirrer, so far as the 
latter comes into account, may be made by quickly pouring a 
quantity of tvater, from a protected vessel heated to a constant 
temperature (about 6o°), to the necessary height in the calorimeter 
(containing the stirrer and thermometer). The water-equivalent 
of the metallic portions (including the thermometer) can be calcu- 
lated from the quantity of heat given up to these portions, by 
multiplying the temperature difference of the water by its weight 
and dividing the product by the temperature elevation of the 
metallic portions. For the dimensions and weights given for the 
calorimeter and stirrer, the combined water-equivalent amounts to 
about 60 to 70 gm. For the water-equivalent of the portion of 
the thermometer immersed see also page 114. 
The water-equivalent of the bomb with brass foot can be accu- 
rately determined by several methods ; 
1. The number of grams of steel, platinum, and brass used are 
* A direct and perhaps more accurate way of determining the water-equivalent 
of apparatus, see Stohmann, Jour, prakt. Chem. 39, p. 528, 1889. 148 
THERMOCHEMICAL CONSTANTS. 
multiplied by the corresponding specific heats (specific heat of steel 
= 0.1097, platinum = 0.0324, and brass = 0.094). 
2. The bomb, together with the stirrer, can be introduced into 
the calorimeter vessel, and water, previously heated to exactly t° 
(6o°), added until the bomb is immersed. The sum of the water- 
equivalents of the bomb, calorimeter and stirrer can then be calcu- 
lated (see p. 147). 
3. The bomb is heated for some time in a water-bath to 
about 30° until the temperature becomes constant to about y-l-g- 
-of a degree; it is then introduced as quickly as possible into the 
calorimeter containing sufficient water at a constant temperature 
equal to that of the room. The temperature elevation of the con- 
tents of the calorimeter, multiplied by the total water-equivalent of 
the same, and divided by the decrease in temperature of the bomb, 
gives the water-equivalent. 
A small correction is to be introduced on account of the water 
which adheres to the bomb during the heating. The approximate 
weight of the same is determined from several weighings of the wet 
bomb. If the outer surface of the bomb is covered with a trace of 
grease, the adhering water amounts to only a few grams, and it is 
necessary simply to subtract the number of grams from the observed 
water-equivalent of the bomb. 
The water equivalent of the bomb, which for the weight given 
would amount to about 350 gra., can be determined by the preced- 
ing methods to from 1 to 2 gm. 
In carrying out the experiment, the bomb is immersed in the 
water so far that only the handle of the closing screw a remains 
uncovered. The calorimeter, for the dimensions of the apparatus 
given, should contain about 2500 gm. of water. 
The preceding is subject to some variation, depending upon 
whether the substance to be combusted is a solid, liquid, or a gas. 
A large excess of oxygen must be used in the case of solids. 
The oxygen is pumped into the bomb until the manometer shows a 
pressure of about 25 atmospheres. A bomb of 300 c.c. capacity 
should contain from 10 to 11 gm. of oxygen. The quantity of 
substance to be burned is so chosen that, after the combustion, the. 
remaining oxygen occupies at least one and a half times the volume HEAT OF COMBUSTION. 
149 
occupied by the gases formed in the combustion. For 10 gm. of 
oxygen usually 3 gm.; i. e., 30 per cent, of the quantity may be used 
in the combustion ; then, on the assumption of complete combustion 
to C02 and H2O, the quantity of substance to be used in the com- 
bustion can be calculated (<?. g., 1 gm. of naphthalene corresponds 
to about 3 gm. of oxygen). 
If one is not certain that the combustion is complete, the com- 
bustion gases are slowly conducted through a solution of palladium 
chloride. The least quantity of CO will produce a black precipi- 
tate, and may thus be detected. 
For many substances, in oxygen under a pressure of 25 atmos- 
pheres, the combustion is not induced by the molten iron wire. 
The combustion may be facilitated in such cases by covering the 
substance with a small weighed quantity of an easily combustible 
substance (a few grams of naphthalene) ; the heat set free in the 
combustion of that substance will start the combustion in the 
original substance. Of course, a small correction must be intro- 
duced in this case. The heat of combustion of the substance used 
to induce the reaction is multiplied by the quotient of the weight 
used, divided by the molecular weight, and the product subtracted 
from the total heat of combustion. Only a few substances (oxalic 
acid, mellitic acid) show difficulties in their combustion according 
to this method. Solid substances should be made as compact as 
possible for the combustion—in the form of pastilles, or, when the 
substance can be fused without decomposition, in the form of a 
solidified fusion. 
A steel arrangement, constructed on the plan of the diamond 
mortar used in crushing minerals, is used as a pastille press. The 
inner part has a suitable width and the bottom can be removed. 
The substance is previously weighed. A press of the hand is fre- 
quently sufficient to produce the necessary compactness in the 
pastille. 
If the substance to be combusted is a volatile liquid (aldehyde, 
ether, benzene, etc.), a correction relative to the heat of vaporiza- 
tion must be introduced, for a portion of the substance is com- 
busted in the gaseous and a portion in the liquid condition. For 
the calculation of this correction, see Stohmann, Jour prakt. Chem. 
40, pp. 78 and 342, 1889. THERMOCHEMICAL CONSTANTS. 
The heat of combustion has reference entirely to the liquid 
state.* The liquid is introduced into a small glass globe, which is 
closed by fusion, and which is so thin-walled that a slight move- 
ment of the bomb, immediately before the beginning of the experi- 
ment, is sufficient to break the globe. Berthelot, Pierre, and 
Matignon,f however, have proposed that the liquid be contained in 
a small platinum capsule, which is surrounded by an envelope of 
gun-cotton, closed at the top by means of a thread of the same 
material. 
Gaseous substances should be mixed with no more oxygen than 
is necessary for their combustion to carbonic acid and water. At 
all events, only a very slight excess of oxygen is to be recom- 
mended (about i per cent.). The combustion in this case is 
almost always complete for atmospheric pressure. The gases 
formed in the combustion should be tested for carbon monoxide. 
The weight of the combusted gas may be determined at the end of 
the experiment by slowly conducting the gases contained in the 
bomb through dissolved and over solid potassium hydrate. The 
apparatus is most conveniently filled (in case it is not necessary to 
mix the gases outside of the bomb) as follows ; After exhausting 
the bomb, the gas to be combusted is first introduced, then the 
volume of oxygen necessary for the combustion is calculated, and 
the same, by observing the pressure indicated by the manometer, is 
introduced into the bomb in slight excess. 
The combustion of the substance introduced into the bomb 
takes place almost instantaneously. Some minutes (three to four), 
however, are required for the equalization of the temperature in 
the calorimeter. The experiment is begun after the bomb has 
remained for some time in the calorimeter. The temperature of 
the apparatus at the beginning of the experiment should be about 
as much below the temperature of the room as it is above the 
temperature when the experiment is completed. The temperature 
* For the comparison of the heats of combustion of different substances it is 
necessary to refer them to the same state (better, the gaseous state). Then the 
heats of fusion and evaporation must be considered. See Ostwald, Lehrb. Allgem. 
Chem., 2. Aufl., Bd. 11, p. 371, 1892. 
f Berthelot, Compt. rend. 115, p. 201, 1892. HEAT OF COMBUSTION. 
151 
elevation usually amounts to several degrees. The influence of 
radiation, therefore, should be taken into account according to 
page 115. 
From the observed thermal effect the heat of combustion of the 
substance is calculated according to page 142. First of all, how- 
ever, small corrections are to be deducted from the number of 
calories calculated from the experiment. 
1. If a is the weight in grams of ferrous oxide formed by the 
burning of the spiral, and if, according to Berthelot, the oxidation 
of 1 gm. of iron to ferrous oxide sets free 16.01 X of heat, then 
a 16.01 X must be deducted from the observed thermal effect. 
2. The nitrogen of the air which was not removed before the 
introduction of the oxygen, and which still remains in the bomb, 
is burned to nitric acid. The acid formed is taken up by the con- 
densed water, and, after being completely washed from the bomb, 
its quantity can be determined by titration (dilute sodium carbonate 
and methyl-orange). For each gram-molecule of aqueous nitric 
acid (63 gm. FIN03aq) formed 143 X, according to Berthelot, are 
to be deducted. 
3. A bomb of 300 c.c. capacity, and at a pressure of 25 atmos- 
pheres, contains somewhat more than 10.5 gm. of oxygen. This 
oxygen must go through the temperature change. As the specific 
heat is 0.2175, number of grams of oxygen (10.5) must be 
multiplied by this number, and the product, which is the water- 
equivalent of oxygen, must be added to the total water-equivalent 
of the colorimeter and bomb. 
The sum of all these corrections has only a slight influence on 
the result. 
The correctness of the bomb should next be tested, naphthalene 
being used in the combustion. 
The quantity of heat set free in the combustion of 1 gm. naph- 
thalene, at constant volume, according to the investigations of 
Berthelot, is 96.94 X. 
(The values for nineteen determinations vary between 97.43 and 
96.51 X.) 
The bomb of Berthelot, Stohmann, and others is made in Paris 
(by Golaz). 
The high price of the apparatus, owing to the large quantity of THERMOCHEMICAL CONSTANTS. 
platinum used in its construction, has hindered somewhat its intro- 
duction into the laboratory. 
Mahler * has recently described a bomb which is analogous to 
that just described, and made of half-tempered steel. The interior, 
instead of being covered with platinum, is furnished with a layer 
of strong enamel, which must be renewed occasionally. This 
bomb can be used not only for technical, but also for scientific 
purposes. Other investigations in this direction, however, are 
desirable. 
On heats of combustion, see Thomsen, Therm. Unters., Bd. IV, p. X; Ost- 
wald, Allgem. Chem. 11, p. 361, 1892; Armstrong, Phil. Mag. (5) 23, p. 73, 
1887 ; Briihl, J. pr. Chem. (2) 35, pp. 181 and 209, 1887 ; Thomsen, Zeit. phys. 
Chem. I, p. 369, 1887, and 7, p. 55, 1891; Dieffenbach, ibid. 5, p. 566, 1890. 
Tables of heats of combustion : Stohmann, Zeit. phys. Chem. 2, p. 29, 1888 ; 
6, p. 335, 1890, and 10, p. 410, 1892; ibid.. Literature on heats of combustion. 
Determination of heats of combustion with the ice-calorimeter: Schuller and 
Wartha, Wied. Ann. 2, p. 371, 1877. 
Heat of Formation.—The heat of formation of an organic 
compound,—i. e., the quantity of heat set free or absorbed in the 
formation of 1 gram-molecule of the substance, can be calculated 
from the heat of combustion of the compound. The calculation 
can be made according to the principle of Hess, by subtracting 
the heat of combustion of the compound from that of its elements. 
We have then : 
or, in large calories K : 
c, H4 =C, 02 + 2(II2) O) - CH4, 04; 
223 = 976 + 2 X 683 2“9- 
See, among others, Ostwald, Allgem. Chem. 11, p. 215, 1892; Berthelot, Mec. 
chim. 1, 329, 1879. 
* Mahler, Compt. rend. 113, p. 774, 1891. CRYSTAL MEASUREMENTS. 
153 
XVI. CRYSTAL MEASUREMENTS. 
1. THE REFLECTION GONIOMETER OF 
WOLLASTON. 
Principle.—The goniometer is used chiefly for measuring the 
angles of crystals,—i. e., those angles which the crystal faces form 
with each other. 
Let the angle which two crystal faces form with each other be 
represented by a—on in (Fig. 61). A is a small mirror, so 
placed that the image of a suitable object at F, when viewed past 
the edge of the crystal by the eye situated at A, will appear in 
the direction A E. The crystal is 
then placed in such a position (om n) 
that the image of F reflected from the 
crystal face 0 n appears in the same 
direction A n as the image formed by 
the mirror E. For this position of 
the crystal the two images of F re- 
flected from the crystal surface on 
and the mirror E to the eye of the 
observer coincide. The crystal is 
then rotated about the crystal edge 
n as axis until the two images again 
coincide, when the crystal will have 
Fig. 61. 
rotated through the angle a'=iBo°—a and taken the position 
no' in' (Fig. 6x). The image of F, in this case, is reflected from 
the surface nm = n in'. The desired angle then is a 180° 
Apparatus I.—The apparatus in its simplest form is represented 
in figure 62. 
A circle E graduated to half degrees is provided with a vernier 
(p. 218), and is movable about the axis G. The instrument is 
provided with a double axis. If the knob Gis turned, the circle 
E and also the jointed arrangement KL M, which carries the 
crystal, are rotated. If, however, the inner axis is turned by means 
of the knob J, the crystal support alone is turned. The graduated CRYSTAL MEASUREMENTS. 
circle may be firmly clamped by means of the pressure screw 
UTS. 
The crystal a is fastened in a suitable position on the small disc 
Q by means of wax. The adjustment of the same (p. 155) is 
made possible, first, by the fact that the axis O which carries the 
disc Q may be turned in its support JVhy means of the knob P ■ 
Fig. 62. 
and, second, by the fact that the arrangement ML K is movable at 
the joints. 
Yrepresents a small mirror which is usually fastened to the foot- 
plate Aof the instrument, and is movable about an axis. For a 
definite position of the mirror the image of a suitable object is 
visible. 
As signal, use may be made of a mark x on the window or (if 
not too near) the cross-bars of a window, the edge of a roof, etc. THE REFLECTION GONIOMETER. 
Or the window may be darkened and then, at a sufficient distance, 
provided with a signal, which is a cross-formed slit about 5 cm. long 
and 0.5 cm. broad, and which is lighted by means of a gas-flame. 
Method of Operation.—The apparatus is set up so that the 
plane which passes through the middle of the signal on the window 
and perpendicular to the plane of the window is parallel to the 
graduated circle EE. If the mirror yis fastened to the foot-plate 
so that the edge next to the window is parallel to the axis of the 
measuring circle, then, for the proper adjustment of the instrument, 
the image of the horizontal bar of the window must be parallel to 
the same edge of the mirror. 
The crystal is fastened to the small disc Q by means of wax, so 
that the edge to be measured, for a suitable adjustment of the joint 
L, falls as nearly as possible in the line of prolongation of the axis 
of the measuring circle. To facilitate the centering of the crystal 
the axis K should be moved in a slide (not shown in Fig. 62, see 
p. 157). If the crystal is approximately centered, then, on rotating 
the knobs G or J through 360°, the edge to be measured should be 
displaced from its position only very slightly. 
The crystal must then be adjusted. For this purpose the mirror 
y is placed so that the horizontal and vertical bars of the window 
are visible in the middle of the field of view. If the eye is placed 
near the approximately centered crystal, then, on rotating the knob 
J, the image of the window-bars reflected from the mirror is seen in 
the two crystal surfaces, the angle between which is to be measured. 
If the horizontal and vertical bars of the window appear inclined in 
the image from the crystal, and at the same time appear normal in 
the mirror and parallel to the edges of the mirror, the adjustment 
is inaccurate. 
The image then reflected from the crystal and that reflected from 
the mirror y are not brought to perfect coincidence on rotating J. 
If the attempt be made to perfect the adjustment by turning the 
knob Pon its axis or by a movement of the jointed contrivance 
K L M, it will be seen in most cases that a movement of either of 
these is not sufficient of itself to cause the images from the two crys- 
tal faces to appear in the same direction as that from the mirror. 
By combining these two movements, however, such an adjustment, 
after a little practice, is readily made. CRYSTAL MEASUREMENTS. 
After the adjustment has been made, it is only necessary to deter- 
mine the angle through which the divided circle must rotate in 
bringing the images from the two crystal faces successively in coin- 
cidence with that from the mirror y. The observed angle, of 
course, is the complement of the angle to be measured. During 
the observations on the two surfaces the eye should remain as 
nearly as possible at the same position. 
With careful adjustment and well-formed crystals, this method is 
Fig. 63. 
accurate to within two to three minutes, which is sufficient for most 
chemical purposes. 
Apparatus II.—A more complete form of apparatus is repre- 
sented in figure 63. 
K is the divided circle with a double axis A a and Bb\ n is 
the vernier, which is illuminated through the white paper r by 
means of a small flame and read by means of the microscope /; 
is a micrometer screw, the threads of which turn in the 
grooves of the circular head B, so that the turning of the knob p THE REFLECTION GONIOMETER. 
produces a very slight rotation of B, thereby increasing the ac- 
curacy of the adjustment. In order that B may be free to move 
until approximately adjusted, the knob p is pressed down until the 
small projection on the spring below enters the opening in the 
frame i, which holds the screw in the lower position. 
The centering and adjustment contrivances are essentially differ- 
ent from those of apparatus I. 
The contrivance for centering consists of two slides lying one 
above the other and joined to the axis of rotation. By means of 
the screws yy these slides can be moved in parallel planes in direc- 
tions which are perpendicular to each other. Attached to this is 
the adjusting apparatus, which consists of two cylindrical sections 
movable, by means of the screws x x, in planes perpendicular to 
each other. A small disc, which serves as the crystal support, is 
fastened to this contrivance by means of the screw v. 
The instrument is also provided with a telescopef with cross-wires 
fastened to the support T. By means of the screw q and bar t the 
telescope may be moved parallel to itself, and may also be rotated 
in a plane perpendicular to t, so that it can be directed exactly 
toward the axis of the divided circle K. 
Method of Operation.—The apparatus is first placed in the 
proper position, which may be determined by means of a mirror 
(p. 154) or by means of the telescope. 
The telescope, which is provided with cross-wires, is focused by 
moving the eye-piece 0 sharply on the signal (the cross-bars of a 
window at the opposite end of the room, etc.). When the image 
of the object and the cross-wires lie exactly in the same plane, then 
a movement of the eye will produce no change in their relative 
positions. 
After the apparatus has been set up, the crystal, which is fast- 
ened on with wax, is centered. 
For this purpose the telescope is changed to a microscope, either 
by removing the eye-piece or by'placing a lens in front of the objec- 
tive. The microscope thus formed is focused on the crystal, which 
can be regarded as centered only when the edge to be measured 
remains in the same position during the rotation of the crystal. 
The crystal is fastened on the disc, so that the edge to be meas- 
ured is approximately centered. One of the two screws y should 158 
CRYSTAL MEASUREMENTS. 
be placed parallel to the telescope. The edge to be measured is 
then raised or lowered by means of the second screw y until it 
appears in the middle of the field of view. If the axis Ais now 
rotated through 90° and the centering screw turned, which is placed 
perpendicular to the telescope, then the edge must remain in the 
same position, and therefore be centered. 
The adjustment, which is made by means of the screws xx, is 
accompanied by certain difficulties until the operator has had some 
experience. 
The microscope is again converted into a telescope, and, after 
focusing on the cross-wires and the crystal, the latter is rotated by 
turning the axis A a around the approximately centered edge which 
is to be measured. The reflected image of the window-bars and 
the crystal surfaces, if necessary with the help of the screws x x, are 
brought into the field of view in the telescope. The adjustment is 
inaccurate as long as the directions of the reflected window-bars 
appear inclined to those of the cross-wires. 
The image reflected from the surface, which is parallel to one of 
the adjustment screws, is brought into the field of view first and 
the other screw turned until the image coincides with the middle 
of the cross-wires ; the image from the second face is then brought 
into view and corrected by means of the first screw ; the adjust- 
ment of the first face is thereby slightly changed, the change being 
smaller the nearer the face is parallel to the screw. By small sub- 
sequent corrections the adjustment is easily obtained, so that the 
images from the two surfaces, as well as from all other surfaces in 
the same zone, move along the vertical wire when the crystal is 
rotated. 
After some experience, the operator, regardless of any special 
rules, can easily make the proper adjustments. The turning and 
reading of the divided circle is accomplished by means of the knob 
B (see p. 155). 
Measurement of Crystal Angles in General.—The crys- 
tals should be carefully selected, and the faces which are to be 
observed should not come in contact with the fingers. They are 
rubbed off with soft leather and placed on a ball of soft wax, care 
being taken not to allow the wax to come in contact with any face 
which is to be measured. THE REFLECTION GONIOMETER. 
159 
In most cases it is desirable to measure all the angles of a given 
zone, so far as the condition of the crystal will permit. If the 
crystal is §mall, one centering is sufficient for all the measurements 
of the angles of parallel edges. It is placed, then, in the middle 
of the zone to be measured ; otherwise each edge is to be sepa- 
rately centered, whereby the adjustment remains unchanged. As 
the accuracy of the results depends upon the condition of the 
crystal faces, it is desirable, first of all, to project as carefully as 
possible, on the plane of a paper, a sketch of the crystal, repre- 
senting the separate faces by the letters a, b, c, etc., and then note 
down, with the measurements of the faces referred to, the necessary 
remarks on the condition of the reflected image, etc. From the 
different measurements of the angles of equal value then is selected 
a mean v'alue, taking into account the accuracy of the various 
measurements. In many cases it is advisable to repeat the measure- 
ments, using different crystals. 
If the crystal face is not uniform, but uneven, curved, or broken, 
several images, or parts of images, are usually seen in the reflec- 
tion. The measurements, of course, are then more or less inaccu- 
rate, depending upon the sharpness of the image. 
Care should be taken, especially for clear, transparent crystals, 
that the somewhat colored images produced by total reflection from 
the interior of the crystal and thrown into the field of view of the 
telescope, are not mistaken for the desired images. 
In case of doubt it is only necessary, during the rotation, to 
observe the crystal with the microscope, formed as previously 
explained, to determine whether the illuminated surface is turned 
from or toward the signal, and to determine, therefore, whether 
the rays from the interior of the crystal or those from the outer 
surface are reflected into the telescope. 
Substances for investigation : Quartz-crystal, prism angle 120°; 
Iceland spar, rhombohedral angles 740 44' and 105° 16'; alum, 
octahedral angle 109° 28'. 
Goniometers with horizontal measuring-circles, see Groth, Phys. 
Krystallographie 11, p. 560, 1885 ; goniometer as refractometer, 
ibid. p. 585. CRYSTAL MEASUREMENTS. 
2. THE MICROSCOPE, WITH POLARIZING 
ATTACHMENTS. 
Apparatus.—The microscope of Fuess, represented in figure 
64, consists, in its essential parts, of the tube b, with a system of 
lenses movable in the double-walled tube p, the objective-stage T, 
the mirror below, and the polarization attachments j and r, which, 
for investigations in polarized light,* can be fastened above the 
eye-piece and below the objective-stage. 
The objective-table T consists of a plate which can be rotated 
around the vertical axis of the instrument. This plate is graduated 
in degrees and can easily be moved with the fingers. The plate i 
firmly fastened to the stand below projects over the true stage. On 
the upper surface of this projection is a mark which serves as an 
index for reading the divisions on the movable plate T. 
The tube ris firmly fastened to the plate i. The polarization- 
tube, closed by means of a lens, can be shoved into this tube from 
below. The polarizing-tube contains a Nicol prism (or Prazmowski 
prism, p. 203), and is rotated in the outer tube r, so that the 
zero point coincides with a definite mark on r. For this position 
the principal section of the prism falls in the plane of the sketch. 
Two springs are fastened to the movable plate by means of the 
screw q, in order to hold the substance to be investigated firmly to 
the stage. 
The tube b can be moved in a vertical direction on the outer 
tube p. 
The instrument is roughly adjusted by taking hold of the tube 
on the edge f and pressing down ; the finer adjustment is accom- 
plished by means of the micrometer screw m. The head of this 
screw is usually graduated, thus making it possible to measure the 
vertical movement of the microscope accurately to the thousandth 
of a millimeter.-j- 
The double-walled tube p consists of two tubes, the inner of 
which can be turned through a small angle by means of the two 
*On polarized light, etc., see the section Rotation of the Plane of Polariza- 
tion, p. 203. 
f Groth, Physik. Krystallographie, pp. 33 and 648, 1885. 161 
MICROSCOPE WITH POLARIZING ATTACHMENTS. 
Fig. 64. 162 
CRYSTAL MEASUREMENTS 
screws n and m (Fig. 65), the axes of which are mutually perpen- 
dicular. 
This makes it possible to center the tube b, a cross-section of 
which is represented by the innermost double ring (Fig. 65), so 
that its vertical axis coincides exactly with the axis of rotation of 
the stage, and hence so that an object brought into the middle of 
the field of view of the objective does not change its position on 
rotating the stage—a condition which is necessary for the measure- 
ment of plane angles. 
Of the different Hartnack objectives 4, 7, and 9, the first, which 
magnifies, according to the eye-piece, from 90 to 200 diameters, is 
most frequently used ; if the magnification is still to be diminished, 
the lower lens of the objective must be removed. The instrument 
is provided with three eye-pieces, the form of which is represented 
Fig. 65. 
Fig. 66. 
in figure 66. Between the upper and lower lenses of the eye-piece 
is a cross-wire or glass micrometer, which can be brought sharply in 
focus by adjusting the inner tube A. A small screw aof the eye- 
piece passes through a vertical slit of the tube b, thus making it 
possible to keep the cross-wires always in the same position, namely, 
that parallel to the two polarizers when the zero points of their 
scales correspond respectively with the fixed marks on the tubes. 
Inasmuch as the position of the principal section undergoes slight 
change in time, it must be tested from time to time by determining 
the directions of vibration in a crystal plate (<?. g., a rhombohedral 
crystal of prismatic form). 
The tube s for the analyzer can be placed on the eye-piece (see 
p. 203). This tube, which contains a second Nicol or Prazmowski 
prism, is provided with a circular scale which can be rotated past 
the fixed mark on the plate f. MICROSCOPE WITH POLARIZING ATTACHMENTS. 
163 
If the analyzer and polarizer are adjusted so that their zero points 
coincide with their corresponding fixed marks, then the two Nicols 
are crossed and their principal sections coincide with the lines of 
the cross-wire. 
The slit tt represented in figure 64 serves as a receptacle for the 
slide zz, which contains a Biot quartz-plate. This plate is intro- 
duced to recognize, through the change of tint of the quartz-plate, 
a slight double refraction in the object, and to determine the direc- 
tions of vibration in the crystal under investigation. 
(a) Measurement of Plane Angles. 
By plane angle is meant that angle which the two edges of a 
crystal face, lying horizontally on the objective-stage, form with 
each other. 
For the measurement of this angle the Nicols are unnecessary ; 
the analyzer should always be removed in such cases. 
The crystal must be centered as accurately as possible; i. e., the 
point of intersection of the two edges whose angle is to be measured 
must be brought into the puddle of the field of view, so that on 
rotating the objective-table it remains in the same position,—at the 
middle point of the cross-wires (see p. 162). This centering, after 
a little practice, is accomplished easily and quickly if, when the 
centering has once been approximately made, the stage be rotated 
and the axis of the tube suitably adjusted by means of the screws 
m and n (Fig. 65), so that the point of intersection of the edges 
during the rotation of the stage describes each time a smaller circle 
around the middle point of the cross-wires. By careful movement 
of the object then the complete centering is easily accomplished. 
One of the two edges is then placed parallel to one of the cross- 
wires, an adjustment which can be accurately made if, instead of 
bringing the edge and wire into complete coincidence, the edge is 
placed slightly to the side of the wire. 
The position of the stage is then read, and afterward rotated 
until the second edge is brought into the position which the first 
had occupied. This angle, through which the objective-stage was 
turned, is, of course, equal to the plane angle to be measured. 
If the measurements are to be made on larger crystals, then the 
least possible magnification should be used. 164 
CRYSTAL MEASUREMENTS. 
See Groth, Phys. Krystall., p. 551, 1885, on the significance of 
the measurement of plane angles. 
(t>) Testing for Double Refraction and Determination of 
the Directions of Vibration in Crystals. 
The polarizer, analyzer, and cross-wires are given the positions 
as outlined on page 163. The Nicols are then crossed and the 
field of view becomes dark. 
With this adjustment of the instrument, the objective-table with 
the object is turned through 360° ; if, then, the substance is amor- 
phous, or belongs to the regular system, the field of view will 
remain dark during the rotation of the object. If, on the other 
hand, a doubly refracting uni-axial or bi-axial crystal is examined, 
the uniform darkness for all positions of the stage is observed only 
for certain few positions of the object—namely, only when the two 
parallel faces, natural or artificial, of the crystal are perpendicular 
to the optic axis (or to an optic axis). 
On the contrary, for all other positions of a doubly refracting 
crystal, and therefore in general, the field of view during the rota- 
tion of the stage through 360° is dark only in four different posi- 
tions, which are go° apart; in the intermediate positions the field 
appears colored (Groth, Physik. Krystall., pp. 71 and 105, 1885). 
If the crystal shows only a slight double refraction, the change 
of intensity between the darkness and the light is very slight, and 
it is necessary in such cases to use the Biot quartz-plate (p. 163), 
which can be shoved into the instrument. 
For special exceptions with reference to the above phenomena, 
see Groth, Physik. Krystall., p. 650, 1885. 
If these four positions, for which the plate is dark, have been 
determined for a doubly refracting crystal which appears colored 
between crossed Nicols, they represent those positions for which 
the plane of vibration of one of the two rays in the crystal is 
parallel to the plane of polarization of the one Nicol. If the 
direction of the planes of polarization of the three Nicols is given 
by the position of the cross-wires (p. 163), then the angles which 
the planes of vibration of the two rays in the crystal plate form 
with the crystal edges is easily determined. It is only necessary to 
place a crystal edge parallel to one of the cross-wires (p. 163) and MICROSCOPE WITH POLARIZING ATTACHMENTS. 
165 
to determine with crossed Nicols, by rotating the stage, that posi- 
tion which causes darkness in the field of view. A second reading 
of the divisions on the stage gives directly the angle which the 
planes of vibration form with the crystal edge. With mono- 
chromatic light, the observation will be sufficiently accurate for 
chemical purposes if, instead of determining the position of maxi- 
mum darkness, the arithmetric mean is taken of two positions 
which appear equally removed from this maximum. The determi- 
nations should be repeated several times, and the crystal should be 
carefully examined at the end of each series of observations, to deter- 
mine whether the crystal edge still remains in the proper position.* 
The determination of the vibration-planes is one of the most 
important measurements in crystallography, and is of itself suffi- 
cient in many cases to enable one to distinguish between the crys- 
tal forms which come into consideration. It is especially necessary 
to determine whether the vibration-planes form angles with certain 
crystal edges (inclined extinction), or whether they are parallel to 
the same (parallel extinction). 
The latter case never occurs in the asymmetric system; in the 
monosymmetric system the parallel extinction occurs only for cer- 
tain sections of the crystal; while in the orthorhombic system 
extinction occurs parallel or perpendicular to each of the three 
crystallographic axes, in the hexagonal and tetragonal systems par- 
allel and perpendicular to the principal axis.f 
Substances for investigation : Alum and sodium chlorate (regu- 
lar) ; potassium ferrocyanide (tetragonal); iodoform and sodium 
nitrate (hexagonal) ; potassium chlorate and ammonium sulphate 
(orthorhombic) ; ferrous chloride and ferrous sulphate (monosym- 
metric); copper sulphate and potassium bichromate (asymmetric). 
The microscope represented in figure 64, page 161, can be used for 
investigations not only in parallel but also in convergent polarized 
light. % 
(c) Investigations in Convergent Light. 
* Groth, Physik. Krystall., p. 651, 1885. 
f O. Lehmann, Krystallanalyse, Leipzig, 1891, pp. 33 and 34. 
I Groth, Physik. Krystall., p. 69, 1885. 166 
CRYSTAL MEASUREMENTS. 
In order to change from measurements in parallel light to 
measurements in convergent light it is sufficient, in general, to 
remove the eye-piece and use a higher-power objective; then 
the characteristic interference figure will be visible instead of the 
crystal. 
The change from one kind of light to the other is still more 
convenient if a Bertrand lens (an achromatic lens of 3-4 cm. 
focal length) is attached to the microscope. The removal of 
the eye-piece is then unnecessary, and it is sufficient for ob- 
servations in convergent light to place this lens in the open- 
ing above the objective (microscope of Fuess, Berlin, Stall- 
schreiberstr., Yoigt and Hochgesang, Gottingen). 
When a plate of a tetragonal or 
hexagonal crystal, cut perpendicu- 
lar to the optic axis, is observed 
in convergent polarized light with 
crossed Nicols, a dark cross with 
a system of colored rings, the in- 
terference figure represented in 
figure 67 is seen. This charac- 
teristic interference figure (see 
theory of Groth, Phys. Krystall., 
p. 75, 1885) is elliptical in shape 
when the surfaces of the crystal 
section are inclined to the optic 
axis. 
Fig. 67. 
If, on the other hand, a section of a bi-axial crystal (orthorhom- 
bic, monosymmetric, or asymmetric), cut perpendicular to the line 
bisecting the optic axes, is observed, the interference figure ap- 
pears as represented in figures 68 and 69. The figure has the appear- 
ance of figure 68 when the section is placed between crossed 
Nicols, so that the plane of its optic axes is parallel to the plane 
of polarization of one of the Nicols. Figure 68 a(a black cross 
with colored lemniscates) is the form shown by thick crystal-plates, 
while the form figure 68 b (a black cross with elliptical rings) is 
characteristic of thin plates. If the section between the crossed 
Nicols is turned so that the plane of the optic axes forms an angle 
of 450 with the plane of polarization of the Nicols, then the form MICROSCOPE WITH POLARIZING ATTACHMENTS. 
167 
of the figure changes and takes on the appearance of figure 69, 
thick plates showing the form 69 a and thin plates the form 69 b. 
The principal difference between uni-axial and bi-axial crystals 
consists in the fact that the interference figure for the former re- 
mains closed on rotating the objective, while for the latter it opens 
Fig. 68. 
and divides into two hyperbolas. For details of these phenomena, 
see Groth, Physik. Krystall., p. 104, 1885. 
Determination of the angle between the optic axes, see Groth, 
Physik. Krystall., p. 115, 1885; distinction between the positive 
and negative character of a doubly refracting crystal, I. c., p. 122. 
Stauroscopic measurements, ibid. p. 618. Cutting, grinding, 
and polishing crystals, ibid. p. 667. 
Fig. 69 
Isomorphism, Retgers, Zeit. phys. Krystall. 3, p. 497, 1889; 
ibid., earlier literature; the same Zeitschr. 4, pp. 189 and 593, 
1889; 6, p. 193, 1890; 8, p. 7, 1891; 9, pp. 266 and 386; and 
10, p. 529, 1892 ; Krister, Zeit. phys. Chem. 5, p. 601, 1890, and 
8, p- 577, 1891 ; Muthmann, Zeit. f. Krystall. 19, p. 357, 1891. REFRACTIVE INDEX. 
CRYSTAL MEASUREMENTS IN GENERAL. 
When a chemist wishes to obtain measurements of a crystal he 
usually seeks the assistance of a crystallographer. In most chemical 
investigations the measurement of crystals is entirely omitted and 
the crystal form referred to only in a general way. 
In fact, the more accurate goniometric and stauroscopic measure- 
ments require more practice than most chemists have had. On the 
other hand, it is advantageous for the chemist to be able to under- 
take, for simple crystal forms, the measurement of the most important 
angles (with a Wollaston goniometer), as well as the surface angle 
under the microscope, also the determination of the vibration 
planes, and even to make observations in convergent polarized light. 
These simpler measurements offer no great difficulty to a chemist 
who understands the principles of crystallography. These measure- 
ments become all the more necessary in recent times, owing to the 
importance of crystal form in the domain of stereochemistry, as 
well as for deciding problems of isomerism in general. 
XVII. REFRACTIVE INDEX. 
i. THE REFRACTOMETER OF ABBE.* 
Principle, Method, and Apparatus (Fig. 70).—The light 
reflected from the mirror g passes through the glass parallelepiped 
C, which consists of a specially formed combination-prism (Fig. 
71), into the cross-wire tube J O. 
The telescope is fastened to the divided sector A, and the double 
prism C with the arm B, so that the position of the prism, with ref- 
erence to the axis of the telescope, can be changed. The telescope 
can also be moved by means of the screw K and fastened in the 
desired position. 
* Abbe, Apparatus for Determining Refraction, Jena, 1874, and Sitzungs-Berichte 
d. Jenaischen Gesellsch. f. Medic, u. Nat., Febr. 21, 1879. 169 
REFRACTOMETER OF ABBE. 
If a liquid (or a suitable substance of smaller refractive index than 
the glass) is placed between the prisms, then the light which enters 
the prisms will, for a definite position of the prism, be totally 
reflected at the surface of the liquid and glass, and will no longer 
enter the telescope in parallel rays. The field of view of the tele- 
scope will then appear more or less darkened, depending upon the 
Fig. 70. 
position of the prism. For a definite adjustment of the prism one- 
half of the field of view will appear bright and the other half dark. 
For this position the refraction due to the liquid can be calculated 
from the angle of total reflection and the index of refraction of the 
prism by a simple formula.* 
* Loc. cit, Abbe, Apparatus, etc., p. 44. 170 
REFRACTIVE INDEX. 
To shorten the calculation, the divisions of the sector A are 
experimentally chosen, so that the index of refraction of the liquid 
for sodium light can be read off directly from the scale. 
In many cases white light is employed. The fact that the differ- 
ent colors do not experience total reflection simultaneously must 
then be taken into account. The dividing line between the light 
and dark portions of the field of view appears colored for white light. 
This dispersion can be corrected by means of the compensator D. 
This compensator consists of a direct-vision prism arrangement 
(p. 182), the two parts of which can be rotated in opposite direc- 
tions by means of the screw t. The adjustment is so made that 
the rays of sodium light experience no divergence.* The influ- 
ence of dispersion is eliminated for certain 
positions of the screw t, which are read off 
on the scale c. The dividing line between 
the dark and light portions of the field of 
view then appears sharp and uncolored. 
The scale c serves for the simultaneous 
measurement of the dispersion. 
Method of Operation.—The apparatus 
is turned by means of the knob K until the 
sector at e comes in contact with the experi- 
ment-table. With the instrument in this 
position, the movable prism is carefully re- 
moved by pressing down the spring (Fig. 71); the prism surfaces 
are cleaned (with alcohol, water, etc.), and, after placing a narrow 
piece of thin paper on the short side, a drop of the liquid to be in- 
vestigated is brought onto the hypothenuse-surface of the fastened 
prism. 
Fig- 7I- 
The movable prism is then replaced and the telescope so adjusted 
that the arm B stands at the first division of the scale. The mir- 
ror is then turned toward the window or some artificial light, so 
that the whole field of view of the telescope appears light. The 
arm is then moved on the scale until the lower half of the field of 
view appears dark. Usually, a broad, colored border appears at the 
dividing line between the dark and light portions. 
*Abbe, Apparatus, etc., /, c., p. 50. REB’RACTOMETER OF ABBE. 
On turning the screw t, the colored border disappears, and the 
colorless dividing-line between the dark and light portions is then 
brought as sharply as possible onto the cross-wires by means of the 
arm B. The positions of the arm and compensator are read off; 
the screw t is then turned until the dividing-line at the middle of 
the cross-wires appears colorless a second time, the arm is read- 
justed, and the positions of the arm and compensator again read off. 
The mean value of the two positions of the arm give directly the 
refractive index for the sodium line D. Inasmuch as the scale is 
graduated to thousandths for refractive indices, the results can be 
estimated, by means of a microscope, to the fourth decimal place. 
The dispersion* between the Fraunhofer lines D and Fcan be 
calculated from the two positions of the compensator by means of 
a table which usually accompanies the apparatus. 
Inasmuch as the refractive index nD and the dispersion np nD 
are known, the refractive index for any wave-length can easily be 
calculated from the Cauchy formula (p. 176). However, a knowl- 
edge of the refractive index for sodium light is usually sufficient. 
The apparatus can also be used for determining the index of 
refraction of solids. 
A thin, polished plate of the substance, together with a drop of 
a chemically indifferent, highly-refractive liquid, is placed between 
the prisms. 
The following highly-refractive liquids are well adapted to these 
measurements; Oil of cassia (n=i.6o), cinnamic aldehyde 
{n— 1.62), sulphur chloride (n— 1.654), selenium chloride (n = 
r.653), phenyl-sulphide (//= 1.623), phosphorus bromide {n 
1.68), monobrom-naphthalene (;z=i.66), and arsenic bromide 
(« 1.781). 
The index of refraction of the liquid compared with air is first 
accurately determined, then the refractive index of the liquid com- 
pared with the solid is determined in the manner described above. 
The first value divided by the second gives directly the index of 
refraction of the solid compared with air. 
To test the accuracy of the instrument it is sufficient to make a 
series of observations with a substance of known refractive index, 
* Abbe, Apparatus, etc., pp. 48 and 75. 172 
REFRACTIVE INDEX. 
with white and also with sodium light. Any necessary correction 
should be applied to the readings on the scale. 
The following are refractive indices for sodium light: 
Water at 200 = 1.3329 (at 150 = 1-3333) 
Alcohol “ = 1.3623 (sp. gr. 20°/4° = 0.8000) 
Acetone “ = X.3591 ( “ “ = 0.7920) 
Ethylidene chloride “ = 1.4165 ( “ “ X.1743) 
Anilin “ 1.5863 ( “ “ = 1.0216) 
Acetic acid “ = 1.3718 ( “ “ = 1.0495) 
Benzene “ = 1.5863 ( “ “ = 0.8799) 
Toluene “ = 1-4955 ( “ “ = 0.8656) 
For other refractive indices see, among others, Tabellen von 
Landolt-Bornstein, pp. 205-220, 1883, and Conrady, Zeit. phys. 
Chem. 3, p. 216, 1889 ; Die Brechungsindices des Wassers, Briihl, 
Ber. d. d. chem. Ges. 24, p. 644, 1891. 
2. THE REFRACTOMETER OF PULFRICH. 
Apparatus and Method in General.—A right-angled prism 
is placed in the upper part of a three-cornered support, fastened to 
the foot of the apparatus (Fig. 72). The horizontal and vertical 
surfaces of the prism form the above angle. The third inner 
prism stands inclined and is perfectly smooth. 
The outer portion of the horizontal prism surface is slightly con- 
cave ; it forms the base of a glass cylinder, which is fastened to the 
prism by means of cement. This cylinder is filled with the liquid 
to be investigated, and is provided with a small thermometer. 
If the rays of light are brought together at the lower edge of the 
glass prism filled with liquid, by means of a lens fastened to the 
foot of the apparatus (not represented in the figure), then the 
light will pass from the liquid into the upper surface of the prism, 
and leave the prism through the vertical surface, provided the angle 
formed with the normal to the surface is less than the limiting 
angle of total reflection. 
The telescope, provided with cross-wires and situated opposite 
the vertical prism surface (as shown in the figure), is fastened to 
a graduated circle with which it rotates. The beginning of the 
total reflection may be observed by adjusting the telescope so that, 
the field of view appears dark in one portion and light in another. REFRACTOMETER OF PULFRICH. 
173 
The position of the telescope is determined, for which one-half 
of the field of view is light and the other half dark. The refrac- 
tive index of the liquid can be calculated by a simple formula 
(p. 176) from the angle through which the divided circle rotates 
in passing from the zero of the 
scale to the required position. 
Apparatus and Method 
in Detail.—The hollow, three- 
cornered support, in the upper 
part of which the prism is fast- 
ened, slides down over a three- 
cornered solid support, which 
is fastened to the foot of the 
apparatus. 
Inasmuch as the relative posi- 
tions of the prism surfaces and 
the divided circle or telescope 
must always be the same, the 
inner and outer supports must 
be so constructed that the prism 
will remain constantly in its 
position. 
The pressure-screw on the 
support should be tightened be- 
fore each experiment; and care 
should be taken that, on remov- 
ing the hollow support from the 
apparatus, no dirt or dust col- 
lects in the space between the 
outer and inner supports. The 
removal of the hollow support 
is, therefore, avoided as much 
as possible, and the glass cylin- 
der which contains the liquid is usually cleaned by means of a 
pipet. 
Fig. 72. 
This cylinder is blackened on the side turned from the source of 
light, and is provided with a metallic cover, in the opening of 
which is placed a thermometer. REFRACTIVE INDEX. 
The cement on the cylinder (resin cement, gum arabic) must be 
frequently renewed. This must be done with the utmost care and 
cleanliness, as the rays of light enter the prism just' above the 
cement.* If the liquid should ooze through the cement during 
the experiment, it should be removed by means of filter paper; the 
vertical surface of the prism should also be kept clean. 
The telescope and divided circle are firmly fastened together. 
The telescope is adjusted for parallel rays of light, and is provided 
with cross-wires. The observer has only to focus the eye-piece 
sharply on the cross-wires, avoiding at the same time any rotation 
of the wires. 
The zero point of the telescope is the horizontal position, 
which is fixed by the zero points of the divided circle and the 
vernier. 
After the telescope has been approximately adjusted, the screw 
below the divided circle is firmly clamped, and the final adjustment 
made by means of the more delicate side-screw. 
The circle is graduated to 0.50. By means of the vernier, 
it is possible to read the scale to one minute. 
Sodium light (sodium chloride, sodium bromide) is usually em- 
ployed as the source of light. Thallium light and lithium light 
may also be used. The light should be as intense as possible, and 
should last for as long a period as possible. For contrivance see 
pages 185 and 207. 
The prism which accompanies the instrument will answer for the 
investigation of most liquids. A prism of higher refractive index 
is necessary only for liquids whose refractive indices are greater 
than 1.6. Upon request, this extra prism will be furnished with 
the instrument. 
Method of Operation.—The determination is carried out in 
an entirely or partially darkened room. The glass cylinder is 
filled with the liquid to be investigated and the screw on the 
support firmly tightened. 
* The glass cylinder in the more modern form of apparatus is provided around 
the interior of the lower end with a right-angled shoulder, which fits down over 
a corresponding shoulder on the prism-support. The cement is placed only 
between the vertical portions of these shoulders, thus leaving the base of the 
cylinder where the light enters perfectly clear. REFRACTOMETER OF PULFRICH. 
175 
The source of light is placed at a distance of about y2 of a meter 
from the apparatus, so that the rays of light are brought together 
at the lower edge of the glass cylinder by means of the lens. 
When the adjustment is correct, a sharp, inverted image of the 
flame, in a darkened room, will be visible on a piece of white 
paper held in front of the cylinder. This image should be some- 
what above the upper surface of the prism, toward the middle of 
the cylinder, as this is most suitable for the entrance of light into 
the prism. 
When the observer is satisfied that the cemented portion is suffi- 
ciently tight and the glass surfaces clean, the telescope is so adjusted 
that the field of view is divided exactly in the middle, the upper 
portion being dark and the lower portion light. The angle through 
which the telescope has been turned from the zero point (horizon- 
tal position) is then read off on the divided circle (to one minute). 
The index of refraction is calculated, according to page 176, 
from this angle /, which the last "ray that enters the prism forms 
with the vertical surface of the prism on passing out. 
The dividing line between the light and dark portions of the 
field of view should be as sharp as possible. If this is not the 
case, the intensity of the light is too low, or the position of the 
flame with reference to the apparatus is not properly adjusted, or 
the prism surfaces are not clean, or, lastly, the cementing has not 
been neatly done. 
Enough liquid to cover the bottom of the cylinder is sufficient 
for the determination ; the cylinder, however, must be carefully 
cleaned, either with the help of a pipette or by removing the sup- 
port B (p. 173)- 
The temperature must be noted for each determination. In 
order to determine approximately the connection between the 
refractive index and the temperature, the liquid should be warmed 
before pouring into the cylinder; then, by repeated simultaneous 
observations of the temperature and refraction, the relation between 
the two can be established. See also page 178. 
The time required for an observation amounts to only a few 
minutes. The different readings on the divided circle should not 
vary more than than 0.5 to one minute; this in general will give 
the refractive index accurate to within one unit in the fourth deci- REFRACTIVE INDEX. 
mal place, an accuracy which is sufficient for most chemical pur- 
poses. 
To ascertain whether the instrument has undergone any change 
after long use, experiments are made with liquids of known refrac- 
tive indices. See table, page 172. 
It is better to carry out an experiment with water before each 
series of determinations. 
Calculation of the Refractive Index n.—lf i is the 
observed angle on the divided circle, and iV'the refractive index of 
the glass compared with air, then the index of refraction of the 
liquid compared with air is: 
n '\liV2 sin 2 i* 
If the refractive index is to be reduced to the vacuum standard, 
n must be multiplied by the refractive index of air (at o° and 760 
mm.) = 1.00027. This reduction, however, is frequently omitted. 
The values of N and n depend upon the wave-length of the 
light used in the experiment. 
The values of N for the sodium, thallium, and lithium flames are : 
N 
Na = 1.61511 
T1 = 1.62043 
Li = 1.60949. 
Sodium light is usually employed. As a matter of convenience, 
the refractive indices n, which correspond to the different values of 
i for sodium light, have been arranged in the form of a table (Sec. 
xxi). The results are given for angles which differ 10' in magni- 
tude ; the intermediate values can easily be calculated by means of 
the differences d. 
Sometimes it is necessary to calculate the refractive index of a 
substance for light of a definite wave-length to light of a different 
wave-length. 
This calculation can usually be made very closely by means of 
the Cauchy formula f : 
"* = A + f,.’ 
* For the development, see Ostwald, Lehrb. allgem. Chem., 2. Aufl., Bd. 
p. 406, 1891. 
f Briihl, Zeit. phys. Chem. I, p. 308, 1887. REFRACTOMETER OF PULFRICH. 
177 
nis the refractive index for light of wave-length X; A and B are 
two constants, the values of which can be determined if the refrac- 
tive indices and n2 for the wave-lengths Xt and X 2 are known. 
The formulas are: 
HX2 « 2 
A . A 1 7l(l a 2 
2 2 
A 1 A 2 
and 
B [nx A) V. 
If the values thus obtained for A and B are substituted in the 
equation 
D 
n\ ■=. A 2 
the refractive index nK can be calculated for any light of known 
wave-length. 
The wave-lengths X (in millionths of a millimeter) for the differ- 
ent kinds of light usually employed are ; 
Potassium (red line) =r 768.0 
Sodium (yellow line) = 589.3 
Lithium (red line) = 670.8 
Thallium (green line) = 534-9 
Hydrogen (red line) Ha = 656.3 
Hydrogen (green line) H(3 = 486.1 
Hydrogen (violet line) Hv = 434.0. 
Choice of Method for Determining the Refractive Index. 
—The apparatus of Abbe or Pulfrich is usually employed for chem- 
ical purposes. These methods are both accurate to from one to two 
units in the fourth decimal place. Both methods are extremely 
simple ; especially the method of Abbe, owing to the small quan- 
tity of liquid required. 
The uncertainty of the temperature is an objection to the method 
of Abbe. The method of Pulfrich has the disadvantage that tthe 
cylinder must be frequently cemented to the prism. 
If the refractive index is to be determined accurately to the fifth 
decimal place, a good spectrometer, with horizontal divided-circle, 
must be employed. Wiedemann and Ebert, Physik. Prakt., p. 255, 
1890) Kohlrausch, Prakt. Phys. vn, p. 146, 1892; Glazebrook 
and Shaw, Physik. Prakt., Leipzig, p. 287, 1891. 
Determination of refractive indices at higher temperatures, Bruhl, 
Ber. d. d. chem. Ges. 24, p. 286, 1891. 178 
REFRACTIVE INDEX. 
Specific Refraction, Atomic and Molecular Refraction. 
—The determination of the refractive index and its relation to 
temperature is not of itself sufficient for chemical problems. 
There are definite relations between the refractive index n and the 
density d determined at the same temperature. These relations are 
independent of the temperature. Such relations which are of im- 
portance in the development of chemical laws are shown by the 
expressions : 
n X n2 —II 
,— and 
d n2 ~f- 2 d 
These expressions are known as the “specific refraction,” or 
simply the “refraction constant.” The second Lorentz-Lorenz 
id formula, for practical and theoretical reasons,* is used almost 
exclusively. 
The refraction constant is further multiplied by the atomic or 
molecular weight, for the development of stochiometric laws. 
The expression 
112 I a 
n2 -f- 2 d 
is called the atomic refraction, and the expression 
«2 1 m 
n2 2 d 
the molecular refraction. 
For the calculations, see Table of Atomic Weights, page 229, and 
also the table on page 235, which gives 
«2 I 
'°gW+-2 
for the different values of n. The molecular refraction is calculated 
to the second decimal place. 
* Briihl, Ber. d. d. chem. Ges. 19, p. 2746, 18S6; Liebig’s Ann. 235, p. 1, 1886; 
and Zeit. phys. Chem. I, p. 310, 1887 ; 7, p. 1, 1891 ; Weegmann, Zeit. phys. 
Chem. 2, pp. 219 and 258, 1888; Schiitt, ibid. 5, p. 348, 1890. APPLICATION OF REFRACTIVE INDICES. 
179 
APPLICATION OF REFRACTIVE INDICES TO 
. CHEMICAL PROBLEMS. 
1. The refractive index may be used to determine the degree of 
parity of a substance; it is also frequently used in technical work 
for the identification of substances. 
For tables of refractive indices see, among others, Landolt-Born- 
stein, Phys. chem.. Tab., pp. 204-220, 1883; Kanonnikoff, Jour, 
pr. Chem. [2] 32, p. 497, 1885 ; Briihl, Zeit. phys. Chem. x. p. 
312, 1887 ; 7, pp. 25 and 159, 1891; Jahn, Wied. Ann. 43, 
p. 280, 1891 ; Conrady, Zeit. phys. Chem. 3, pp. 216 and 223, 
1889. 
2. The refractive index can often be advantageously employed to 
determine the concentration of a solution or mixture. 
If 100 parts of a mixture of a solution contain p parts of the one, 
and therefore 100 p parts of the other constituent, and n and d 
represent the refractive index and density of the mixture (solu- 
tion), nv n.2, and dv d 2 the corresponding values for the two con- 
stituents of the mixture, we have the following equations : 
n i «, x , «„ I 
s~.100 = -t—p + 
and 
«2 I 100 I p «22 I 100 p 
«2 -f- 2 d «J2 -f- 2d} «22 -j- 2 d 2 
If, therefore, the refractive indices for a number of concentra- 
tions are known, or if the refraction constants of a solution and 
those of its constituents are known, then the concentration can be 
approximately determined from one of these two formulas. On 
the other hand, the refraction constant of a liquid or solid can be 
approximately calculated from the refraction values of their solu- 
tions or mixtures of known concentrations. As to the degree of 
accuracy, see the work of Schiitt, Zeit. phys. Chem. 5, p. 349, 
1890, and 9, p. 349, 1892, and the bibliography in the same 
Zeitschr. 5, p. 349. 
3. The refraction constants (atomic and molecular refractions) 
are of considerable value in the determination of the constitution of 
organic compounds. REFRACTIVE INDEX. 
The molecular refraction of a compound is equal to the sum of 
its atomic refractions. * 
If m is the molecular weight of a substance, the molecule of 
which consists of p, q, r . . ~ atoms of the elements whose atomic 
weights are av a 2, a3 . . ~ and n and d are the refractive index 
and density of the substance, and nv n2, n3 . . . and dv dv dz . . . 
the corresponding values for the elementary atoms contained in the 
body, then 
n2 I m n-.2 X a, n„2 I a,, «,2 I a* , 
= i- 4- n -L jl. r -2 4- 
n2 -j- 2 d r nx2 2dx J «22 -f- 2d2 nz2 2d3 
The atomic refractions of most elements are known. The 
molecular refraction of a compound, then, can be (1) determined 
directly; (2) calculated from the sum of the atomic refractions. 
The observed and calculated values should agree. This is usually, 
but not always, the case. Frequently the influence of the consti- 
tution of the compound must be taken into account. 
* The Landolt-Briihl theory may be formulated as follows: 
I. Position isomerides have equal specific and molecular refractions ; saturation 
isomerides have different refraction constants. 
2. Polymers never show equal specific refractions nor multiple molecular re- 
fractions corresponding to the molecular weights. 
3. A change of complex atomic groups to simpler groups is always accom- 
panied by a decrease in the refraction. 
4. The optical effect of building up a more complex substance is the same, 
whether an open-chain compound (amylene, diamylene) or a closed-ring com- 
pound (paraldehyde, cymhydrene, menthol, etc.) or compounds with several 
rings (pinene, cyneol) result. 
5. The molecular refraction of truly saturated bodies is approximately equal 
to the sum of the atomic refraction calculated from the empirical formula. All 
those compounds which exhibit' only single-linking of atoms may be considered 
saturated; these represent the true paraffins or derivatives of the general formula 
(C„H2n+2)-xH2. 
6. All unsaturated compounds show a refractive increment which is approxi- 
mately proportional to the number of ethylene, acetylene, or carbonyl groupings. 
The less the dispersive power of the substance, the more nearly this proportion- 
ality holds true. 
See Briihl, Zeit. phys. Chem. I, p. 340, 1887, and ibid. 7, p. 189, 1891, and 
Weegmann, ibid. 2, pp. 222 and 369, 1888. On the influence of dispersion, see 
Briihl, Liebig’s Ann. 235, 1, and Ber. d. d. chem. Ges. 19, p. 2746, 1886. APPLICATION OF REFRACTIVE INDICES. 
181 
If a compound containing C, H, O is investigated, then the 
influence of the single, double, and triple linking of carbon atoms 
on the refraction must be taken into account. The sum of the 
* 
atomic refractions must be increased by a “ refraction increment ” 
= 1.7 units (for sodium light) for each double bond between two 
carbon atoms. The atomic refraction of carbon, when singly 
linked to oxygen, is also different from that when it is doubly 
linked, and these values are less than for carbon atoms bound 
together with one or two bonds. (See table below.) 
If, therefore, the molecular refraction calculated on the assump- 
tion of single linkings is less than the observed value, it indicates, 
when the manner in which the oxygen is linked does not come 
into consideration, the presence of double bonds between carbon 
atoms. The number of double bonds may be found by dividing 
the difference between the observed and calculated values by x.7. 
The following table contains some of the most important atomic 
refractions, calculated from the rf formula of Conrady,* Bruhl,-j- 
-and Landolt for sodium light and the C-line of hydrogen. 
|= represents the double linking; |= the triple of carbon; 
C' represents a carbon atom in the middle of a chain of carbon 
atoms; C° a single carbon atom; O' hydroxyl-oxygen; O" car- 
bonyl-oxygen ; O2 ether-oxygen; and N' a nitrogen atom singly 
linked to carbon. 
Atomic 
Weight. 
Atomic 
Refrac- 
tion for 
Sodium 
Light. 
Approximate 
Atomic 
Weight. 
Atomic Re- 
fraction for 
Sodium Light. 
Conrady. 
Atomic Refraction 
FOR THE C-LINE. 
Landolt. 
Bruhl. 
1.707 
I.707 
1.78 
1.836 
1= 
2.22 
C' 
II.97 
2.494 
12 
2.501 
2.48 
2-365 
c° 
II.97 
2.586 
12 
2.592 
2.48 
H 
I 
I.051 
X 
I.OSI 
1.04 
1.103 
O' 
15.96 
I-5I7 
l6 
1.521 
1.58 
I. 506 
O" 
15.96 
2.281 
l6 
2.287 
2.34 
2.328 
O2 
15.96 
1.679 
l6 
1.683 
1.58 
1-655 
N' 
14 
2.76 
Cl 
35-37 
5-976 
35-5 
5-998 
6.02 
6.014 
Br 
79.76 
8.900 
80 
8.927 
8.95 
8.863 
I 
126.54 
14.12 
126.5 
14.12 
13-99 
13.808 
* Conrady, Zeitschr. phys. Chem. 3, p. 226,1889. Bruhl, ibid. 7, p. 19X, 1891. SPECTRUM ANALYSIS. 
The difference between certain of these values is rather small. 
C' and C° differ very slightly, the difference between O' and O2 
being somewhat larger. 
On the relations for nitrogen, see Lowenherz, Zeit. phys. Chem. 6, p 552, 
1890; Briihl, Zeit. phys. Chem. 7, p. 176, 1891, and Ber d. d. chem. Ges. 26, 
p. 806, 1893; Trapesonzjanz, Ber. d. d. chem. Ges. 26, p. 1428, 1893; for sul- 
phur: E. Wiedemann, Wied. Ann. 17, p. 577, 1882; Nasini, Gazz. Chim. Ital. 
13, p. 296, 1883, and Rend. Lincei 2, p. 623, 1886; 6, pp. 259 and 284, 1890 ; 
Nasini and Costa, Verdfifentl. chem. Instit. Rom, Ref. Zeit. phys. Chem. 9, p. 
639, 1892. 
On the relation of refraction to the constitution of compounds, influence of the 
double bond, etc., see Briihl, Ber. d. d. chem. Ges. 12, p. 2135, 1879, and 19, p. 
3103, 1886; Liebig’s Ann. 200, p. 139, 1880; Zeit. phys. Chem. I, p. 311, 
1887 ; Wallach, Liebig’s Ann. 245, p. 19X, 1888. 
Kanonnikoff, Jour. pr. Chem. (2) 32, p. 497, 1885 ; Weegmann, Zeit. phys. 
Chem. 2, p. 229, 1888; Landolt and Jahn, molecular refraction and dielectric 
constant, Zeit. phys. Chem. 10, p. 289, 1892; refraction of gases, Briihl, Zeit. 
phys. Chem. 7, p. 1, 1891. 
Determination of dispersion: Briihl, Zeit. phys. Chem. X, p. 357, 1887, and 7, 
p. 140, 1891, ibid, literature; Nasini, Roma. Accad. d. Lincei Rendiconti feb- 
brajo, 1887 ; Weegmann, Zeit. phys. Chem. 2, p. 235, 1888; Barbier and Roux, 
Compt. rend. IX2, p. 582, 1891 ; Gladstone, Jour. Chem. Soc. 59, pp. 290 and 
589, 1891. 
XVIII. SPECTRUM ANALYSIS.* 
1. THE DIRECT-VISION SPECTROSCOPE. 
Many elements and compounds which give characteristic emis- 
sion or absorption spectra may be recognized by means of the 
small apparatus represented in figure 73. 
Two brass tubes, movable one in the other, contain a combina- 
tion of crown and flint-glass prisms which cause the dispersion of 
* For the theoretical consideration of spectrum phenomena see, among others, 
Kayser, Lehrbuch der Spectralanalyse, and H. W. Vogel, Praktische Spec- 
tralanalyse. SPECTROSCOPE OF BUNSEN. 
the light that passes through. The rays of light enter through the 
slit i-, and pass through the lens c and the prism combination into 
the eye-piece 0. 
Fig. 73. 
The instrument is adjusted by means of the sun spectrum. The 
inner tube is moved to such a position in the outer tube that the 
Fraunhofer lines of the sun spectrum appear sharp. 
2. THE SPECTROSCOPE OF BUNSEN. 
Apparatus (Fig. 74).—This consists, in its essential parts, of a 
collimator A, through which the light enters, the observing-tube 
B, the scale-tube C, and the prism P. 
Fig. 74. 
The collimator is so adjusted that the rays of light which enter the 
slit in the plate f fall parallel on the prism F, by means of which they 
are dispersed ; the image of the spectrum is formed in the telescope B. 184 
SPECTRUM ANALYSIS. 
The image of the micrometer scale in the tube C is also visible 
just above the image of the spectrum. By means of this the rela- 
tive positions of the different portions of the spectrum can be 
determined. 
Adjustment of the Apparatus.—lt is, above all, necessary 
that the rays of light leave the collimator in a parallel direction, and 
that the image of the slit appears distinct in the telescope. To 
accomplish this the eye-piece of the telescope is adjusted so that 
the cross-wires appear sharp. The telescope is then removed from 
its support and focused sharply on some distant object (church 
steeple, tree, etc.). By means of a mark this adjustment of the 
telescope for parallel rays is fixed once for all. 
The prism is then removed and the telescope placed directly 
opposite the collimator A. The slit is illuminated and its position 
adjusted so that the slit and cross-wires appear sharp at the same 
time, and so that no parallax is produced on moving the eye. By 
raising or lowering the telescope the middle of the slit can be 
made to coincide with the middle of the cross-wires. 
If the prism has not already been adjusted to the position of 
minimum deviation, it may be so adjusted in the following 
manner : 
The slit is illuminated with sodium light, the prism is given a 
chance position, the direction of the outgoing rays determined by 
means of the naked eye, and the telescope turned so that the 
sodium line coincides with the cross-wire. The prism is then turned 
in the direction of the refracting edge, the telescope being moved 
at the same time. This rotation is continued until the image of the 
slit begins to move in the opposite direction. This position of the 
prism, for which the change in direction begins, is the position of 
minimum deviation. The prism should be fixed in this position. 
Finally, it is necessary that the image of the scale should be dis- 
tinct in the telescope. 
The scale-tube is illuminated by means of a small flame, which 
should not be placed too near the tube, and given such a position 
that the image of the scale is visible above the spectrum. The 
scale-tube is then drawn out until the scale divisions appear sharp 
in the telescope, and so that the image of the scale produces no 
parallax with the image of the slit on moving the eye. The hori- SPECTROSCOPE OF BUNSEN. 
zontal position of the scale is brought about by rotating the scale- 
tube. 
Reduction of Scale Values to Wave-lengths.—lt is es- 
pecially desirable, for scientific purposes,* that the positions of the 
different portions of the observed spectrum be expressed not in 
terms of an arbitrary scale, but in wave-lengths of the light 
employed. 
The scale-tube is given such a position that the division 100 coin- 
cides with the middle of the sodium lines. This coincidence is 
preserved in all the movements of the telescope. The reduction of 
the scale values to wave-lengths is accomplished then by means of 
elementary spectra or the sun spectrum. 
In the first case a series of salts, which show characteristic lines 
of known wave-lengths throughout the whole range of the spectrum, 
Fig. 75. 
are vaporized in the Bunsen burner which illuminates the slit. The 
following lines, whose positions in the spectrum are shown in figure 
75, are especially adapted to this purpose ; 
Wave-lengths in Millionths 
of a Millimeter (A .io 6). 
Potassium red line Ka 768 
“ blue “ Kj3 404.6 
Lithium red “ Lia 670.8 
Sodium yellow “ Na 589.0-589.6 
Thallium green “ T1 534-9 
Strontium blue “ Srs 460.8 
768 
As a matter of convenience for introducing the substances into 
the flame, the molten chlorides of the metals may be fastened, in 
* For technical purposes, identification of colors, determination of concentra- 
tions, etc., this calculation to wave-lengths is unnecessary. 186 
SPECTRUM ANALYSIS. 
the form of beads, on platinum wires and a number of such wires 
arranged in a horizontal position, movable around a vertical axis; 
or, still better, a spoon of platinum gauze (p. 205) may be em- 
ployed. See also the arrangements of Pringsheim, Wied. Ann. 45, 
p. 426, 1892, and Kayser, Lehrb. d. Spektralanalyse, p. 77, 1883. 
If an exhausted Geissler tube be partially filled with hydrogen and 
the electric spark (small induction coil with three chromic-acid 
elements) passed through the tube, the four hydrogen lines Ha, 
Up, Hy, and ZTS (A= 656.3, 486.1, 434.0, and 410.2), corre- 
sponding to the Fraunhofer lines C, F, G, h (Fig. 75), are visible 
and may be used for reducing the scale divisions to wave-lengths. 
The accuracy of this reduction to wave-lengths depends upon the 
number of lines observed * and their distribution in the different 
portions of the spectrum. 
When the scale divisions corresponding to a number of lines have 
been once determined, the relation of the same to the wave-lengths 
is represented graphically. 
The scale divisions are laid off as abscissas, and the wave-lengths 
as ordinates, on millimeter paper. It is possible, then, by means of 
the curve which is determined by these points, to represent the 
position of any line in wave-lengths. 
A greater accuracy may be obtained by means of the sun spec- 
trum. 
The slit is illuminated by direct sunlight or bright clouds, and 
then, according to the accuracy desired, the positions of 10, 20, or 
50 characteristic Fraunhofer lines are determined. A number of 
the most important of these lines are shown in figure 75. The 
wave-lengths of the lines, which are not given in the previous page, 
are as follows: 
A-lO 6 A-10—6 
Line A 760.4 Line C 517.3 
“ a 718.6 “ //j 396.6 
“ 687.0 “ H2 393.4 
“ E 527.0 
When a larger number of Fraunhofer lines are observed, refer- 
ence may be made to Angstrom’s Tables; or to Kayser’s Lehrbuch 
* Landolt-Bornstein, Tables of Spectrum Lines, pp. 200-203, 1883. 187 
SPECTROSCOPE OF BUNSEN. 
iiber Spektralanalyse ; likewise to that of G. and H. Kriiss, Kalo- 
rimetrie und quantitative Spektralanalyse. 
Special Rules for Spectrum Observations. Emission 
and Absorption Spectra.—The chlorides are usually employed 
to obtain metallic spectra. These are volatilized on a platinum 
wire in the outer portion of the Bunsen flame ; difficultly volatile 
oxides should be moistened with hydrochloric acid. 
The observer must not be deceived by the sodium lines which 
are always visible, or the faint green and blue lines which are due 
to the lower part of the Bunsen flame. 
For observations of very faint lines, the flame which illuminates 
the scale should be removed until the cross-wire has been adjusted 
to the desired line; the scale is then illuminated and the position 
of the cross-wire determined. 
It is also necessary that all foreign light be excluded during the 
observations. The prism and the objectives of the three tubes are 
therefore covered with a black cloth ; a screen of black paper is 
also placed around the eye-piece of the telescope, to protect the 
eye from the illuminating flame. 
The spectroscope is usually provided with a comparison prism, by 
means of which the lower half of the slit can be covered. By this 
arrangement it is possible to determine the identity of substances 
without accurate measurements. 
Direct light is allowed to enter the upper half of the slit, while 
light from a flame placed to one side (Fig. 74), through total 
reflection, enters the lower half of the slit. The substance to be 
investigated is introduced into one flame, and the comparison 
substance into the other. The two spectra will appear one above 
the other, and in case of identity of the two substances the lines 
of the one spectrum must be the prolongations of the lines of the 
other. 
For qualitative observations of the absorption spectra of colored 
solutions, the solution to be investigated should be placed in a 
glass prism with parallel sides (Fig. 80, p. 195), between the flame 
(petroleum flame) and the slit-tube. Inasmuch as the absorption 
spectra depend upon the concentration of the solution, the obser- 
vations are extended to solutions of different concentrations, 
dilute and concentrated. The temperature and the nature of the SPECTRUM ANALYSIS. 
solvent also influence the absorption. The spectroscope should be 
placed in a room of almost constant temperature (about iß°) ; 
then the influence of temperature for 
all observations within the temper- 
ature-interval 15 to 210 can be 
neglected.* 
The positions of maximum dark- 
ness, for an absorbing substance, are 
the most important absorption bands. 
The positions, in wave-lengths, of 
the edges of the absorption bands are 
determined for solutions of different 
concentrations. The greater the dilu- 
tion, the narrower the bands, and the 
more nearly do they coincide for dif- 
ferent solutions. If the darkness of 
the observed bands increases sym- 
metrically about the middle position,, 
then the arithmetic mean of the band 
edges for very dilute solutions repre- 
sents approximately the position of 
maximum darkness. This position, 
then, from observations on extremely 
dilute solutions, can be interpolated.f 
The determination of the position of 
maximum darkness is especially desir- 
able for the identification of sub- 
stances. 
Spectrum investigations in general 
depend not only upon the positions- 
of the lines and bands, but also on 
their distinctness and dimensions; a 
sketch—or better, photograph—should 
therefore be made of the observed 
spectrum. 
Potassium. 
Carbon. 
Fig. 76. 
* Bremer, Zeit. anorg. Chem. I, p. 112, 1892. 
t Kriiss, Zeit. phys. Chem. 2, p. 314, 1888. UNIVERSAL SPECTROSCOPE OF KRUSS. 
189 
The sketch may be prepared as shown in figure 76. The lines and 
bands are represented by black lines and shadings of equal length. 
The intensity bf the spectrum lines may be indicated by the inten- 
sity of the lines in the sketch; or, better, by the curve in the same 
line where abscissas correspond to scale divisions or wave-lengths 
and the ordinates to intensities. 
On the application of photography to spectrum analysis, see 
Ostwald, Zeit. phys. Chem. 9, p. 582, 1892. 
3. THE UNIVERSAL SPECTROSCOPE OF 
This instrument is a modification of the Bunsen-Kirchhoff ap- 
paratus, and consists, as does the ordinary apparatus, of the prism, 
a collimator with comparison-prism, a scale-tube, and the observing 
telescope {A, B, and C, Fig. 77). 
KRUSS.* 
Fig. 77. 
The advantages in the construction of this apparatus are: 
1. The different parts of the apparatus have been adjusted as far 
as possible by the manufacturer. 
2. The measuring contrivance is especially accurate. 
3. The instrument is provided with an arrangement on the slit- 
* Reference; A. Kriiss, in Hamburg. 190 
SPECTRUM ANALYSIS. 
tube for quantitative measurements according to the method of 
Vierordt. 
The collimator A can not be adjusted ; the manufacturer has 
taken special care that the slit stands exactly in the focus of the 
objective and parallel to the refracting edge of the prism. The 
single slit is generally used, the dopble slit being attached only for 
the method of Vierordt (p. 193). 
The sides of the slit are made of platinum, and the width of the 
opening can be regulated and determined by means of a micrometer 
screw. The slit should be narrowed until the spectrum image is as 
sharp as possible. If the platinum edges of the slit are not clean, 
then the spectrum will contain horizontal streaks. In such cases 
the edges should be cleaned by drawing a piece of glazed paper 
through the almost closed slit. 
The scale-tube B is also free from adjustment. The scale is 
placed in the focus of the objective, and the tube fixed so that the 
middle of the sodium line* coincides with the scale division 100. 
For all measurements where extreme accuracy is not required, the 
scale may be used and the contrivance on the observing telescope 
neglected. The scale divisions are reduced to wave-lengths, as 
described on page 185. 
The observing telescope Cis provided with cross-wires. The 
telescope and cross-wires are adjusted by means of the special con- 
trivance represented in figure 78, which is used instead of the scale 
for fine measurements, especially for carrying out the method of 
Vierordt. 
The telescope is turned about its vertical axis by means of the 
screw and measuring contrivance i\lx i\, situated directly below the 
eye-piece o. The micrometer screw is provided with a graduated 
head rx (100 divisions) ; the number of whole rotations can be read 
directly from the contrivance lx iv 
After adjusting the cross-wires, then, to a definite place in the 
spectrum, it is possible to represent the relative positions in the 
spectrum to four places. The first two are expressed by the 
divisions on the index lx iv and the others by the screw-head ry 
* The sodium line D, as is known, consists of two lines, visible when the slit is 
very narrow. UNIVERSAL SPECTROSCOPE OF KRIJSS. 
Inasmuch as the cross-wires can be moved by means of the 
micrometer screw l 2 r2, it is necessary, before using the contrivance 
lx rv to place I] r2 on the zero. 
This second micrometer screw, with the contrivance /2 r2 for 
moving the cross-wires, is used for fine measurements in the spec- 
trum. 
From the known relation between the value of these two microm- 
eter screws, the results obtained by either contrivance can be 
calculated into terms of the other, likewise into scale divisions, so 
Fig. 78. 
that it is possible to make control-measurements by three inde 
pendent methods. 
The contrivance r212 has still a special use. The cross-wires 
move in the slide h through an opening in the eye-piece ; this slide 
lies in the focal plane of the eye-piece, and is provided with the 
slit k, which, for observing faint lines and for carrying out the 
method of Vierordt, is used to screen the portions of the spectrum 
not in use. 
In case the positions in the spectrum are determined by moving 
Irv then l 2rv as already mentioned, must be adjusted to o. The 
cross-wires for this adjustment are in the middle of the field of SPECTRUM ANALYSIS. 
view, provided the contrivance has first been shoved from right to 
left as far as possible into the eye-piece. For this adjustment of 
the instrument, l 2 r2 on o and the cross-wires in the middle of the 
field of view, the slit kis closed. If the slide is then shoved from 
left to right in the eye-piece, until the movement is again stopped 
by means of a special contrivance on the instrument, the field of 
view will be dark, owing to the spectrum being covered by the 
closed slit, and the line of contact of the two sides of the slit will 
coincide with the middle of the cross-wire. If the slit is unsym- 
raetric, as in the older form of apparatus, then, on opening to a 
definite width by moving l 2 r2, the left side remains stationary and 
the width of the slit or the spectrum region can be read off directly 
from the measuring contrivance r2 lr 
In the more recent form of apparatus the slit opens symmetri- 
cally on the two sides, and the light from the two edges of the 
spectrum region has a mean wave-length, which was established in 
the previous adjustment of the cross-wires by moving lx rv while 
the width of spectrum field is determined by means of /2 r2. 
The divisions on rx lx and r212 are reduced to wave-lengths accord- 
ing to the method on page 185. The positions of 20 to 30 
Fraunhofer lines should be determined for this purpose. The 
spectrum region is then represented in wave-lengths (e.g., 
A 612.7 604.3). 
The universal spectroscope is provided with two prisms: x. A 
single flint-glass prism, with a refracting angle of 6o° and a mean 
dispersion of A— H2 =40 30'; 2. a Rutherford prism, with a 
dispersion of A H2 = 8-n°. 
On account of the greater intensity of the spectrum, the first 
prism should always be used for ordinary qualitative investigations 
and where the determinations are to be made as quickly as possible. 
The Rutherford prism is placed in the instrument only when it is 
necessary to widen the range of the spectrum and attain the 
greatest accuracy possible in the measurements. 
The prisms are placed in a closed, light-proof cap D (Fig. 77), 
and are held in the position of minimum deviation by the pressure 
of a spring fastened to the lower side of the knob K. By means 
of a simple contrivance the prisms can be automatically adjusted to 
the position of minimum deviation for any movement of the ob- 
serving telescope. SPECTROPHOTOMETER. 
4. THE UNIVERSAL SPECTROSCOPE AS 
SPECTROPHOTOMETER. 
Method of Yierordt.* 
Principle and Calculation.—The object of the photometric 
measurements is to determine the amount of absorption for a 
definite range of the spectrum when the light is passed through an 
absorbing medium. These measurements are especially valuable in 
the investigation of liquids (solutions). 
The method of Yierordt depends upon the use of a double slit, 
which can be fastened on the collimator of a spectroscope instead 
of the single slit. 
The intensity of a definite kind of light is proportional to the 
width of the slit. If, therefore, the spectroscope is provided with 
two slits, one directly above the other, either of which can be ad- 
justed independently of the other, then two spectra in contact will 
be formed, the intensities of which will be different, provided the 
slits are of equal width and illuminated by lights of different inten- 
sities. If, however, the widths of the slits are so adjusted that the 
two spectra for any definite range are of equal intensities, then the 
intensities of the two lights are proportional to the widths of the 
slits. If the intensity of one light be placed =l, the intensity of 
the other is obtained from the relative widths of the two slits, which 
can easily be determined. 
The absorption of light by a layer of liquid depends upon the 
thickness of the layer. The results are referred, therefore, to 
a layer of liquid 1 cm. in thickness. 
The operation is usually carried out so that the light which 
enters one slit has passed through a layer of the given liquid 1 ram. 
in thickness, while the light from the same source, which enters the 
other slit has passed through a layer of the same liquid 11 mm. in 
thickness. If the slits be then adjusted so that the two resulting 
spectra are of the same intensity, and the intensity of the original 
light be placed = 1, then the ratio of the widths of the two slits 
* Yierordt, Use of the Spectroscope for Photometry in Absorption Spectra, 
Tubingen, 1873. SPECTRUM ANALYSIS. 
gives directly the intensity J' of the light after passing through a 
layer of the liquid i cm. in thickness. 
The extinction-coefficient e is calculated from the value of J', 
and may be defined as the reciprocal value of the thickness which a 
substance must have in order to decrease the intensity of the light 
which passes through it to jL of the original intensity, e and 
J' bear to each other the simple relation that e— log. J'. For 
the development of this relation, see Kruss, Kolorimetrie und Spek- 
tralanalyse, p. 78, 1892, and Methoden der Analyse, p. 84, 1892. 
The abbreviated table of Yierordt for the calculation of e from J’ is 
given on page 233. 
In the case of solutions the extinction-coefficient depends upon 
the concentration c, where c represents the number of grams of 
dissolved substance in 1 c.c. of solution. So nearly is this co- 
efficient proportional to the concentration that the quotient 
e 
—A) i. e., the absorption ratio for each dissolved substance may 
be regarded as constant. 
In general, the intensity f , the extinction-coefficient e, and the 
absorption-ratio A should be determined in different portions of 
the spectrum for each concentration of solution. 
Apparatus and Method of Operation,—The universal 
spectroscope may be used advantageously. 
The single slit is replaced by a double slit (Fig. 79) ; i. e., one 
slit divided into two halves by means of a horizontal contrivance, so 
that each half can be adjusted independently of the other by means 
of the two fine measuring screws tx and t„. To obtain good results it 
is necessary that the slits should open symmetrically on both sides.* 
The width of the slit is read off in terms of the scale divisions 
on the head of the measuring screw. Each rotation of the screw 
corresponds to xoo divisions. The width of one slit is placed =l, 
corresponding to xoo scale divisions. To produce the same inten- 
sity of light for a definite color, the other slit must be 30 scale 
divisions in width; then 0.3 represents the intensity J', from 
which the extinction-coefficient e may be obtained directly from 
the table (p. 229). 
* Kruss, Kolorimetrie und-Spektralanalyse 1, p. 86, 1892. SPECTROPHOTOMETER. 
195 
The liquid to be investigated is placed in a vessel of the form 
represented in figure 80,—a glass vessel with parallel sides, and 
11 mm. ih thickness. The vessel is provided with the Schulz 
Fig. 79. 
glass body a, a rectangular glass prism 10 mm. in thickness. The 
light, therefore, must pass through a layer of liquid i or n mm. in 
thickness. In the observation the intensity of the light which 
passes through a layer of the liquid i cm. in thickness is compared 
with the intensity of the same light when passed 
through the prism a into the lower slit. If the 
upper slit is adjusted to 100 divisions in 
width, and the lower slit adjusted so that the 
lights are of equal intensities, then the value 
of J' can be read off directly from the lower 
screw-head. 
The liquid in the glass vessel must be free from 
air-bubbles; these can be removed by means of 
a platinum wire. In case a very volatile solvent 
is used, a vessel which can be closed must be 
used to contain the liquid. 
The vessel containing the liquid is placed on a suitable stand 
directly in front of the slit (Fig. 79). The apparatus is illumi- 
nated by means of an electric light, the Auer light, or a petroleum 
lamp B, as shown in the figure. 
Fig. 80. 196 
SPECTRUM ANALYSIS. 
The lamp is placed directly in line with the collimator R, about 
10 cm. from the vessel containing the liquid ; the broad surface of 
the flame should be parallel to the direction of the collimator. 
The two halves of the slit must be equally illuminated by the 
flame. The middle of the flame, therefore, must be of the same 
height as the dividing line between the two halves of the slit. To 
determine when this condition is fulfilled the one slit is opened 30 
divisions and the other adjusted so that the intensities of the cor- 
responding spectrum regions are the same.* If the lamp is prop- 
erly adjusted, then the second slit must be of the same width 
(= 30 divisions) as the first. 
It is further necessary, when the opening of the slit is closed 
slowly, that the graduated screw-head should stand at o the instant 
at which all the light is extinguished. If this is not the case, the 
screw-head and vernier must be adjusted to this condition. 
The vessel containing the liquid must be placed directly in front 
of the slit, so that the upper surface of the glass prism is horizontal 
and in the same plane with the line dividing the two halves of the 
slit. If this condition is not fulfilled, a broad, shadowy band 
appears in the spectrum, the width of which must be reduced to a 
rather heavy line by adjusting the foot-screws of the stand so that 
the upper surface of the prism is horizontal. This line is finally 
brought into coincidence with the dividing line of the two slits, 
which is made visible by opening the slits to different widths. 
This adjustment is made by regulating the height of the horizontal 
surface of the prism by means of the broad screw contrivance on 
the stand. See page 198 on the use of the Hiifner-Albrecht rhomb. 
The scale attached to the observing telescope (p. 191) is used to 
determine the exact wave-lengths of the spectrum region investi- 
gated ; and the limits of a definite spectrum region are determined 
by means of the eye-piece slide described on page 191. 
To obtain accurate results, the method should be carried out in 
that portion of the absorption spectrum where there is no sudden 
change of intensity, but where the intensity increases or decreases 
gradually. There is less liability to error when the slit in the eye- 
* The adjustment of the two slits to equal illuminations should be made sev- 
eral times. This can be more easily accomplished in the green portion of the 
spectrum. SPECTROPHOTOMETER. 
piece is as narrow as possible; the minimum width, however, 
should not be less than 50 divisions on the micrometer screw. 
Other conditions must also be observed in observations on solu- 
tions : • 
1. The solution must be approximately at the temperature of the 
room ; in regard to the influence of temperature on the constant of 
the apparatus, see page 188. A temperature difference of 4to 50 
may be neglected. Care must be taken that the heat from the 
source of light does not produce a greater variation than 50 (Bre- 
mer, Zeit. anorg. Chem. 1, p. 112, 1892). 
2. The influence of the solvent on the value of J', owing to the 
absorption and reflection of light, must not be neglected. 
If the glass vessel is filled with water, the upper slit must be 
adjusted to a width of 90.5 divisions on the micrometer, while the 
lower slit is 100 divisions in width, in order that the two intensi- 
ties shall be equal. In the investigation of all aqueous solutions, 
then, the upper micrometer must be placed on 90.5, and the lower 
on 100, for the starting point of the measurement. 
According to Kriiss, if the lower micrometer is adjusted to 100, 
the upper one, for various solvents, should be adjusted as follows : 
For alcohol (90 per cent.) = 95.0 
For alcohol absolute = 110.0 
For ether aqueous = 98.0 
For ether anhydrpus = 91.5 
For chloroform anhydrous = 112.0 
For benzene anhydrous = X 02.5 
For glacial acetic acid anhydrous = 88.0 
The measurements were made within the spectrum region : 
A 5x3.1 A 523.0. It is desirable, however, that the amount of 
absorption be determined for each solvent, for the values may vary 
from those given above. 
3. It is also necessary to determine the most suitable concentra- 
tion. 
The best results are obtained when the concentration is so chosen 
that the lower half of the slit, for adjustment to equal intensity, 
must be narrowed from the division 100 to from 30 to 10 on the 
micrometer; the value of J' then becomes 0.3 to o. 1. If the solu- 
tion is so slightly colored that J' amounts to more than 0.3 (about SPECTRUM ANALYSIS. 
0.5 or 0.6), then the accuracy may be increased by adjusting the 
micrometers on 50 instead of 100, corresponding to a half turn 
of the screw. The value thus obtained for J' must be multiplied 
by 2. 
The widths of the slits should not exceed 100 divisions; in case 
the solution is too concentrated, it should be diluted, or better, a 
stronger light, the Auer or electric light, should be employed. 
Inasmuch as the absorption ratio A undergoes a slight 
e 
change in many cases, and apparently depends upon the degree of 
ionization * for electrolytes (electrolytic dissociation), the value 
of A must be determined for different concentrations when an 
accurate study of the absorption ratio is undertaken. 
Uses of the Hiifner-Albrecht Rhomb in the Method of 
Vierordt.—This recently}- proposed improvement of the Vier- 
ordt spectrophotometer may be appropriately considered here. 
The double slit D (Fig. 81), provided with the regular microm- 
eter screws ml and m 2, is fastened on the collimator S. Ais the 
liquid vessel with the Schultz glass prism g, which rests on a 
micrometer stand. The glass rhomb R is placed between the 
liquid vessel and the double slit. The object of interposing this 
body is to separate the two spectra by a sharp, fine line, and thus 
avoid the disturbing influence of the rather heavy dividing line 
which occurred in the preceding method (p. 196). 
The rhomb must be adjusted and fastened by means of the screws 
sx and s2, so that its horizontal edge next to the slit is of the same 
height and in immediate contact with the dividing line between the 
two slits, and so that the horizontal section of the rhomb lies in 
the prolongation of the optic axis of the collimator. 
The upper rays of the light 11', which pass through the layer of 
liquid 11 mm. in thickness, fall upon the lower half, and the lower 
rays tx t', which pass through the Schultz glass prism, fall upon the 
upper half of the slit, the rays t and tx coming in contact at the 
horizontal edge of the rhomb next to the slit. The rays t' and //, 
which illuminate the lowest and uppermost portions of the slit, 
* J. Traube, Ber. d. d. chem. Ges. 25, p. 2989, 1892. 
f Kriiss, Zeit. anorg. Chem. 1, p. 122, 1892. SPECTROPHOTOMETER. 
leave, on their passage through the liquid vessel, a free space sev- 
eral millimeters broad, into which the upper surface of the prism g 
may be shoved without producing the troublesome conditions 
previously.mentioned. See Hiifner, Zeit. phys. Chem. 3, p. 563, 
1889, in regard to the use of the rhomb. 
Inasmuch as the upper half of the slit is illuminated by the lower 
light in this method, the lower measuring screw m 2 should be placed 
Fig. 81. 
on 100, and the upper half of the slit (provided with the larger 
screw-head is adjusted so that the intensities of the illumina- 
tions are equal (pp. 196, 198, and 199). 
Before the experiment is begun, the source of light must be 
placed (p. 196) so that the upper and lower spectra are of equal 
intensities when the slits are of equal widths. The rhomb R 
should be protected from foreign light by covering it with a 
cap. 200 
SPECTRUM ANALYSIS. 
The following results, obtained by G. Kriiss for the spectrum of 
potassium permanganate, may be noted: 
i c.c. of solution contains 
Spectrum region 0.00025 gm. 0.000125 Sm. 0.0000625 gm. Absorption 
J' e J' e J' e A 
A 494.7 A 486.5 0.043 1.36654 0.230 0.63828 0.477 0-32149 0.0001909 
A 486.5 A 480.9 0.076 1.17393 0.287 0.54212 0.539 0.26842 0.0002251 
A 480.9 A 474.8 0.154 0.81248 0.440 0.35655 ——- 0.0003277. 
The mean of all the extinction-coefficients in one spectrum 
region for the different concentrations is used in the calculation of 
the absorption ratio. 
The polarization-spectrophotometer of Gian, and especially of 
Hiifner, is used as frequently, perhaps, as the spectrophotometric 
method of Vierordt. Gian, Wied. Ann. 1, p. 351, 1877 ; Hiifner, 
Jour, prakt. Chem. (2) 16, p. 290, 1877 ; and Zeit. phys. Chem. 
3, p. 562, 1889. On the comparison of the two methods, see G. 
and H. Kriiss, Kolorimetrie und quantitative Spektralanalyse, and 
Kriiss, Zeit. anorg. Chem. 1, p. 104, 1892. The disadvantage of 
the polarization-spectrophotometer, owing to the greater loss of 
light, may be overcome somewhat by the use of the Auer gas-light. 
Application of Absorption Spectra.—The qualitative and 
quantitative investigations of absorption spectra may be applied in 
the following directions: 
1. It is frequently possible to accurately determine the concen- 
tration of colored solutions from the extinction-coefficient e and 
the absorption ratio 
A =L. 
e 
When A is known (if necessary, for several concentrations), the 
concentration may be calculated from the extinction-coefficient e 
by means of the formula c— Ae. See G. and H, Kriiss, Kolo- 
rimetrie und Spektralanalyse, 1892. 
2. Absorption-spectra are of great analytical value for identify- 
ing elementary and complex substances. 
On elementary spectra, see, among others, Kriiss and Nilson, Ber. 
d. d. chem. Ges. 20, p. 2134, 1887 ; on the significance of the 
maximum darkness for the identification of color substances, see 
page 187. ROTATION OF THE PLANE OF POLARIZATION. 
201 
3. Absorption spectra are closely related to the constitution of 
the compounds. See Kock, Wied. Ann. 32, p. 167, 1887 ; G. 
Kriiss, Zeit. phys. Chem. 2, p. 312, 1888 ; ibid, earlier litera- 
ture; C. Liebermann, Ber. d. d. chem. Ges. 21, p. 2527, 1888; 
Hartley, Jour. Chem. Soc., p. 641, 1888; Althausse and Kriiss, 
Ber. d. d. chem. Ges. 22, p. 2065, 1889; Schiitze, Zeit. phys. 
Chem. 9, p. 109, 1892; Grebe, ibid. 10, p. 673, 1892; Weigle, 
ibid. 11, p. 22, 1893. 
4. Absorption phenomena are of special interest in the theory of 
solutions. Walther, Wied. Ann. 36, p. 518, 1889; Rigollot, 
Compt. rend. 112, p. 38, 1891; Knoblauch, Wied. Ann. 43. 
p. 738, 1891 ; Ostwald, Zeit. phys. Chem. 9, p. 579, 1892 ; 
Lellmann, Lieb. Ann. 270, p. 204, 1892. 
XIX. ROTATION OF THE PLANE OF 
POLARIZATION. 
General.—The particles of ether in a ray of ordinary light 
vibrate in different directions perpendicular to the line of propa- 
gation, while in plane polarized light the particles vibrate in a 
single plane. This plane is called the plane of polarization.* 
Light may be polarized in various ways: very simply by allow- 
ing a ray of ordinary light to pass through a Nicol prism. This 
consists of a definite combination of two sections of Iceland spar 
(Landolt, Optisches Drehungsvermogen, p. 3, 1879), so that 
the entering ray of light is divided into two polarized rays, and 
so that only the one (extraordinary) ray passes through the prism, 
while the other (ordinary) ray is removed by total reflection. 
If two such Nicol prisms are placed in similar positions in a 
tube, the polarized ray of light which leaves the first prism will 
* According to Fresnel, the particles of ether vibrate perpendicular to the plane 
of polarization; the above assumption of Neumann, owing to its greater sim- 
plicity, will be taken here. 202 
ROTATION OF THE PLANE OF POLARIZATION. 
also pass unobstructed through the second prism ; if the second 
prism is rotated through an angle of xBo°, the ray will still pass 
through, for the planes of polarization of the two prisms are par- 
allel for this position. If, however, the second prism is rotated 
through 90 or 270°, the planes of polarization of the two prisms 
will be perpendicular to each other, and the light which passes 
through the first prism will be completely extinguished by the 
second. If the eye is placed behind the second prism, and one of 
the prisms is rotated through 360°, four positions 90° apart will be 
seen to be positions of maximum light and maximum darkness, 
while the intermediate positions will exhibit varying degrees of 
illumination. 
The first .prism is called the polarizer; the second, situated next 
to the eye, the analyzer. 
If the polarizer and analyzer are illuminated with homogeneous 
light and adjusted to the positions of maximum darkness, and a 
transparent substance—a liquid in a tube—is introduced between 
them, the dark field of view in many cases becomes illuminated, 
and one of the prisms must be rotated through a definite angle to 
again restore the maximum darkness (principle of the simple 
polarimeter). 
One speaks of the rotation of the plane of polarization of a 
substance and of the angle of rotation, distinguishes optically 
active and inactive substances, and calls the substance dextro- or 
levorotatory, according to the sense of the rotation—i. e., 
according as the analyzer must be rotated to the right or left to 
restore the maximum darkness (p. 208). 
Specific Rotatory Power.—The rotatory power of liquids 
and dissolved substances only will be considered here. 
The amount of rotation of the plane of polarization depends: 
1. On the nature of the substance. 
2. On the number of optically active molecules, which influence 
the ray of light; for homogeneous liquids, therefore, on the length of 
the column and density of the liquid through which the light passes ; 
for solutions, on the length of the column and the concentration. 
3. On the wave-length of the light used in the observations. 
4. On the temperature at which the observation is made. 
5. On the nature of the solvent, in the case of solutions. ROTATION OF THE PLANE OF POLARIZATION. 
203 
Let a represent the angle of rotation—i. e., the angle through 
which the analyzer must be rotated to the left or right to restore 
the original condition, after interposing a tube filled with an opti- 
cally active liquid ; let d be the density of the liquid, and I the 
length of the column of liquid ; then 
r -i a 
W = id 
is called the specific rotatory power, or the specific rotation of a 
homogeneous liquid. 
The specific rotatory power may be defined as that rotation of 
the plane of polarization produced when the light passes through 
an optically active substance 1 dm. in length, which contains 
1 gm. of substance per c.c. of volume. 
The molecular rotatory power represents the rotation produced by 
one gram-molecule of the substance under the conditions mentioned 
for the specific rotatory power. 
We have then : 
r ma m [«] 
[m\ = —— 
100 I a 100 
The values are divided by 100 to avoid large numbers. 
If c is the number of grams of substance contained in 100 c.c. of 
a solution, the specific rotatory power for the given concentration 
is calculated by the formula ; 
r n 100 a 
M 
likewise 
m a 
[»] = 
If p grams of substance are contained in 100 gm. of solution, and 
the density of the solution is d, then the specific rotatory- 
power is 
_ _ zoo a 
M = 1 
and the molecular power is 
m a 
M = -[JT- 
The calculations for solutions are made according to 
the above formulas; however, the temperature, the concentration, 
and the solvent should be considered. 204 
ROTATION OF THE PLANE OF POLARIZATION. 
In general, the specific rotation of a substance is in no way pro- 
portional to the concentration of the solution. The value of [«], 
therefore, should be calculated for different concentrations, and the 
relation of the specific rotation to concentration expressed by 
formulas of the form [«] = A -f- B q and [a] A -(- B q -(- C q1; 
where q is the number of grams of the solvent in 100 gm. of solu- 
tion, and A, B, and C are constants, the values of which can be 
easily determined from three or more determinations of [a] for 
different values of q. A is the true specific rotatory power of the 
pure substance, for in this case q = o. 
In order to determine whether the two- or three-constant formula 
is to be used, [a] should be determined for widely varying con- 
centrations, and the relation of [a] to q represented graphically by 
placing the corresponding values in a system of coordinates 
(p. 186). If the curve is a straight line, the formula [a] = A B q 
should be employed ; otherwise the formula 
[a] A -j- B q Cq2 
is used; e.g., for tartaric acid the first formula is used ; for sodium 
light it becomes [«] = 1.950 -f- 0.1303 q. 
If the true specific rotatory power of the dissolved substance is 
to be determined as accurately as possible, the substance should be 
dissolved in an inactive solvent which permits of very high concen- 
trations. The observations should be made with several solvents. 
The more concentrated the solution is, the smaller are the devia- 
tions in the values of [a] calculated for the given concentration 
and for the pure substance. The true specific rotatory power can 
not be calculated for sparingly soluble substances. It is sufficient 
in such cases to establish the above interpolation-formulas which 
show the dependence of the specific rotatory power on the concen- 
tration. 
Sodium light is usually employed in these observations; the less 
intense lithium light or the too volatile thallium light are seldom 
used. When lithium light is used, a red glass is placed between the 
flame 'and the apparatus to hold back the yellow rays. The kind of 
light used is indicated by a sub-index, thus [«] D (specific rotation 
for sodium light) ; [«]u for lithium light, etc. 
If the observations are to be made with light in other portions of ROTATION OF THE PLANE OF POLARIZATION. 
205 
the spectrum, a combination of polariscope and spectroscope is 
used (Landolt, Drehungsvermogen, p. Ix 9, 1879). 
The light used should be as constant as possible and of as great 
an intensity as possible. 
A lamp similar to that represented in figure 82 may be used 
to produce homogeneous sodium 
light, ais a Bunsen burner, b a 
chimney with an opening in one 
side, and d a movable rod, to 
which is fastened a platinum wire 
and a platinum-gauze spoon. Com- 
mon salt is melted in this spoon and 
volatilized in the hottest portion 
of the flame. 
The following simple contriv- 
ance is also to be recommended 
for producing a strong and lasting 
sodium light : 
A strong platinum wire is cov- 
ered with platinum gauze. The 
necessary sodium chloride, or, 
better, sodium bromide, on ac- 
count of the greater intensity of 
light, is fused, finely powdered, 
and placed in a platinum boat. 
The platinum gauze is then heated 
to redness and rolled in the sodium 
salt. A Miinke burner is used as 
the source of light (p. 186). 
Influence of Temperature, 
Liquid-tube, and Liquid.—An 
elevation of i° in temperature for a 
column of liquid 2 dm. in length 
diminishes the angle of rotation 
several tenths of a degree. The 
observation temperature, therefore, must be noted for all accurate 
measurements. It is advantageous to make the observations at 
a constant temperature of about 20°. This can be easily done 
Fig. 82. ROTATION OF THE PLANE OF POLARIZATION. 
if the liquid-tube is surrounded by a metallic mantle (Fig. 83), 
which is filled with water during the experiment, and which is pro- 
vided with a thermometer opening at d. 
If the apparatus is not provided with this contrivance, tubes of 
the ordinary form (Fig. 84) are used. These are glass tubes A, 
usually 1 to 2 dm. long ; they are ground off at the ends exactly 
perpendicular to their axes, and are closed by means of parallel 
Fig. 83. 
glass plates (g} g2), which can be fastened on by means of the screw 
arrangements mx nv m 2 n.,. 
The glass plate must not be pressed down too strongly, for glass 
under pressure becomes doubly refracting; this would influence the 
rotation of the plane of polarization, and hence introduce an error. 
It is better, therefore, to place a rubber ring on the inner glass 
Fig. 84. 
surface. In all cases, however, the influence of these plates for new 
instruments should be tested. 
The exact length of the tube should be given by the manufacturer; 
otherwise see the measuring contrivance of Landolt, Drehungsver- 
mogen, p. 125, 1879. 
The tube and glass plates must be carefully cleaned. The pres- 
ence of air-bubbles must be avoided in filling the tube. The liquid POLARIMETER OF MITSCHERLICH. 
207 
should be clear. In case of filtration, care must be taken to 
prevent any change in the concentration of the solution. 
the weights should be given in percentages. For accu- 
rate determinations, the weighings should be reduced to the vacuum 
standard (p. 12). The specific gravity is determined by means 
of the pyknometer (p. 19). The results should be accurate to 
the fourth decimal place. 
Special attention should be called to the bi-rotation and similar 
phenomena, according to which the rotatory power of many solu- 
tions undergoes a change with time, and frequently becomes con- 
stant after the lapse of considerable time (Ostwrald, Allgem. Chem., 
2. Aufl., Bd. 1, p. 496, 1891, and Sonnenthal, Zeit. phys. Chem. 9, 
p. 656,1892). 
The apparatus (Figs. 85 and 86) consists in its simplest form 
of a polarizing Nicol a, by means of which the light on entering the 
tube is polarized. The rays of light are made parallel by means 
of a lens; and, after passing through the empty or filled tube f, 
they enter the second analyzing prism b, which is usually fastened 
to a graduated circular disc (with vernier, p. 215), by means of 
which the prism can be rotated. Sometimes, as in the figure, the 
disc is fixed in position ; in such cases the vernier is fastened to 
the prism and may be rotated by means of the handle c. 
1. THE POLARIMETER OF MITSCHERLICH. 
The observations are carried out in a (at least, partially) dark- 
ened room ; foreign light may be excluded by a black screen placed 
behind the sodium light. 
The empty tube is first placed in the apparatus, the analyzer 
rotated through 360°, and the two positions, 180° apart, are 
determined for which the Nicols are crossed (positions of maxi- 
mum darkness). The field of view then appears somewhat like 
figure 87 ; black streaks occur in the middle of the field. The 
zero of the scale can be adjusted to this position by rotating the 
polarizer with the help of the screw e; this adjustment, however, 
is usually made by the manufacturer. 
After determining the zero point, the tube is filled with liquid, 
and the angle measured through which the analyzer must be ROTATION OF THE PLANE OF POLARIZATION. 
rotated to the right or left to restore the condition of maximum 
darkness. 
If the angle, calculated from the zero point, is smaller when 
the analyzer is turned to the right than when turned to the left, 
a dextrorotatory substance is usually present, while in the opposite 
case a levo body is present. If, for example, the analyzer must 
be rotated 40° to the right or 140° to the left to restore the maxi- 
mum darkness, the substance 
is dextrorotatory. 
To determine this with 
certainty, in doubtful cases, 
where considerable rotation 
is produced, a tube of half 
the length or a solution of 
half concentration is used. 
The rotation then will be 
only half as great as in the 
first case. In the above ex- 
Fig. 86. 
Fig. 85. 
Fig. 87. 
ample therefore, the analyzer must be rotated 20° or 200° to the 
right, or adjusted from the left to the numbers no° or 290°, then ; 
„ , . 140° 
290° = 360° —. 
For accurate measurements a large number of observations should 
be made, and the adjustment made for the two positions of maxi- 
mum darkness, ißo° apart; the results obtained frequently show 
slight variations. The differences between the separate observa- 
tions usually amount to several tenths of a degree. 
The Mitscherlich apparatus has been modified in recent times POLARISTROBOMETER OF WILD. 
209 
somewhat on the principle of the half-shadow instrument. A 
small telescope is placed in front of the analyzer and a quartz 
plate of definite thickness is introduced behind the polarizer. On 
rotating the analyzer, the two halves of the field of view become 
evenly and unevenly shaded, as in the case of the Laurent and 
Lippich apparatus described farther on. This new construction of 
the Mitscherlich apparatus is more sensitive than the older form. 
2. THE POLARISTROBOMETER OF WILD. 
This apparatus (Figs. 88 and 89) is capable of sharper adjust- 
ment than that of Mitscherlich. 
A Savart plate * s, formed of two quartz or calcite plates, is 
placed between the polarizing and analyzing Nicols. A number of 
dark interference bands (Fig. 90) are produced by this plate, 
which vanish for definite positions of the prisms. In the measure- 
Fig. 88. 
ments, the instrument is adjusted to these positions of maximum 
illumination. 
The polarizer, which is illuminated by sodium light, is fastened 
to the graduated disc E provided with a vernier; this disc can be 
rotated by means of the knob P fastened to the toothed rod Q. 
The readings are made by means of the telescope T, in which is 
placed at Van inclined mirror, which reflects the light from a small 
gas-flame onto the vernier. It is to be noticed, inasmuch as the 
polarizer is rotated, that a rotation of the disc E to the left, and 
therefore of the knob P to the right, corresponds to a dextro- 
rotatory substance. 
The zero point is adjusted by determining, during the rotation 
of Q, the four positions 90° apart, for which the interference bands 
* Wiillner, Physik, 3. Aufl., Bd. 11, p. 604, 1875. 2 10 
ROTATION OF THE PLANE OF POLARIZATION. 
(Fig. 90) vanish. By means of the screw M these positions can be 
made to correspond with the scale divisions o°, 90°, 180°, and 
270°, provided this adjustment has not already been made. 
Fig. 89. 
The instrument can be adjusted very sharply to the maximum 
illumination. The apparatus is provided with a small cross-wire 
telescope (Fig. 88, c, d, e), the eye-piece of which is focused 
sharply on the cross-wires. In adjusting to 
maximum illumination the cross-wires should 
be placed symmetrically with reference to the 
darkened edges of the field of view. 
The direction in which the substance rotates 
the plane of polarization is determined as on 
page 208, greater care being necessary, how- 
ever, owing to there being four zero points. 
Let the zero points be o°, 90°, xBo°, and 
270°, and, after introducing the filled tube, suppose the positions 
of maximum illumination to be 40°, 130°, 220°, and 310° ; a ro- 
tation of 40° to the right or 50° to the left is to be considered. 
Fig. 90. HALF-SHADOW APPARATUS OF LAURENT. 
A tube of half length or solution of half concentration is then ex- 
amined, and if the substance is dextrorotatory, the positions of 
maximum illumination will be 20°, uo°, 200°, and 290°, or if 
levo-, 65°, 1550, 2450, and 3350. 
In the case of strongly rotating substances the angle of rotation 
sometimes amounts to more than 90°. By examining tubes of 
different lengths, however, it is an easy matter to determine 
whether the angle is aor 900 + a. 
For extremely accurate work the measurements should be made 
from each of the four zero points; usually, however, it is sufficient 
to measure from two points xBo° apart. After a little practice, the 
separate observations should not vary more than a few hundredths 
of a degree. 
The measurements are carried out in a somewhat darkened room. 
The liquids should be clear; any coloration should, if possible, be 
avoided. 
3. THE HALF-SHADOW APPARATUS OF 
LAURENT. 
The sodium light enters this polarimeter (Figs. 91 and 92) 
through a diaphragm, which is provided with a plate of potassium 
bichromate crystal, in order to remove the foreign light which 
accompanies the yellow light. 
On leaving the lens e, the rays pass parallel into the Nicol d, and 
then enter a second diaphragm f half of which is covered with a 
quartz or mica plate of definite thickness cut parallel to the axis. 
From here the rays pass through the liquid-tube p into the analyzer 
g, thence through the lenses i and h (Fig. 92) of the telescope K, 
through which the observations are made. 
The characteristic part of the apparatus is the quartz or mica 
plate, the thickness of which is chosen so that the rays of sodium 
light which pass through suffer a change of phase of half a wave- 
length. 
If the polarizer is adjusted so that the plane of polarization of 
the light is parallel to the axis of the quartz, then for each position 
of the analyzer the two halves of the field of view will be equally 
illuminated. If, however, the polarizer is placed at an angle a with 2 12 
ROTATION OF THE PLANE OF POLARIZATION. 
this axis, the plane of polarization of the rays of light which pass 
through the quartz plate will suffer a like displacement, but in the 
opposite direction (Landolt, Drehungsvermogen, p. 115, 1879). 
For this second adjustment the circular field of view appears 
divided into two halves (Fig. 93), which for most positions of the 
Fig. 91. 
Fig. 92. 
Nicol are unequally illuminated (Fig. 93, 1 and 2), but which for 
two positions 180° apart are uniformly illuminated. 
The instrument can be adjusted sharply to this mean, uniform 
illumination ; this is the zero position from which the measure- 
ments are made. HALF-SHADOW APPARATUS OF LAURENT. 
213 
The apparatus (Fig. gi) is constructed so that the analyzer, 
fastened to the telescope and vernier, can be moved by means of 
an arm on the fixed circle c. The vernier is read by means of the 
microscopd L. 
As already mentioned, the plane of the polarizer must form an 
angle with the axis of the quartz plate, thereby producing unequal 
illuminations of the two halves of the field. This is accomplished 
by means of the contrivance JK, by means of which the polarizer 
can be rotated. 
The apparatus is firsf adjusted to the parallel position, so that for 
any position of the analyzer the two halves of the field of view are 
equally illuminated. The polarizer is then rotated through the 
angle aby means of JK. The smaller the angle is, the more 
sensitive is the instrument; the more brilliant the light and the 
clearer the liquid, the smaller can a be. The proper adjustment of 
Fig. 93. 
the polarizer is that position corresponding to the greatest change of 
shade in the field of view for a slight movement of the analyzer. 
At the beginning of the observation the telescope is focused 
sharply on the diaphragm, so that the dividing line at the edge of 
the quartz plate appears sharp. 
In determining the zero point the tube should be filled with 
water, in order that the intensity of the light may be the same as 
that when the active liquid is observed. In case the field of view 
is too dark, on account of the liquid being colored or not being 
clear, the illumination may be increased by a slight rotation of the 
polarizer; this, however, renders the instrument less sensitive. 
If a dextrorotatory substance is observed, the angle on the circu- 
lar disc will be smaller when turned to the right than when turned 
to the left; for strongly rotating substances, the method on page 
208 is used. 214 
ROTATION OF THE PLANE OF POLARIZATION. 
The mean of a large number of results, measured from the two 
zero points xBo° apart, should be taken as the true value. 
The apparatus can be used only for sodium light, for the thick- 
ness of the crystal plate has already been adjusted for L 
4. THE HALF-SHADOW APPARATUS OF 
LIPPICH. 
The essential features in the method of operation for the Laurent 
apparatus apply also to this much-used apparatus. 
The main difference in the construction consists in that the 
quartz plate is replaced in this apparatus by a third Nicol prism, 
which covers half of the field of view. 
On rotating the polarizer by means of an arm, its plane of polar- 
ization forms an angle with that of the smaller middle prism. This 
angle should be as small as possible (p. 213). 
This apparatus has the advantage over that of Laurent in that 
homogeneous light of any wave-length can be used. With the 
finer construction of this apparatus the angles may be read to 
0.001 or 0.002°. On observations with this apparatus, see, among 
others, Sonnenthal, Zeit. phys. Chem. 9, p. 660, ibid. Rimbach, 
p. 700, 1892. 
On the technically important apparatus of Soleil-Ventzke for investigations of 
sugar, see Landolt, Drehungsvermogen, p. 149, 1879. 
Tables of the Rotatory Power, Landolt-Bornstein, Phys. chem. Tab., p. 224, 
xBBj. 
The significance of the rotatory power in stereochemistry, see Meyerhoffer, 
Stereochemie, Leipzig, 1892, and Hantzsch, Grundriss der Stereochemie, Breslau, 
1893.* The other uses for scientific and technical purposes, especially for deter- 
mining the concentrations of solutions, see Landolt, Optisches Drehungsvermogen, 
1879, anh ®er- d* h- diem. Ges. 21, p. 191, 1888. For further recent literature 
see Hartmann, Ber. d. d. chem. Ges. 21, p. 221, 1888 ; Pribram, Sitzungsber. 
Wien. Akad. (97) II b, June, 1888, and Ber. d. d. chem. Ges. 22, p. 6, 1889 ; Long, 
Sill. Ann. Jour. 36, p. 351» 1888, and 38, p. 264, 1889; Sorokin, Jour. russ. 
Ges. p. 417, 1888; Ref. Zeit. phys. Chem. 4, p. 482, 1889; Kanonnikow, Jour, 
russ. Ges. pp. 571 and 686, ISBB, and p. 369, 1890 ; Ref. Zeit. phys. Chem. 4, 
p. 482, 1889, and 6, p. 88, 1890; Sonnenthal, Zeit. phys. Chem. 9, p. 660; 
Rimbach, ibid. 9, p. 700, 1882. 
On magnetic rotation, see Perkin, Ber. d. d. chem. Ges. 15, p. 1363, 1882 ; 
Jour. Chem. Soc. 45, p. 422, 1884; 52, p. 362; 1887; 53, p. 561, 1888; 55, GENERAL CONTRIVANCES FOR MEASUREMENTS. 
215 
p. 680, 1889. Jour, prakt. Chemie N. F. 32, p. 523, 1885 ; Chem. News 59, 
p. 247, and 60, p. 253, 1889; 62, p. 255, 1890; 64, p. 269, 1891 ; Jahn, Sitz- 
ungsber. Berl. Akad. p. 237, 1891, and Wied. Ann. 43, p. 280, 1891; Wachs- 
muth, Wied. Ann. 44, p. 377, 1891, and Schonrock, Zeit. phys. Chem. 11, 
P- 753, i 893- 
XX. GENERAL CONTRIVANCES FOR 
MEASUREMENTS. 
1. THE VERNIER (CIRCULAR VERNIER). 
The arc A (Fig. 94) is fixed in position, while the arc 8,. the 
vernier, is movable about the central point of the two arcs. Ais 
graduated in degrees and half degrees, B is divided so that 30 of 
Fig. 94. 
its divisions correspond to 29 half-degree divisions on the main 
circle; therefore each division on the vernier is one minute of arc 
smaller than one division on A. GENERAL CONTRIVANCES FOR MEASUREMENTS. 
The vernier is adjusted so that its zero point coincides with the 
zero point of the circle ; the first division then is removed i', the 
second 2', the third 3', etc., from the corresponding divisions on 
the circular scale. 
If the vernier is rotated through a definite angle, the magnitude 
of which is to be determined, the number of whole and half degrees 
through which the index o of the vernier has moved, is read off 
directly from the main circle. 
This reading is sufficient only in case the zero of the vernier 
coincides with a division on the circle ; usually, therefore, a definite 
number of minutes must be added to the first reading. The 
number of the division on the vernier which coincides with a 
division on the main scale, represents the number of minutes to be 
added. 
The vernier is usually read by means of a microscope, which 
must be placed so that the division to be observed falls in the 
middle of the field of view. The field of view is illuminated, 
when necessary, by means light reflected from a small mirror; 
a small white paper-screen may also be used for this purpose. 
The apparatus with vernier attachment is frequently constructed 
so that the vernier is fixed and the circle movable. 
2. THE CATHETOMETER. 
The cathetometer is used to measure the vertical distance between 
two points. 
The column M (Fig. 95) resting on the foot D, which is sup- 
ported by the screws mx m 2 mt, is movable about its axis. 
On this column are two sliding contrivances F and F', with 
which the telescope B is fastened, and which are connected to the 
counter-weight Q by means of a cord passing over the pulley T. 
The slide F' can be clamped at any desired height by means of 
the screw K, after which the slide F can be raised or lowered by 
means of the micrometer screw J. The telescope B provided with 
the spirit-level L is fastened to Fby means of the forks G and G'. 
The telescope can be leveled by means of the screw o. 
In the middle of the column Mis an inlaid silver strip, which is 
graduated in small divisions. By means of a vernier in the opening THE CATHETOMETER. 
Fig. 95. 21 8 
GENERAL CONTRIVANCES . FOR MEASUREMENTS. 
at F it is possible to determine the vertical distance between two 
positions of the telescope with great accuracy. 
In carrying out the measurements it is necessary (i) that the axis 
of the column is exactly vertical; and (2) that the axis of the tele- 
scope is exactly horizontal. 
To adjust the axis of rotation to a vertical position, the column 
is turned so that the axis of the telescope is parallel to the line 
joining mx and mr After adjusting the spirit-level by means of 
these screws, the column is turned through an angle of xBo°, and 
the level again adjusted by means of the screw 0 and the foot-screws 
m 1 and w2; the adjustment must be such that the level remains 
unchanged for these two positions 180° apart. When this is accom- 
plished, the column is rotated so that the axis of the telescope is 
perpendicular to the line joining m 1 and m 2; the level is then 
adjusted by means of the screw mr The final adjustment must be 
such that the level remains unchanged during a complete rotation. 
To determine whether or not the axis of the telescope is hori- 
zontal, the cross-wires of the telescope are adjusted sharply on a 
definite mark ; the telescope is then removed from its position, 
turned end for end, and replaced in its position. The column is 
then rotated through 180°, when the cross-wires must again coincide 
with the mark, provided the axis of the telescope is horizontal. If 
the cross-wires do not fall exactly on the mark, half of the distance 
must be corrected by means of the screw 0. 
3. THE THERMOMETER. 
The Beckmann Thermometer.—Besides the ordinary mer- 
cury thermometer, the Beckmann thermometer is especially valuable 
in physico-chemical measurements. This thermometer can not be 
used for determining definite temperatures, but only for determining 
definite temperature differences (depression of the freezing point, 
elevation of the boiling point, thermochemical measurements, etc.). 
The thermometer, provided with an arbitrary scale divided into 
0.01 or 0.020, is represented in figure 36, page 82. The char- 
acteristic part, the mercury reservoir at the upper end, is shown in 
figure 96. 
By means of this reservoir at the upper end of the thermometer- THE THERMOMETER. 
219 
tube, the quantity of mercury in the lower bulb of the thermometer 
can be increased or decreased. 
If a definite temperature change is to be measured, the ther- 
mometer js heated to approximately the desired temperature; if, 
then, the mercury thread is too long, the thermometer is heated to 
i or 20 above the temperature, until the thread extends to the 
mercury in the upper reservoir. By gently tapping the lower 
end of the thermometer with the hand, the mercury thread is 
broken off from the excess of mercury in the reservoir. If the 
quantity of mercury in the lower reservoir should be too small, the 
adjustment is made in a manner similar to that 
just described : the thermometer is heated until 
the thread extends to the mercury in the reser- 
voir, and, after cooling to approximately the 
desired temperature, gently tapped with the 
hand, as before. 
These and other thermometers, constructed 
in recent times by F. O. R. Gotze, in Leipzig, 
have been adjusted so that the same thermo- 
meter can be used for freezing-point and boil- 
ing-point determinations. 
It must also be noticed that for such ther- 
mometers, owing to the separation of the mer- 
cury at higher temperatures, the degree becomes 
somewhat smaller ; the elevation of the boiling 
point is thereby diminished. Inasmuch as this 
error may amount to more than i per cent., it 
is necessary for accurate measurements that the thermometer be 
calibrated, in case the corrections for different temperatures are not 
known. 
Fig. 96. 
Mercury thermometers for measuring temperatures up to 550°, see Reckling- 
hausen, Ber. d. d. chem. Ges. 26, p. 1514, 1893 ; see, further. The Measurement 
of High Temperatures, by C. Earns, Leipzig, 1892. 
A simple air thermometer: Lothar Meyer, Ber. d. d. chem. Ges. 26, p. XO5O, 
1593. 
Thermometer Testing and Temperature Corrections.— 
The testing and correcting of thermometers may be divided as 
follows: (a) Determination and correction of the zero point; 
the boiling point; (V) correction for the value of the degree ; 220 
GENERAL CONTRIVANCES FOR MEASUREMENTS. 
(d) correction for the projecting thread of mercury ; (<?) correc- 
tion of the caliber error. 
Determination of the Zero Point.—The thermometer is 
kept for a considerable time at a temperature not much above o°, 
packed in melting snow or immersed in pulverized ice moistened 
with distilled water. The water formed must be carefully removed. 
The determination should also be made by lowering the tempera- 
ture of the room. 
The thermometer is left in the ice for an hour or so, after 
which the temperature is read. This temperature, equal to that of 
the ice, is represented by E . 
If the thermometer is heated to a higher temperature, the capac- 
ity of the mercury reservoir increases, owing to the expansion of 
glass. On subsequent cooling, this change, in many cases, is not 
completely corrected until weeks or even months have elapsed. 
This causes a lowering of the position of the mercury, a depression 
of the zero point, the amount of which depends on the kind of 
glass, the temperature to which it has been heated, and the length 
of time heated. After heating for some time at ioo°, the depres- 
sion for ordinary glass amounts to i°, for Jena normal glass a mean 
of 0.056° (Bottcher, Zeit. f. Instrumentenkunde, p. 409, 1888). 
Owing to this depression of the zero point, it is better that 
thermometers which are to be used for temperatures approximately 
equal to zero should be kept in a room of as low a temperature as 
possible, and should be surrounded by snow for a considerable 
time before use. If the thermometer is to be used for higher tem- 
peratures, then the zero point ElOO should be determined; i.e., the 
zero point which a thermometer shows after remaining for some 
time in ice, when the same thermometer, about half an hour before, 
had been heated to ioo°. This zero point is also used as the basis 
for graduating thermometers. For use at higher temperatures, the 
zero point is determined for the corresponding temperature; e.g., 
Em, Em, etc. In such cases the change of the zero point may be 
considerable. If E0 and Ewo are known, and /is a temperature 
between o and ioo°, then we have approximately : 
E =£loo+ E° Iof10° (100 /)* 
* Landolt, Zeit. phys. Chem. 4, p. 351, ISB9. THE THERMOMETER. 
22 1 
For thermometers of Jena normal glass the equation is approx- 
imately : 
Et = ElOO -(-0.00056(100—/). 
This zero correction must always be subtracted from the observed 
temperature 
Determination of the Boiling Point.—The apparatus rep- 
resented in figure 97 may be used for this purpose. The ther- 
mometer B is fastened in the top 
of the double-walled vessel A C, 
so that the mercury thread, when 
adjusted to the boiling point, 
stands at the top of the stopper, 
and so that the mercury reservoir 
is at least 2 cm. above the surface 
of the boiling liquid. The vapor 
escapes at r; a small water man- 
ometer is placed at r' to measure 
the excess of pressure p in the 
vapor chamber. The pressure in 
the apparatus is slightly greater 
than the atmospheric pressure, 
owing to the narrowness of the 
outlet-tube r. After heating for 
a suitable length of time, the tem- 
perature is read off. The baro- 
metric pressure is simultaneously 
read, reduced to o° (p. 224), and 
then added to the slight excess of 
pressure p, which must first be 
reduced to mercury units. If bis the corrected barometric pres- 
sure in millimeters, then the boiling point t of water (between 715 
and 770 mm.) is given to o.oi° by the equation : 
Fig. 97. 
See also Tabellen von Landolt-Bornstein, p. 40, 1883. 
Correction for the Degree Value.—lf A is the boiling point 
t = xoo° 0.0375° (b 760). 
* Kohlrausch, Prakt. Phys. vn, p. 82, 1892. 222 
GENERAL CONTRIVANCES FOR MEASUREMENTS. 
reduced to 760 mm., and Em the freezing point, with a ther- 
mometer previously heated to ioo°, then the degree value of the 
thermometer is: 
100 
C J? 9 
° 0 
and the degree-value correction which is to be added to the ob- 
served temperature t is : 
Correction for the Projecting Mercury Thread.—This 
correction is given by the formula of Landolt,* as follows; 
g = {G-i)t. 
/= 0.000131 (« io) t, 
where n is the length of the projecting thread and t is the observed 
temperature. The correction /isto be added in all temperature 
measurements. 
The corrections for the projecting mercury thread are given in 
the table (p. 236) calculated by Rimbach for thermometers of 
Jena glass (graduated to o.i° for o— ioo°) and for (o—360°). 
This correction, however, should be avoided whenever possible. 
See Guillaume, Compt. rend. 112, p. 87, 1891, and Mahlke, 
Zeit. f. Instrumentenkunde 13, p. 58, 1893. 
Calibration of the Thermometer.—The errors arising from 
the unequal diameters of the tube are, especially for high tempera- 
tures, of considerable magnitude. For accurate measurements, 
therefore, the calibration of the thermometer must not be neglected. 
For this purpose the mercury thread is broken off from the 
main quantity of mercury, of such a length a, measured in 
degrees, that n = is approximately a whole number. For 
thermometers which are used for high temperatures a=so ; in 
general, a= 20 or io°. 
The mercury thread may be broken off by tapping the thermo- 
meter after it has been turned upside down. If the thread is too 
long or too short, the process is repeated, and, inasmuch as the 
thread usually breaks at the top of the mercury bulb,f its length 
* Landolt, Zeit. phys. Chem. 4, p. 353, 18S9. 
f To obtain a thread of any desired length, see Kohlrausch, Prakt. Phys. vix, 
p. 84, 1892. THE THERMOMETER. 
223 
can be first adjusted by means of ice-water to the desired value 
and the thermometer then gently tapped. 
If a definite interval—e.g., from o to 100—is to be calibrated, 
then the number of scale divisions which correspond to the length 
of the thread in the different intervals o to a, ato 2 a . . . (n —1) a 
to 100 must be determined. The thread must be moved in this proc- 
ess from one interval to another, and the readings should be unin- 
fluenced by parallax. The parallax can be avoided by placing the 
thermometer on a plane mirror and making the reading with the 
eye in the same straight line with the scale division and its image. 
The use of a cross-wire microscope provided with a micrometer 
screw and slide contrivance is still better. 
Let E be the zero point and 100 -f- the boiling point of the 
thermometer, and suppose the length of the thread in scale divi- 
sions for the different intervals to be as follows: 
Intervals. 
O a 
a— 2 a 
(n —l) a 100 
Scale Divisions. 
a + dj 
a -j- d 2 
a 6n, etc. ; 
then, if we write 
£ s“f ~f“ ”f" •• • 
n 
the correction table* of the thermometer (without regard to 
the correction of the zero point) is as follows : 
Scale Division. 
a 
2 a 
m a 
Correction. 
A-cl, 
2 A (cl, -|- d 2) 
mA (d, + d 2 • • • dm). 
These corrections are to be added to or subtracted from the cor- 
responding scale divisions according as their values are positive or 
negative. The results are then represented graphically, and the 
correction for each degree obtained from the curve, f 
General.—When all of these corrections for a temperature 
*See Kohlrausch, Prakt. Phys. vn, p. 86, 1892. 
I See also the calibrations of Neumann-Thiesen, Carl’s Repert. Exp. Phys. 
15, ,P. 285. 224 
GENERAL CONTRIVANCES FOR MEASUREMENTS. 
determination have been obtained, it is unnecessary to make a com- 
parison with an air thermometer, and the accuracy of the tempera- 
ture is increased more than tenfold. 
If a good, standard thermometer is at hand, a correction table 
for any thermometer can be obtained by comparison with the 
standard. A calibration is then unnecessary. 
The two thermometers are fastened together, with their mercury 
bulbs side by side, and heated to different temperatures in a ther- 
mostat. A better method, however, is the simultaneous heating of 
the two thermometers in the vapors of boiling liquids, whereby 
the change from one temperature to another can be easily accom- 
plished by means of a good pressure regulator (p. 95). 
A microscope, provided with cross-wires, or an eye-piece micro- 
meter, and movable in a vertical direction, should be used for 
reading the thermometer scale in all accurate determinations. The 
thermometer should always be shaken or gently tapped before the 
reading is made. It is also to be observed that the position of the 
top of the mercury thread, for a definite temperature, deviates 
slightly, according as the mercury rises or falls to the position in 
question. 
4. THE BAROMETER 
A good barometer (mercury barometer) should be free from air 
and aqueous vapor. 
The top of the mercury is read with the naked eye avoiding 
parallax, or with a cathetometer. 
The most important correction is the reduction of the barometric 
pressure to o°. If bis the observed barometric pressure, t the 
temperature, and 0.000181 the coefficient of cubical expansion 
of mercury, then the barometric pressure reduced to o° is 
b0 =b— 0.000181 bt. 
When the expansion of the measuring scale is to be taken into 
account, the coefficient of expansion of brass can be taken as 
0.000019 and that of glass as 0.000008; the barometric pressure 
is then calculated to o° : 
For a brass scale by the formula b0 b 0.000162 b t 
“ “ glass “ “ “ “ b—0.000173 £ A 
(Tables of Landolt-Bornstein, p. 26, 1883). THE BAROMETER. 
225 
If the diameter of the barometer-tube is less than about 20 mm., 
the capillary depression must be taken into account. The correc- 
tions for tubes of different diameters are given in Landolt-Bornstein’s 
Tables, p. 21, 1883. These corrections are to be added to the 
height of the mercury column. 
The reduction of the barometric pressure to 450 geographical 
latitude is, in general, unnecessary for chemical purposes (Kohl- 
rausch, Prakt. Phys. yii, p. 74, 1892). 226 
TABLES. 
XXL TABLES. 
TABLE OF ATOMIC WEIGHTS. 
According to Ostwald and 
Clarke,* 
on the Basis of o=i6. 
Aluminium, . , . . 27 x 0 27.11 
Ostw. Clk. 
Molybdenum, , . . 95.90 95-99 
Ostw. Clk. 
Antimony, 120.30 120.43 
Argon, 
Neodymium, . . . 140.80 140.80 
Nickel, 59-00 58-69 
Arsenic, 75 00 75-01 
Nitrogen, ..... 14.04 14.04 
Barium, . . 137.00 137-43 
Bismuth, 205.00 208.11 
Osmium, 192.00 190.99 
Oxygen, x 6.00 16.00 
Boron, n.oi 10-95 
Bromine, 79-96 79-95 
Palladium, 106.00 106.36 
Phosphorus, .... 31.03 31.02 
Cadmium, 1X2.10 111.95 
Calcium, 40.00 40.07 
Platinum, 194.80 194.89 
Potassium, .... 39.14 39-11 
Carbon, 12.00 12.00 
Cerium, 140.20 139-35 
Praseodymium, . . . 143.60 143.60 
Rhodium, 103.00 103.01 
Caesium, 132.90 132.89 
Rubidium, 85.40 85.43 
Chlorine, 35.45 35-45 
Chromium, .... 52.20 52.14 
Ruthenium, .... 103.80 x0x.68 
Samarium, .... 150.00 150.26 
Cobalt, 59-00 58.99 
Columbium, .... 94 20 93-73 
Scandium, .... 44.10 44-12 
Selenium, 79-10 79.02 
Copper 63.30 63.60 
Erbium, 166.00 166.32 
Silicon, 28.40 28.40 
Silver, 107.938 107.92 
Fluorine, 19.00 19.06 
Sodium, 23.06 23.05 
Gadolinium, 156.76 
Gallium, 69.90 69.91 
Strontium, .... 87.50 87.6 X 
Sulphur, 32.06 32.07 
Germanium 72.30 72.48 
Glucinum (Berylium), 9.10 9.08 
Tantalum, .... 183.00 182.84 
Tellurium, . ... 125.00 127.49 
Gold, 197.20 197.23 
Helium, 
Terbium, 160.00 
Thallium, 204.10 204.15 
Hydrogen, .... 1.007 1.008 
Indium, 113.70 113.85 
Thorium, ..... 232.40 232.63 
Thulium, 171.00 170.10 
lodine, 126.86 126.85 
Tin, 118.10 119.05 
Iridium, 193-20 193.12 
Iron, 56.00 56.02 
Titanium, 48.10 48.15 
Tungsten, 184.00 184.83. 
Lanthanum, .... 138.50 138.64 
Lead, 206.91 206.92 
Uranium, 239.40 239.59 
Vanadium 51.20 51.38 
Lithium, 7.03 7.03 
Magnesium, .... 24.38 24.28 
Ytterbium, . . . .173.20 173.19 
Yttrium, 89.10 89.02 
Manganese, .... 55-00 54-99 
Mercury, 200.40 200.00 
Zinc, 65.50 65.41 
Zirconium, 90.70 90.40 
* [Clarke’s latest report, Jour. Amer, 
Chem. Soc. 20, p. 171, 1898.—Tr.] TABLES. 
227 
TABLE OF OBACH, ABRIDGED ACCORDING TO OSTWALD. 
f 
for a 
1000 a 
(Electric Conductivity.) 
to a 999. 
o 
1 
2 
3 
4 
5 
6 
7 
8 
9 
oo 
1.0000 
010 
020 
030 
040 
050 
060 
071 
081 
091 
OI 
101 
in 
122 
132 
142 
152 
163 
i73 
183 
194 
02 
204 
215 
225 
235 
246 
256 
267 
278 
288 
299 
03 
309 
320 
33i 
341 
352 
363 
373 
384 
395 
406 
04 
4i7 
428 
438 
449 
460 
47i 
482 
493 
5°4 
5i5 
05 
526 
537 
549 
560 
571 
582 
593 
605 
616 
627 
06 
638 
650 
661 
672 
684 
695 
707 
718 
73o 
74i 
07 
753 
764 
776 
788 
799 
811 
823 
834 
846 
858 
08 
870 
881 
893 
905 
917 
929 
941 
953 
965 
977 
09 
989 
*001 
*013 
*025 
*038 
*050 
*062 
*074 
*087 
*099 
IO 
O.IIII 
124 
136 
148 
161 
173 
186 
198 
211 
223 
II 
236 
249 
261 
274 
287 
299 
312 
325 
338 
35i 
12 
364 
377 
39° 
403 
416 
429 
442 
455 
468 
481 
13 
494 
508 
521 
534 
547 
561 
574 
588 
601 
614 
H 
628 
641 
655 
669 
682 
696 
710 
723 
737 
75i 
15 
765 
779 
793 
806 
820 
834 
848 
862 
877 
891 
l6 
905 
919 
933 
947 
962 
976 
990 
*005 
*019 
*034 
17 
0.2048 
063 
077 
092 
107 
121 
136 
iSi 
166 
180 
l8 
195 
210 
225 
240 
255 
270 
285 
300 
3!5 
33i 
19 
346 
361 
376 
392 
407 
422 
438 
453 
469 
484 
20 
500 
516 
53i 
547 
563 
579 
595 
610 
626 
642 
21 
658 
674 
690 
707 
723 
739 
755 
771 
788 
804 
22 
821 
837 
854 
870 
887 
903 
920 
937 
953 
970 
23 
987 
*004 
*021 
*038 
*055 
*072 
*089 
*106 
*123 
*141 
24 
0.3158 
175 
193 
210 
228 
245 
263 
280 
298 
316 
2.5 
333 
35i 
369 
387 
405 
423 
441 
459 
477 
495 
26 
514 
532 
5So 
569 
587 
605 
624 
643 
661 
680 
27 
699 
717 
736 
755 
774 
793 
812 
831 
850 
870 
28 
889 
908 
928 
947 
967 
986 
*006 
*025 
‘045 
*065 
29 
0.40S5 
104 
124 
144 
164 
184 
205 
225 
245 
265 
3° 
286 
306 
327 
347 
368 
389 
409 
430 
451 
472 
31 
493 
5U 
535 
556 
577 
599 
620 
641 
663 
684 
S2 
706 
728 
749 
771 
793 
815 
837 
859 
881 
.903 
33 
925 
948 
970 
993 
*015 
*038 
*060 
*083 
*106 
*129 
34 
0.5152 
175 
198 
221 
244 
267 
291 
314 
337 
361 
35 
385 
408 
432 
456 
480 
504 
528 
552 
576 
601 
36 
625 
650 
674 
699 
723 
748 
773 
798 
823 
848 
37 
873 
898 
924 
949 
974 
*000 
*026 
*051 
*077 
*103 
3« 
0.6129 
155 
181 
208 
234 
260 
287 
313 
340 
367 
39 
393 
420 
447 
475 
502 
529 
556 
584 
611 
639 
40 
667 
695 
722 
750 
779 
807 
835 
863 
892 
921 
41 
949 
978 
’ 007 
*036 
*065 
*094 
*123 
*153 
'182 
*212 
42 
0.7241 
271 
301 
331 
361 
39i 
422 
452 
483 
513 
43 
544 
575 
60 6 
637 
668 
699 
73i 
762 
794 
825 
44 
857 
889 
921 
953 
986 
*018 
*051 
*083 
*116 
*149 
45 
0.8182 
215 
248 
282 
3i5 
349 
382 
416 
45° 
484 
46 
5J9 
553 
587 
622 
657 
692 
727 
762 
797 
832 228 
TABLES 
0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
47 
868 
9°4 
939 
975 
Oil* 
048* 
084* 
121* 
i57* 
194* 
48 
0.9231 
268 
305 
342 
380 
418 
455 
493 
53i 
57° 
49 
608 
646 
685 
724 
763 
802 
841 
881 
920 
960 
5o 
1.000 
004 
008 
0X2 
016 
020 
024 
028 
033 
°37 
5i 
041 
045 
°49 
053 
058 
062 
066 
070 
075 
079 
52 
083 
0S8 
092 
096 
IOX 
105 
110 
114 
119 
123 
53 
128 
132 
137 
141 
146 
151 
i55 
160 
165 
169 
54 
174 
179 
183 
l88 
193 
198 
203 
208 
212 
217 
55 
222 
227 
232 
237 
242 
247 
252 
257 
262 
268 
5« 
2 73 
278 
283 
288 
294 
299 
304 
3°9 
3*5 
320 
57 
326 
33i 
336 
342 
347 
353 
358 
364 
37o 
375 
58 
381 
387 
392 
398 
404 
410 
4i5 
421 
427 
433 
59 
439 
445 
45i 
457 
463 
469 
475 
481 
488 
494 
bo 
5 00 
506 
513 
519 
525 
532 
538 
545 
55i 
558 
6i 
564 
57i 
577 
584 
59i 
597 
604 
611 
618 
625 
62 
632 
639 
646 
653 
660 
667 
674 
681 
688 
695 
63 
703 
710 
717 
725 
732 
740 
747 
755 
762 
770 
64 
778 
786 
793 
801 
809 
8.7 
825 
833 
841 
849 
65 
857 
865 
874 
882 
890* 
899 
907 
9i5 
924 
933 
6b 
941 
95° 
959 
967 
976 
985 
994 
003* 
012* 
021* 
67 
2.030 
040 
049 
058 
067 
077 
086 
096 
106 
i*5 
68 
125 
135 
145 
155 
165 
175 
185 
195 
205 
2*5 
69 
226 
236 
247 
257 
268 
279 
289 
300 
311 
322 
70 
333 
344 
356 
367 
378 
390 
401 
4i3 
425 
436 
7i 
448 
460 
472 
484 
497 
S09 
521 
534 
546 
559 
72 
571 
584 
597 
610 
623 
636 
650 
663 
676 
690 
73 
704 
717 
73i 
745 
759 
774 
788 
802 
817 
831 
74 
846 
861 
876 
891 
906 
922 
937 
953 
968 
984 
75 
3.000 
016 
032 
049 
065 
082 
098 
US 
132 
149 
76 
167 
184 
202 
219 
2 37 
255 
274 
292 
3x0 
329 
77 
348 
367 
386 
405 
425 
444 
464 
484 
505 
525 
78 
545 
566 
587 
608 
630 
651 
673 
695 
717 
739 
79 
762 
785 
808 
831 
854 
878 
902 
926 
950 
975 
80 
4.000 
025 
051 
076 
102 
128 
155 
181 
208 
236 
81 
263 
291 
319 
348 
376 
405 
435 
465 
495 
525 
82 
556 
587 
618 
650 
682 
7*4 
747 
780 
814 
848 
83 
882 
917 
952 
988 
024* 
061* 
098* 
135* 
173* 
211* 
84 
5.250 
289 
329 
369 
410 
452 
494 
536 
579 
623 
85 
667 
711 
757 
803 
849 
897 
944 
993 
042* 
092* 
8b 
6.143 
194 
246 
299 
353 
407 
463 
5i9 
576 
634 
87 
692 
752 
813 
874 
937 
000* 
065 * 
130* 
197* 
264* 
88 
7-333 
403 
475 
547 
621 
696 
772 
850 
929 
009* 
89 
8.091 
174 
259 
346 
434 
524 
6iS 
7°9 
804 
901 
90 
9.000 
IOX 
204 
3°9 
417 
526 
638 
753 
870 
989 
9i 
IO.XI 
IO-33 
10.36 
10.49 
10.63 
10.77 
10.90 
11.05 
11 20 
u-35 
92 
ii-5o 
11.66 
11.82 
11.99 
12.16 
I2-33 
12.51 
12.70 
12.S9 
13.08 
93 
13.29 
*3-49 
13 7i 
13-93 
14-15 
14-38 
1463 
14.87 
i5 13 
*5 39 
94 
15-67 
15-95 
16.24 
16.54 
16.86 
17.18 
17-52 
17.87 
18.23 
18.61 
95 
19.00 
19.41 
19.83 
20.28 
20.74 
21.22 
21.73 
22.26 
22.81 
23-39 
9b 
24.00 
24.64 
25-32 
26.03 
26.78 
27-57 
28.41 
29 30 
30.25 
31.26 
97 
32-33 
33-48 
34-7i 
36.04 
37-46 
39.00 
40.67 
42 48 
44-45 
46.62 
98 
49.00 
51.6 
54-6 
57-8 
61.5 
65-7 
70.4 
75 9 
82.3 
89.9 
99 
99.0 
no 
124 
142 
166 
199 
240 
33 2 
499 
999 TABLES. 
229 
TABLE FOR THE CALCULATION OF REFRACTIVE INDICES 
FOR SODIUM LIGHT ACCORDING TO PULFRICH. 
Deg. 
Min. i 
Refrac- 
tive 
Index. 
d 
Deg. Min. 
Refrac- 
tive 
Index. 
» 
d 
Deg. 
Min. 
Refrac- 
tive 
Index. 
d 
O 
° 
I,6l 511 
0,1 
8 
0 
1,60 910 
2,5 
16 
0 
1,59 HI 
4,8 
10 
5ID 
0,1 
10 
885 
2,5 
IO 
093 
4,9 
20 
S°9 
0,1 
20 
860 
2,6 
20 
044 
4.9 
3° 
508 
0,2 
30 
834 
2,7 
30 
1,58 995 
5,° 
4° 
506 
0,2 
40 
So 7 
2-7 
40 
945 
5,i 
5° 
5°4 
o,3 
5° 
780 
2,8 
5° 
894 
5,i 
I 
o 
1,61 501 
0,3 
9 
0 
1,60 752 
2,8 
17 
O 
i.S8 843 
5,2 
IO 
498 
0,4 
10 
724 
2,9 
IO 
791 
5>2 
20 1 
494 
0,5 
20 
695 
2,9 
20 
739 
5-2 
3° 
489 
o,5 
30 
66b 
3,° 
3° 
687 
5-3 
40 j 
484 
o,5 
40 
636 
3,° 
40 
634 
5-3 
50 
479 
c,6 
50 
606 
3,1 
50 
S81 
5,4 
2 
o 
1,61 473 
0,6 
10 
O 
1,60 575 
3,2 
x8 
0 
1,58 527 
5,4 
IO 
467 
0,7 
10 
543 
3,2 
10 
4 73 
5,4 
20 
460 
0,8 
20 
5“ 
3,2 
20 
419 
5,5 
30 
45 2 
0,8 
30 
479 
3,3 
3° 
364 
5,5 
40 
444 
0,9 
40 
446 
3,3 
40 
3r9 
5,6 
50 
435 
0,9 
50 
413 
3,4 
50 
253 
5-7 
3 
O 
i,6x 426 
1,0 
11 
0 
1,60 379 
3,4 
19 
O 
1,58 196 
5,7 
IO 
416 
1,° 
10 
345 
3,4 
10 
139 
5,7 
20 
406 
1,1 
20 
311 
3,5 
20 
082 
5,8 
30 
395 
i, 1 
30 
276 
3,6 
30 
024 
5,8 
40 
3*4 
1,2 
40 
240 
3,6 
40 
i,57 966 
5,9 
5° 
372 
1,2 
50 
204 
3,7 
5° 
9°7 
5,9 
4 
O 
i,61 360 
1,3 
12 
0 
1,60 167 
3,7 
20 
0 
i,57 848 
6,0 
IO 
347 
1,4 
10 
130 
3,7 
10 
788 
6,0 
20 
333 
1,4 
20 
093 
3,8 
20 
728 
6,0 
3° 
3i9 
1,4 
30 
055 
3,9 
3° 
668 
6,1 
40 
305 
1,5 
40 
016 
3,9 
40 
607 
6,1 
50 
290 
1,5 
50 
i,59 977 
4,o 
50 
546 
6,1 
5 
0 
1,61 275 
1,5 
13 
0 
i,59 937 
4,o 
21 
0 
i,57 485 
6,2 
10 
260 
1,6 
10 
897 
4,1 
10 
323 
6,2 
20 
244 
1,7 
20 
856 
4,1 
20 
361 
6,3 
30 
227 
1,8 
30 
815 
4,2 
30 
298 
6,4 
40 
209 
1,8 
40 
773 
4,2 
40 
234 
6,4 
SO 
191 
1,9 
50 
73i 
4,2 
50 
170 
6,4 
6 
0 
1,61 172 
1-9 
14 
0 
1,39 689 
4,3 
22 
0 
i,57 i°6 
6,4 
10 
153 
1,9 
10 
646 
4,3 
10 
042 
6,5 
20 
134 
2,0 
20 
603 
4,4 
20 
1,56 977 
6,5 
30 
114 
2,I 
30 
559 
4,5 
30 
912 
6,6 
40 
093 
2,1 
40 
5H 
4,5 
40 
846 
6,6 
5° 
072 
2,2 
50 
469 
4,6 
50 
780 
6,7 
7 
O 
1,61 050 
2,2 
15 
0 
1,59 423 
4,6 
23 
0 
1,56 713 
6,7 
IO 
028 
2,3 
10 
377 
4,6 
10 
646 
6,7 
20 
005 
2,3 
20 
3 3i 
4,7 
20 
579 
6,8 
3° 
1,60 982 
2,3 
30 
284 
4,7 
30 
5“ 
6,8 
40 
959 
2,4 
40 
237 
4,8 
40 
443 
6,8 
50 
935 
2,5 
50 
189 
4,8 
50 
375 
6,9 
8 
O 
1,60 910 
16 
0 
i,59 141 
24 
0 
11,56 3^6 TABLES. 
Deg. Min. 
Refrac- 
tive 
Index. 
d 
Deg. Min. 
Refrac- 
tive 
Index. 
d 
Deg. Min. 
Refrac- 
tive 
Index. 
d 
24 
0 
1,56 306 
7,o 
32 
0 
I.S2 570 
8,6 
40 
0 
1,48 168 
9,7 
10 
236 
7,o 
10 
484 
8,6 
10 
071 
9,7 
20 
166 
7,o 
20 
398 
8,6 
20 
1,47 974 
9,7 
30 
096 
7,i 
30 
312 
8,7 
30 
877 
9,7 
40 
025 
7,i 
40 
225 
8,7 
40 
780 
9,7 
50 
i,55 954 
7,i 
50 
138 
8,7 
50 
683 
9,7 
25 
0 
i,55 883 
7i 
33 
0 
1,52 051 
8,8 
41 
0 
i,47 586 
9,8 
10 
812 
7,2 
10 
i,5i 963 
8,8 
10 
488 
9,8 
20 
740 
7,2 
20 
875 
8,8 
20 
390 
9,8 
30 
668 
7,3 
30 
787 
8,8 
3° 
292 
9,8 
40 
595 
7,3 
40 
699 
8,8 
40 
194 
9,8 
5° 
522 
7-4 
50 
611 
8,9 
5o 
096 
9,8 
26 
0 
i,55 448 
7 4 
34 
0 
i,5i 522 
8,9 
42 
O 
1,46 998 
9,8 
10 
374 
7,4 
10 
433 
9,0 
10 
900 
9,9 
20 
3°° 
7,5 
20 
343 
9,0 
20 
801 
9,9 
30 
225 
7,5 
30 
253 
9,o 
30 
702 
9,9 
40 
150 
7,5 
40 
163 
9,o 
40 
603 
9,9 
5o 
075 
7,6 
5° 
0 73 
9,o 
5o 
504 
9,9 
27 
0 
i,54 999 
7,6 
35 
0 
i,5o 983 
9,1 
43 
0 
1,46 405 
9,9 
10 
923 
7,6 
10 
892 
9,i 
10 
306 
9,9 
20 
847 
7,7 
20 
801 
9,1 
20 
207 
9,9 
3° 
77 0 
7,7 
3° 
710 
9,i 
30 
108 
9,9 
40 
693 
7,8 
40 
619 
9,2 
40 
009 
10,0 
5o 
615 
7,8 
50 
527 
9,2 
50 
i,45 909 
10,0 
28 
0 
i,54 537 
7,8 
36 
0 
1,50 435 
9.2 
44 
0 
i,45 809 
10,0 
10 
459 
7,9 
10 
343 
9,2 
10 
709 
10,0 
20 
380 
7,9 
20 
251 
9.2 
20 
609 
10,0 
30 
301 
7,9 
30 
159 
9,3 
3° 
509 
10,0 
40 
222 
7,9 
40 
066 
9,3 
40 
409 
10,0 
5o 
I43 
8,0 
50 
i,49 973 
9,3 
50 
3°9 
10,0 
29 
0 
1,54063 
8,0 
37 
0 
1,49 880 
9,3 
45 
O 
i,45 2°9 
10,0 
xo 
i,53 983 
8,1 
10 
787 
9,4 
10 
109 
10,0 
20 
902 
8,1 
20 
693 
9,4 
20 
009 
10,0 
30 
821 
8,x 
3° 
599 
9,4 
3° 
i,44 9°9 
10,0 
40 
740 
8,2 
40 
505 
9,4 
40 
809 
10,1 
5o 
658 
8,2 
50 
411 
9,4 
5o 
708 
10,1 
3° 
0 
i,53 576 
8,2 
38 
0 
i,49 317 
9,5 
46 
O 
1,44 607 
10,1 
10 
494 
8,2 
10 
222 
9,5 
10 
506 
10,0 
20 
412 
8,3 
20 
127 
9,5 
20 
406 
10,1 
30 
329 
8,3 
30 
032 
9,5 
30 
305 
10,1 
40 
246 
8,3 
40 
1,48 937 
9,5 
40 
204 
10 0 
5o 
163 
84 
50 
842 
9,6 
50 
104 
10,1 
31 
0 
i,53 °79 
8,4 
39 
0 
1,48 746 
9,6 
47 
0 
1,44 003 
10,0 
10 
1,52 995 
8,4 
10 
650 
9,6 
10 
1,43 903 
10,1 
20 
911 
8,5 
20 
554 
9,6 
20 
802 
10,1 
30 
826 
8,5 
3° 
458 
9,6 
30 
701 
10,1 
40 
74i 
8,5 
40 
362 
9,7 
40 
600 
10,1 
5o 
656 
8,6 
50 
265 
9,7 
5o 
499 
10,1 
32 
0 
1,52 570 
40 
0 
1,48 168 
48 
0 
1,43 398 TABLES. 
Deg. Min. 
Refrac- 
tive 
Index. 
d 
Deg. Min. 
Refrac- 
tive 
Index. 
d 
Deg. Min. 
Refrac- 
tive 
Index. 
d 
48 
0 
'1,43 398 
10,1 
56 
0 
1,38 610 
9,8 
64 
0 
i,34 191 
8,5 
10 
297 
10,1 
10 
513 
9,7 
10 
106 
8,5 
20 
196 
10,0 
20 
416 
9,7 
20 
021 
8,5 
30 
096 
10,X 
3° 
319 
9,7 
30 
i,33 936 
8,4 
40 
1,42 995 
10,1 
40 
222 
9,7 
40 
8521 
8,4 
5o 
894 
10,1 
5o 
125 
9,6 
50 
768 
8,4 
49 
0 
1,42 793 
10,0 
57 
0 
1,38 O29 
9,6 
65 
0 
1,33 684 
8,3 
10 
693 
10,1 
10 
i,37 933 
9,6 
10 
601 
8,3 
20 
592 
10,1 
20 
837 
9,6 
20 
518 
8,2 
3° 
491 
10,1 
3° 
741 
9,6 
30 
436 
8,2 
40 
39° 
10,1 
40 
645 
9,5 
40 
354 
8,2 
5o 
289 
10,1 
5o 
550 
9,5 
50 
272 
8,1 
50 
0 
1,42 188 
XO, I 
58 
0 
i,37 455 
9,5 
66 
0 
i,33 191 
8,1 
10 
087 
10,0 
10 
360 
9,5 
10 
no 
8,1 
20 
1,41 987 
10,1 
20 
265 
9,5 
20 
029 
8,0 
3° 
886 
10,0 
30 
170 
9,5 
30 
1,32 949 
8,0 
40 
786 
10,1 
40 
075 
9,4 
40 
869 
7,9 
5o 
685 
10,1 
50 
1,36 981 
9,4 
50 
790 
7,9 
51 
0 
1,41 584 
10,0 
59 
0 
1,36 887 
9,3 
67 
0 
1,32 711 
7,9 
10 
484 
10,1 
10 
794 
9,3 
10 
632 
7,8 
20 
383 
10,0 
20 
701 
9,3 
20 
554 
7,8 
30 
283 
10,0 
30 
608 
9,3 
30 
476 
7,7 
40 
183 
10,0 
40 
515 
9,3 
40 
399 
7,7 
5o 
083 
10,0 
5o 
422 
9,3 
5o 
322 
7,7 
52 
0 
1,40 983 
10,1 
60 
0 
i,36 329 
9,2 
68 
0 
1,32 245 
7,6 
10 
882 
10,0 
10 
2 37 
9,2 
10 
169 
7,6 
20 
782 
10,0 
20 
145 
9,2 
20 
093 
7,5 
30 
682 
10,0 
30 
053 
9,2 
30 
013 
7,5 
40 
582 
10,0 
40 
i,35 961 
9,i 
40 
i,3i 943 
7,4 
5° 
482 
9,9 
5o 
870 
9,i 
5o 
869 
7,4 
53 
0 
1,40 383 
10,0 
61 
0 
i,35 779 
9,i 
69 
0 
i,3i 795 
7,4 
10 
283 
10,0 
10 
688 
9,o 
10 
721 
7,3 
20 
183 
9,9 
20 
598 
9,0 
20 
648 
7,3 
30 
084 
9,9 
30 
508 
9,o 
3° 
575 
7,2 
40 
1,39 985 
9,9 
40 
418 
8,9 
40 
S03 
7,2 
50 
886 
9,9 
5o 
329 
8,9 
5o 
43i 
7,2 
54 
0 
i,39 787 
9,8 
62 
0 
i,35 240 
8,9 
7o 
0 
1,31 359 
7,i 
10 
689 
9,9 
10 
iSi 
8,9 
10 
288 
7,o 
20 
590 
9,9 
20 
062 
8,8 
20 
218 
7,o 
3° 
49i 
9,9 
30 
i,34 974 
8,8 
30 
148 
7,o 
40 
392 
9,8 
40 
886 
8,8 
40 
078 
6,9 
5° 
294 
9,8 
5o 
798 
8,8 
5o 
009 
6,8 
55 
O 
i,39 196 
9,8 
63 
0 
i,34 7io 
8,7 
7i 
0 
1,30 941 
6,8 
10 
098 
9,8 
10 
623 
8,7 
10 
873 
6,8 
20 
000 
9,8 
20 
536 
8,7 
20 
805 
6,7 
30 
1,38 902 
9,8 
30 
449 
8,6 
30 
798 
6,7 
40 
804 
9,7 
40 
363 
8,6 
40 
671 
6,6 
5o 
707 
9,7 
50 
2 77 
8,6 
5o 
605 
6,6 
56 
0 
1,38 610 
64 
O 
1,34 191 
72 
0 
1,30 539 232 
TABLES. 
n2 I 
TABLE FOR CALCULATING log. FROM THE REFRAC- 
® n2 2 
TIVE INDEX n ACCORDING TO CONRADY. 
n2 I 
log. —-o—. = o, . . . I. 
& ;?2 -f- 2 
n = 
o 
1 
2 
3 
4 
5 
6 
7 
8 
9 
Diff. 
Ap- 
prox. 
i,3° 
2 
7182 
7315 
7447 
7579 
7710 
7841 
7972 
S102 
8231 
8360 
131 
i 
8488 
8616 
8744 
8871 
8998 
9124 
9250 
9375 
9500 
9625 
127 
2 
9749, 
9873 
9996 
*0119 
*0241 
*0363 
*0485 
*0606 
0726 
*0846 
123 
3 
3 
0966 
1085 
1204 
1323 
1441 
1559 
1676 
1793 
1909 
2025 
ns 
4 
2141 
2256 
2371 
2486 
2600 
2714 
2828 
2941 
3054 
3166 
114 
5 
3278 
3390 
35oi 
3612 
3723 
3S33 
3943 
4053 
4162 
4271 
1X0 
6 
4379 
4487 
4595 
4703 
4810 
49*7 
5023 
5129 
5235 
534i 
107 
7 
5446 
555i 
5656 
5760 
5864 
5968 
6071 
6174 
6277 
6379 
104 
8 
6481 
6583 
6684 
6785 
6886 
6986 
7086 
7186 
7286 
738 s 
100 
9 
74S4 
7583 
7681 
7779 
7877 
7974 
8071 
8168 
8265 
8361 
97 
1,40 
8457 
8553 
8648 
8743 
8838 
8933 
9027 
9121 
9215 
9309 
95 
i 
9402 
9495 
9588 
9681 
9773 
9865 
9957 
*0048 
*0139 
*0230 
92 
2 
4 
0321 
0412 
0502 
0592 
0682 
0771 
0860 
0949 
1038 
1127 
90 
3 
1215 
1303 
1391 
1479 
1566 
1653 
1740 
1827 
1914 
2000 
87 
4 
2086 
2x72 
2258 
2343 
2428 
2513 
2597 
2681 
2765 
2849 
85 
5 
2933 
3017 
3100 
3183 
3266 
3348 
343° 
3513 
3595 
36771 
82 
6 
3758 
3839 
392° 
4001 
4082 
4162 
4242 
4322 
4402 
4482 
80 
7 
456i 
4640 
4719 
4798 
4877 
4955 
5033 
Sin 
5189 
5267 
78 
8 
5344 
5421 
5498 
5575 
5652 
5728 
5804 
5880 
5956 
6032 
76 
9 
6107 
6182 
6257 
6332 
6407 
6482 
6656 
6630 
6704 
6778 
75 
i,5° 
6852 
6926 
6999 
7072 
7145 
7218 
7291 
7363 
7435 
7507 
73 
i 
7579 
7651 
7723 
7794 
7865 
7936 
8007 
8078 
8x48 
8218 
7i 
2 
8288 
8358 
8428 
8498 
8567 
8636 
8706 
8775 
8844 
8913 
69 
3 
8981 
9049 
9118 
9186 
9254 
9322 
9389 
9457 
9524 
959i 
68 
4 
9658 
9725 
9792 
9858 
9925 
9991 
*0057 
*0123 
*0189 
*02,55 
66 
5 
5 
0320 
0385 
0451 
0516 
0581 
0645 
0710 
0774 
0839 
0903 
65 
6 
0967 
1031 
1095 
1158 
1222 
1285 
1348 
1411 
H74 
1537 
63 
7 
1600 
1663 
1725 
1787 
1849 
1911 
1973 
2035 
2096 
2158 
62 
8 
2219 
2280 
2341 
2402 
2463 
2523 
2584 
2644 
2704 
2764 
61 
9 
2824 
2884 
2944 
3003 
3062 
3122 
3681 
3240 
3299 
3357 
60 TABLES. 
2 33 
TABLE OF EXTINCTION-COEFFICIENTS CORRESPONDING 
TO THE DIFFERENT VALUES OF ,P ACCORDING 
TO VIERORDT, ARRANGED BY G. KRUSS 
u 
g 
h 
2 w 
H 
Z 
w 
xf On i-h On co xh O irifON CM Tfvo N vD VO conO eo 
H NO EO EO W~) EO V-O ET)VO VO CO O O 
ON *H COED 00 conO 00 — conO 00 — conO 00 h 
ro t*- rt IT) 1-0 ED idvO MD VO N IN NCO 00 
ro co ro co ro co ro to ro ro fC fO fO rc ro ro ro ro ro 
CM 
CM 
00 
ro 
iJ-UNO t)- ro N 
ro NO NO ON O M 
On M tx OnO 
GO On O' On ON O 
ro tn to toto rI- 
M 
CM 
M 
O 
oh 
•- m m m CM ro 'xJ-NO 
ro tJ- eonO On O 
CM ro Tf eonO O 
OOOOOOOm 
'xhoh’rt-Tt-Tf'rfr^-Tt- 
IN 
CnM t|-Nw 
CM rt* EO NO CO 
CM CO rt- vONO 
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ON 
rt- 
u 
u 
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o 
o 
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0 
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0 
0 
o 
0 0 
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d 
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EO ET) EO EO Tt- 
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EO CO O CO EO 
rf- to CO 
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ro O OO EO n O CO 
CO ro Cl M M N H 
nt* Tf Tf- Tt 
eo ro 
M M 
Tj- 
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Tj- 
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On CO 
ON On 
ro ro 
eo rj- ro cm i-i 
On On Qn Qn On On Cn 
ro rO ro ro ro ro ro 
O Onoo EO Tt- ro CM 
On CO 00 00 00 CO 00 CO 00 
rO ro ro ro ro ro co ro ro 
o o 
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OEFFI- 
h 
Z 
5 
ONNHOOTfMHH*- 
EOCO ro CM nO CM vO CM NO 
On *-* fO ED N h N 
LT) EO EO LO EO’O VO 'O VO 
M W M C) N N M M N M 
,26922 
EOCO 0 CO 0 On ro rf m tJ- COCO O NO m OnnO NO nO CO 
'O N N COCO EO o NO moo Th H- N H 00 EOM O l>» eo 
m ro in N ON h eo 00 on M 00 m M ion Onh OO O 
N n N N KX O) X X 00 On On On On O O O O O w m m m cm 
CM CM CM CM CM CM CM CM <N CM CM CM CM CM COCOrorOCOrOCOrOCOCO 
M Tf H NO EO CM EO 
ro *- On eo CM 
ro EO on CM rf 
cm cm cm cm ro ro ro 
ro co co ro co ro ro 
w 
U 
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d 
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d 
d o 
d 
ro O CO io fOO CO EoroOOO iO f<p 0 00 io fO O 00 eo ro O 00 innQOO 
nD vO CM CM CM m m w O O O O On 
IT) ET, IT, IT) lO EO EO EO EO 
EO ro O 00 eo ro O 00 eo ro O CO EorOO 
On On On CO CO 00 CO In no NO nO vO 
o o 
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d o d d 
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d 
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o 
d 
d o 
o 
U 
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h 
TION- 
3EFFI- 
h 
Z 
M 00 INN 
NO vO 
rOvO On CM 
ro fO t}- 
— W H H 
Ou-nNwMnOmOO fOOO vOvO 0"nN rONO 
ONO w fO ifi N 5i h ix. O Tt- 00 n no 
i/GOO w xfoo i-i 'tNQ mNO m i> O i-x o 
irNNO NO NO tx lx txOO CO 00 On On On O 
N w rooo nonoO ONNONorONo 00 no rovO NO 
HNO H O MOO ro-rf-ONHNOOO r<GNoO rooo HO On 
tx w OTOO m ro NONO On O M rj-NO 00 O w ■rfuiN 
O O w M M M M M M M r0f0r0r0 
MMMMMMMMMMNMMMNMMMMM 
U 
o o 
o 
o 
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o 
o 
o 
o 
o 
0 
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d 
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ro co 
I-- 
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CM CM 
r-. 
EO O 
M M 
i>. 
EO O EO O EO O lO o EO O EO C EO 
o O On on00 00 NO eo eo 
nOnDnOnOnOnOnOnOnOnO 
O eo O EO O EO o eo O CO eo ro C 00 io co O 00 eo ro O OO eo 
Th ro co cm cm t-i >—( o O On on On On go oo oo OO' vo 
OOVOOOVOVOOVO EOEOEOEOEOLOEOEOEOEOEOEOEOEO 
O 0 
o 
o 
0 
o 
o 
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0 
o o 
o o d o 
d 
o 
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o 
d 
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d 
d 
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d 
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d 
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d 
Extinc- I 
Z E h 
OfcZ 
P !i! W 
co roco 
ro N N !>. CM 
00 rO N M 
O 0 M M CM 
o o o o o 
00 
OO 
NO 
cm 
O 
N N\£HOW N O OnONH 
UN M OnNhv£) O NT) O OnunO 
W ND O unco O ro nt>00 O M n/goO 
rOfC't + 't>'UOUN vtnnO no nD no 
OOOOOOOOOOOOO 
On eo ro CM ro eo On eo CM m « ThOO Q 
eo m eo CM On NO row CNN 
O ro eo00 O rONO 00 *- On cm ion O 
N- 00 00 CO CON ON ON on o O O m 
OOOOOOOOOOOO'h-wm 
M rt 
eo ro 
CO NO 
t—( HH 
hM VH 
On NO 
M O 
ON CM 
w CM 
i- EO K 
On GO 
rj- O 
CM CM CO 
U 
o o 
o 
0 
o 
o 
O 
o 
o 
o 
0 
o o 
o o o d 
d 
d 
o 
o 
d 
o 
d 
d d 
o 
o 
d 
o 
o 
d d 
d 
o 
o 
d 
d 
o' 
d d 
cT 'S 
o o o o 
ONOO 
On O' CTn On 
o o 
>-n xf- 
ON ON 
o 
CO 
On 
O O O mO mO "lO 
ci m o On Onoo 00 ix Ixno o mini- fO ro N N m — o O 
ON ON OnOO oooooooooooooooooooooooooooooooooooooo 
EO O EO O 
On ONOO GO 
n- 
EO o EO O 
N- t'-'.NO NO 
NT) O no o 
no no tJ- rh 
NNNN 
6 o 
o 
o 
0 
o 
o 
o 
o 
o 
0 
o o 
d d o o 
o 
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o 
d 
o 
o 
d 
o o 
o 
o 
o 
o 
o 
o d 
o 
o 
o 
o 
d 
d 
d o 
o' J' 
Extino 
TION- 
COEFFI- 
CIENT. 
J' 
Extino 
TION- 
COEFFI- 
CIENT. 
J' 
Extino 
TI ON- 
COEFFI- 
CIENT. 
Extino 
TION- 
COEFFI- 
CIENT. 
0,381 
0,41908 
°>333 
o,47756 
0,285 
0,54516 
0,237 
0,62526 
0,380 
0,42022 
0,332 
0,47887 
0,284 
0,54669 
0,236 
0,62709 
0,379 
0,42137 
o,33i 
0,48018 
0,283 
0,54822 
0,235 
0,62894 
0,37^ 
0,42251 
o,330 
0,48149 
0,282 
0,54976 
0,234 
0,63079 
o,377 
0,42366 
0,3291 
0,48281 
0,281 
0,55130 
0,233 
0,63265 
0,376 
0,42482 
0,328 
0,48413 
0,280 
0,55285 
0,232 
0,63452 
o,375 
0,42597 
0,327 
0,48546 
0,279 
0,55440 
0,231 
0,63639 
0,374 
0,42713 
0,326 
0,48679 
0,278 
o,55596 
0,230 
0,63828 
0-373 
0,42830 
0,325 
0,48812 
0,277 
o,55753 
0,229 
0,64017 
0,372 
0,42946 
o,324 
0,48946 
0,276 
o,559io 
0,228 
0,64207 
0,371 
0,43063 
0,323 
0,49080 
0,275 
0,56067 
0,227 
0,64398 
o,37o 
0,43180 
0,322 
0,49215 
0,274 
0,56225 
0,226 
0,64590 
0,369 
0,43298 
0,321 
0,4935° 
0,273 
0,56384 
0,225 
0.64782 
0,368 
0,43416 
0,320 
0,49485 
0,272 
0,56544 
0,224 
0.64976 
0,367 
o,43534 
°;3I9 
0,49621 
0 271 
0,56704 
0,223 
0,65170 
0,366 
0,43652 
0,318 
0,49758 
0,270 
0,56864 
0 222 
0,65365 
0,365 
0,4377! 
0,317 
0,49895 
0,269 
0,57025 
0,221 
0,65561 
0,364 
0,43890 
0,316 
0,50032 
0,268 
0,57187 
0,220 
0,65758 
0,363 
0,44010 
0,315 
0,50169 
0,267 
o,57349 
0,219 
0,65956 
0,362 
0,44130 
0,314 
0,50308 
0,266 
o,575i2 
0,218 
0,66155 
0,361 
0,44250 
o>3T3 
0,50446 
0,265 
0,57676 
0,217 
0,66355 
0,360 
0,4437° 
0,312 
0,50585 
0,264 
0,57840 
0,216 
0,66555 
o,359 
0,44491 
0,311 
0,50724 
0,263 
0,58005 
0,215 
0,66757 
o,358 
0,44612 
0,310 
0,50864 
0,262 
0,58170 
0,214 
0,66959 
0,357 
0,44734 
0,309 
0,5x005 
0,261 
0,58336 
0,213 
0.67163 
0,356 
0,44855 
0,308 
o,5H45 
0,260 
0,58503 
0,2X2 
0,67367 
0,355 
0,44978 
0,307 
0,51287 
0,259 
0,58671 
0,211 
0,67572 
o,354 
0,45100 
0,306 
0,51428 
0,258 
0,58839 
0,210 
0,67779 
0,353 
0,45223 
0,305 
o,5i57i 
0,257 
0,59007 
0,209 
0,67986 
0,352 
0,45346 
0,304 
0,51713 
0,256 
0,59176 
0,208 
0,68194 
o,35i 
o,4547o 
0,303 
0,51856 
0,255 
0,59346 
0,207 
0,68403 
o,35o 
0,45594 
0,302 
0,52000 
0,254 
o,595i7 
0,206 
0,68614 
o,349 
o,457i8 
0,301 
0,52144 
0,253 
0,59688 
0,205 
0,68825 
0,348 
0,45843 
0,300 
0,52288 
0,252 
0,59860 
0,204 
0,69037 
o,347 
0,45968 
0,299 
o,52433 
0,251 
0,60033 
0,203 
0,69251 
0,346 
0,46093 
0,298 
o,52579 
0,250 
0,60206 
0,202 
0,69465 
o,345 
0,46219 
0,297 
0,52726 
0,249 
0,60381 
0,201 
0,69681 
o,344 
0,46345 
0,296 
0,52871 
0,248 
0,60555 
0,200 
0,69897 
o,343 
0,46471 
0,295 
0,530x8 
0,247 
0,60731 
0,199 
0.70115 
0,342 
0,46598 
0,294 
0,53166 
0,246 
0,60907 
0,198 
0.70334 
o,34i 
0,46725 
0,293 
0,53314 
0,245 
0,61084 
0,197 
0,70554 
0,340 
0,46853 
0,292 
0,53462 
0,244 
0,61262 
0,196 
0,70775 
o,339 
0,46981 
0,291 
o,536h 
0,243 
0,61440 
0,195 
0.70995 
0,338 
0,47109 
0,290 
o,5376i 
0,242 
0,61619 
0,194 
0,71220 
o,337 
0,47238 
0,289 
°,539I9 
0,241 
0,61799 
O.I93 
0.71445 
0,336 
0,47367 
0,288 
0,54061 
0,240 
0,61979 
0,192 
0,71670 
o,335 
0,47496 
0,287 
0,54212 
0,239 
0,62161 
0,191 
0,71897 
o,334 
0,47626 
0,286 
0,54364 
0,238 
0,62343 
0,190 
0.72125 
234 
TABLES TABLES 
235 
J' 
% 
Extinc- 
TION- 
COEFFI- 
CIENT. 
J' 
Extinc- 
TION- 
COEFFI- 
CIENT. 
J' 
Extino 
TION- 
COEFFI- 
CIENT. 
J' 
Extinc- 
TION- 
COEFFI- 
CIENT. 
0,189 
0,72354 
0,145 
0,83864 
0,102 
0,99140 
0059 
1,22915 
0.188 
0.72585 
0,144 
0,84164 
0,101 
0,99568 
0,058 
1,23658 
0.187 
0 728x6 
0,143 
0,84467 
0,100 
1,00000 
0,057 
1,24413 
0,186 
0,73049 
0,142 
0,84772 
0,099 
1,00437 
0,056 
1,25182 
0.185 
0,73283 
0.141 
0,85079 
0,098 
1,00878 
0,055 
1,25964 
0,184 
0.73519 
0,140 
0,85388 
0,097 
1,01323 
0,054 
1,26761 
0 183 
o,73755 
o,i39 
0,85699 
0,096 
1,01773 
i ,02228 
0,053 
1,27573 
1,28400 
0 182 
o,73993 
0,138 
0,86013 
0,095 
0,052 
0,181 
0.74233 
0,137 
0,86328 
0,094 
1,02688 
0,051 
1,29243 
0,180 
o,74473 
0,136 
0,86647 
0,093 
1,03152 
0,050 
1,30103 
0,179 
o,747'5 
0.135 
0,86967 
0,092 
1,03622 
0,049 
1,30981 
0,178 
0,74958 
o,i34 
0,87290 
0,091 
1,04096 
0,048 
1,31876 
0,177 
0,75203 
o,i33 
0,87615 
0,090 
1,04546 
0,047 
1,32719 
0,176 
o,75449 
0,132 
0,87943 
0,089 
1,05061 
0,046 
1,33725 
0,175 
0,75697 
0,131 
0,88273 
0,088 
1,05552 
0,045 
1,34679 
0 174 
0.75946 
0,130 
0,88606 
0,087 
1,06094 
0,044 
1,35655 
0,173 
0,76196 
0,129 
0,88942 
0,086 
i,o65<;i 
0,043 
1,36654 
0.172 
0.76448 
0,128 
0,89279 
0,085 
1,07059 
0,042 
1,37676 
0,171 
0.76701 
0,127 
0,89620 
0,084 
',07573 
0,041 
1,38722 
0.170 
0,76956 
0,126 
0,89963 
0,083 
1,08093 
0,040 
i,39794 
0,169 
0 77212 
0,125 
0,90309 
0,082 
1,08619 
0,039 
1,40894 
0,168 
o,7747o 
0,124 
0,90658 
0,081 
1,09152 
0038 
1,42022 
0,167 
o,77729 
0,123 
0,91010 
0,080 
1,09692 
0,037 
1,43180 
0 166 
0,77990 
0,122 
0,91365 
0,079 
1,10238 
0,036 
i,4437o 
0,165 
0.78252 
0,121 
0,91722 
0,078 
1,10791 
0,035 
1,45594 
0,164 
0,78516 
0,120 
0,92082 
o,o77 
1*35r 
0,034 
1,46853 
0 163 
0,78782 
o,i 19 
0,92446 
0,076 
.1,11919 
0.033 
1,48149 
0,162 
0.79049 
O.IlS 
0,92812 
0,075 
1,12494 
0,032 
1,49485 
0,161 
0 79318 
0,117 
0,93182 
0,074 
1,13077 
0.031 
1,50864 
0.160 
0,79588 
0,116 
o,93555 
0,073 
1,13668 
0030 
1,52288 
0,159 
0,79861 
0,115 
o,9393i 
0,072 
1,14267 
0,029 
i,5376i 
0 158 
0,80135 
0,114 
0,94310 
0,071 
1,14875 
0,028 
1,55285 
0.157 
0,80411 
0,113 
0,94963 
0,070 
1,15491 
1,16116 
0,027 
1, c; 6864 
0,156 
0,80688 
0,112 
0,95079 
0,069 
0,026 
1,58503 
0.' 55 
0,80967 
0,1 II 
0,95468 
0,068 
1,16750 
0,025 
1,60206 
0,154 
0 81248 
0,110 
0,95861 
0,067 
i,i7393 
0,024 
1,61979 
o,i53 
0,81531 
0,109 
0,96258 
0,066 
1,18046 
0023 
1,63828 
0,152 
0,8x816 
O.IoS 
0,96658 
0,065 
1,18709 
0,022 
1,65758 
0.151 
0,82103 
0,107 
0,97062 
0,064 
1,19382 
1,20066 
0,021 
1,67779 
0,150 
0,82391 
0,106 
o,9747o 
0,063 
0,020 
1,69897 
0,149 
0,82682 
0.105 
0,97882 
0,062 
1,20761 
0,015 
1,82391 
0,148 
0,82974 
0,104 
0,98297 
0,061 
1,21468 
0,010 
2,00000 
0.147 
0.146 
0,83269 
0,83565 
0,103 
0,98719 
0,060 
1,22185 
0 005 
2,30103 236 
TABLES. 
CORRECTION TABLE FOR THE PROJECTING THREAD OF 
MERCURY IN A STANDARD THERMOMETER OF 
JENA GLASS ACCORDING TO RIMBACH. 
o—ioo° graduated in 0. Length of degree, about 4 mm. ; 
t observed temperature ; t° temperature of the surrounding air ; 
n number of degrees through which the thread projects. 
= 30 
Oo 
Ln 
40 
45 
So i 55 
60 
65 
70 
75 
80 
85 
n = 10 
0,04 
0,04 
0,05 
0,0 n 
0,05 i 0,06 
0,06 
0,07 
0,08 
0,09 
0,10 
0,10 
20 
0,12 
0,12 
0,13 
0,14 
0,15 0,16 
0,17 
0,18 
0,19 
0,20 
0,22 
0,23 
30 
0,21 
0,22 
0,23 
0,24 
0,25 0,25 
0,27 
0,29 
0,31 
o,33 
o,35 
0 37 
40 
0,28 
0,29 
Q.31 
o.33 
o,35 1 0,37 
o,39 
0,41 
o,43 
o,45 
0,48 
0,51 
50 
0,36 
0,38 
0,40 
0,42 
0,44 | 0,46 
0,48 
0,50 
o,53 
o,57 
0,61 
0,6s 
60 
0,45 
0,48 
0,51 
o,53 
o,55 0,57 
0,60 
0,63 
0,66 
o,6q 
o,73 
0,78 
70 
— 
— 
— 
— 
— 0,66 
0,69 
°,71 
o,75 
0,81 
0,87 
0,92 
80 
— 
— 
— 
— 
0.76 
0,81 
0,87 
o,93 
1,00 
1,06 
90 
— 
— 
— 
— 
— 
0,92 
0.99 
1,06 
i,'13 
1,20 
100 
— 
— 
— 
— 1 — 
— 
— 
0,10 
x,i8 
1,26 
i,34 
Tables for thermometers of Jena glass from o 360°, see Rimbach, Ber. 
d. d. chem. Ges. 22, p. 3074, 1889. INDEX. 
ABBE, refractometer, x6B 
Absorption, coefficient of, 57 
heat of, 138 
spectra, 187, 193 
Andrews, spec, heat determination, 120 
Araometer, 27 
Atomic weights, table of, 226 
Axial angle of crystals, 166 
Crystals, measurement of, 166 
Crystal-float method, 17 
DENSITY, 13 
of gases, 32 
of liquids, 19 
of solids, 14 
Depression of the freezing point, 8l 
Dielectric constant, 75, 182 
Diffusion, 57 
Dilation, 31 
Dilution, heat of, 139 
Direct-vision spectroscope, 183 
Dispersion, 171, 183 
Double refraction in crystals, 164 
Drop method, 49 
Dumas, vapor den. determination, 32 
BALANCE, chemical, 9 
Barometer, 224 
Beckmann, depression of freezing point, 
81 
97. 103 
thermometer, 218 
Berthelot, heat of combustion, 14X 
Boiling point, 90 
elevation of boiling point, 
elevation of, 97 
Bomb, calorimetric, 141 
Bunsen spectroscope, 183 
ice-calorimeter, 121 
ELECTRIC conductivity, 58 
Electro magnetic rotation, 214 
Electromotive force, 72 
Elevation of the boiling point, 97 
Emission spectra, 187 
Expansion, coefficient of, 76 
Extinction-coefficient, 194 
CALIBRATION of a wire, 73 
of a capillary tube, 
46 
of a thermometer, 
FORMATION, heat of, 152 
Freezing point, depression of, 81 
Fusion, heat of, 126 
Calorie, 109, 132 
Calorimeters, 112, 119, 121, 134 
Capillarimeter, 46 
Capillarity, 45 
Capillary electrometer, 71 
Cathetometer, 216 
GLAN, polarization spectrophotome 
ter, 200 
Chemical equilibrium, 57 
Combustion, heat of, 141 
Conductivity, electric, 58 
molecular, 69 
Contraction, 31 
Goniometer, 153 
HEAT of combustion, 141 
of dilution, 139 
of formation, 152 
of fusion, 126 
Convergent light, 165 
Critical pressure, 97 
temperature, 97 
of hydration, 140 
of neutralization, 133 INDEX 
Heat of precipitation, 138 
of solution, 137 
of vaporization, X 29 
Hofmann, vapor density, 34 
Hiifner polarization spectrophotome- 
Reaction velocity, 57 
Refraction, index of, 168 
atomic, 178 
molecular, 178 
specific, 178 
Refractometer, 168, 172 
Regnault-Pfaundler, specific heat, 115 
Rotation of the plane of polarization, 
ter, 200 
Hydration, heat of, 140 
Hydrostatic balance, 19, 25 
ICE-CALORIMETER, 121 
electro-magnetic, 214 
Rotatory power, molecular, 203 
specific, 202 
lons, velocity of, 71 
Isomorphism, 167 
JONES-SCHLEIERM ACHER, 
boiling-point determination, 93 
SCHIFF, specific heat, 117 
Siwoloboff, boiling point, 93 
Solidifying point, 79 
Solubility, 56 
Solution, heat of, 137 
Specific gravity, 13 
Specific heat, 109 
of liquids, 117 
of solids, ill 
Spectrophotometer, 193, 200 
Spectroscope, 182, 183, 189 
Spectrum analysis, 182 
Stalagmometer, 49 
Stauroscope, 167 
Strouhal and Barns, calibration of a 
KOHLRAUSCH, electric conduc- 
tivity, 58 
Kopp, specific heat, Ix 7 
Kriiss, spectroscope, 189 
LAURENT, half-shadow apparatus, 
211 
Lippich, half-shadow apparatus, 214 
Lunge and Neuberg, vapor density, 41 
MELTING point, 79 
Meyer, V., vapor density, 38 
Micropolaris'cope, 160 
Mitscherlich, polarimeter, 207 
Mohr-Westphal, balance, 24 
Molecular refraction, 178 
volume, 28 
wire, 73 
THERMOCHEMICAL constants, 
_ 134 
Thermometer, 218 
Thermostat, 65 
Transport numbers, 71 
OSMOTIC pressure, 57 
PASTILLE press, 149 
Poiseuille-Oslwald, viscosity determina- 
VAPOR density, 32 
pressure, 90 
Vaporization, heat of, 129 
Vernier, 215 
Vibration, directions of. in crystals, 164 
Vierordt, spectrophotometer, 193 
Viscosity, constant of, 53 
tion, 53 
Polarimeter, 207, 211, 214 
Polaristrobometer, 209 
Pressure regulator, 95 
Pulfrich, refractometer, 172 
Pyknometer, 14, 19 
WATER-EQUIVALENT, no, 
RAABE turbine, 66 
Radiation, 115 
113 
Wild polaristrobometer, 209 
Wollaston, goniometer, 153 
Raoult, depression of freezing point, 79