595 
THE 
REFRACTION OF SOUND. 
" / 
WILLIAM B. TAYLOR. 
FROM THE SMITHSONIAN REPORT FOR 1875. 
W ASHING'TON : 
SMITHSONIAN INSTITUTION. 
1 885. 595 
T ZE3I IE 
REFRACTION OF SOUND. 
BY 
/ 
WILLIAM B. TAYLOR. 
FROM THE SMITHSONIAN REPORT FOR 1876. 
WASHINGTON: 
SMITHSONIAN INSTITUTION. 
1 885. THE REFRACTION OF SOUND. 
William B. Taylor. 
As ordinarily received by the ear, sound may be considered as an 
aerial impulse or succession of impulses radiating in all directions 
from the origin of disturbance', and consisting in the main of a small 
to-and-fro movement generating an expanding wave of compression of 
determinate velocity, necessarily followed by a corresponding wave of 
attenuation. This vibration is a mass-movement of the air, and not a 
molecular movement; and the surface or surfaces of similar phase of 
movement are equidistant from the origin; or, in other words, the 
wave-fronts are essentially spherical. 
The transmission of sound through liquid and solid mediums, though 
similar in character, and subject to similar perturbations, will not here 
be considered. 
Sound, while differing widely from light in the character of its waves 
and their order of magnitude, yet thus moves like light in radial lines, 
and like light is diverted from its rectilinear course whenever its waves 
undergo an unequal retardation or acceleration; that is, whenever any 
segment of a series of advancing wave-fronts (regarded as an acoustic 
beam) receives froln any cause an unequal velocity on its opposite sides, 
such beam is bent toward the side of least velocity, and from the side 
of greatest velocity; the line of impulse or of acoustic effect being 
always perpendicular to the surface of the wave front. 
By sound-beams, or sound-rays, the longitudinal direction of sound is 
to be understood; by sound-waves, the transverse surfaces of simul- 
taneous movement are to be understood. The amplitude of the wave- 
motion is very minute, being ordinarily a barely visible magnitude. It 
lies in the direction of the wave-length, or of the sound-ray. In the 
case of light, the amplitude of vibration is transverse to the wave- 
length, or to the direction of the ray. 
If we imagine a symmetrical boat on a perfectly still sea or lake, 
mechanically propelled by oars of precisely similar character and move- 
ment, it is obvious that such a boat must advance in a perfectly straight 
course. If placed in a uniform current, the boat, though drifting with 
the current, would still maintain a rectilinear path. If, however, such 
moving boat were to enter a current, or to encounter a difference of cur- 
rent ou its opposite sides, or were it to encounter water of different 
density, as by passing obliquely from salt-water into a margin of fresh 
water, then, at the moment of transition, the oars meeting with unequal 
205 206 
THE REFRACTION OF SOUND. 
resistances, the course of the boat would be changed, or 44 refracted.** 
This image may be taken as a rough illustration of the phenomenon of 
44 refraction” generally. 
There are three different methods in which sound-waves passing 
through a gaseous medium may suffer such unequal disturbance of 
velocity: first, by variations of density in the medium, sound moving 
more slowly through a dense air than a rare oue, the pressure being the 
same; second, by variations of elasticity in the medium, sound moving 
more swiftly with increase of elasticity, the density being the same; 
and, third, by variations of motion or current in the medium, sound trav- 
eling by convection faster with the wind by a small percentage, accord- 
ing to its velocity, and more slowly against the wind.* 
There is no doubt that light also would be subject to all three of these 
forms of refraction, as its velocity is necessarily retarded by an increase 
of density in the medium, by a. reduction of the elasticity of the medium, 
and by an adverse motion of the medium. 
A fourth cause of velocity disturbance in the case of sound is found 
in the temperature of the medium, sound moving more swiftly in a heated 
atmosphere than in a cooler one. This cause of acoustic refraction is 
practically a highly important one; though it may be theoretically 
resolved into one of the preceding conditions, since the only dynamic 
effect of heat on a gas is to increase its elasticity if the volume be con- 
stant by confinement, or to increase its volume if uuconfined without 
changing its elasticity. 
The relation of these atmospheric conditions to each other is exceed- 
ingly simple. 
The density of a perfect gas (the inverse of its volume) varies directly 
as the pressure, the temperature being constant, or inversely as the 
absolute temperature, the pressure being constant. 
The elasticity of a perfect gas varies directly as the pressure, the den- 
sity being constant, or inversely as the density, the pressure being con- 
stant. It also varies directly as the absolute temperature, the volume 
being constant.* 
From these relations it follows that increase of atmospheric pressure 
does not affect the velocity of sound; for although the density is directly 
proportional to the pressure, and this diminishes the velocity, yet as the 
elasticity is also directly proportional to the pressure, and this increases 
the velocity by precisely the same amount, the two effects are neutral- 
ized. 
*The ratio of the velocity of the wind to that of sound (one or two per cent.) is too 
small to be of any account directly. Differentially, it becomes very important. A uni- 
form wind has no practical effect on sound except to slightly flatten or lower the pitch 
in its own direction, and to sharpen or raise the pitch in the opposite direction. 
t According to Waterston, “ when air is compressed or dilated, the absolute tempera- 
ture varies as the cube root of the density, and the tension as the fourth power of the 
absolute temperature, or cube root of the fourth power of the density,” {llep. Brit. 
Assoc., 1853, p. 12 of Abstracts.) This would indicate a striking departure from tho 
condition of a perfect gas. THE REFRACTION OF SOUND. 
207 
We have as the laws of sound-motion in a perfect gas : 
1st. Its velocity is directly proportional to the square root of the elas- 
ticity of the air. 
2d. Its velocity is inversely proportional to the square root of the den- 
sity of the air. 
3d. Its velocity is directly proportional to the square root of the abso- 
lute temperature of the air. 
The theoretical case of unequal elasticity of the medium, presenting 
no practical examples, excepting in the passage of sound from water 
into air obliquely, or from air into water, may be here neglected; and 
the remaining actual conditions of acoustic refraction are limited to three, 
viz: those of density-inequality, wind-inequality, and temperature- 
inequality. It is important to observe that the two fundamental princi- 
ples underlying the discussion of acoustic refraction of whatever origin 
are, first, that the directions of progressive impulse are always at right 
angles to the surface of the wave-front, and, secondly, that any deforma- 
tion of the spherical surface of the wave front must accordingly deflect 
the line of acoustic propagation from its original radial direction. 
1.—REFRACTION FROM INEQUALITY OF DENSITY. 
In 1852, Mr. Carl Somlhauss was the first to demonstrate acoustic 
refraction, and he exhibited it by means of a lens of carbonic-acid gas. 
It may be here premised that, in accordance with the previous sum- 
mary, hydrogen, having at the pressure of the atmosphere the same elas- 
ticity, should, from this circumstance alone, transmit sound with the 
same velocity as ordinary air; but as its rarity is fourteen times greater, 
the velocity of sound in this medium is increased nearly four times, so 
that while at ordinary temperature (65° F.) sound in air would move 
over 1,125 feet in a second, or one mile in 4.7 seconds, it would move 
over 4,250 feet per second (or one mile in 1£ second) in an atmosphere 
of hydrogen. On the other hand, as carbonic acid, at the same pressure 
and with nearly the same elasticity, has a density rather more than 50 
per cent, greater than air, it would retard the velocity of sound about 
one-fifth, or reduce it to 912 feet per second, or one mile in 5.7 seconds. 
Mr. Sondhauss first employed a thin membranous balloon formed of 
gold-beaters’ skin, but obtained more decided results by forming the 
envelope of a double convex lens with two spherical segments of col- 
lodion film, attached to a leaden hoop, in which were suitable openings 
for the introduction of the gas. The ticking of a watch placed at some 
distance behind such lens was heard most distinctly at a focal point in 
front of the lens. 
“ In order to arrive at a more certain decision, the experiment was 
arranged in such manner that while the observer sat at the other side 
of the lens with closed eyes and listened for the ticking of the watch, 
the lens was alternately removed and again brought into position, 
whereby it was shown that the ticking of the watch disappeared every 208 
THE REFRACTION OF SOUND. 
time upon the removal of the lens and was immediately audible again 
when the lens was replaced between the watch and the ear.”—(Poggen- 
dorff's Annalen, 1852, lxxxv, 381, translated and republished in the Phil. 
Mag. February, 1853, v, 75.) 
The accompanying Fig. 1, representing a vertical section of the gas 
Fig. 1.—Carbonic-acid lens. 
lens through its center, will serve to give a more definite idea of the 
action it exercises on the sound-waves passing through it. For any 
small area, the wave-front, at some distance from its origin, may be con- 
sidered as practically a plane surface, and 1,2, 3, &c., (Fig. 1,) may rep- 
resent the successive positions of a single advancing wave-front. On 
entering the convex surface of the carbonic-acid lens at its central 
point a, the wave-face is at once retarded, and successive annuli of the 
wave passing the surface at increasing degrees of obliquity, the form of 
the wave front becomes concave, as shown at 3 and 4, advancing concen- 
trically according to the law of normal impacts, with a uniform though 
retarded velocity, as shown at 4, 5, 0, 7, &c. On emerging first from 
the outer margin of the reversed convex surface b, the wave-front is 
accelerated in passing into the common air, and meeting the boundary 
of the same obliquely becomes still more concave, as shown at 8, 9, 10, 
&c. Advancing concentrically, its impulses converge with uniform 
velocity, but increasing energy, toward a focal point, /. 
It is obvious that if this convex envelope were filled with hydrogen, 
the action would be just reversed, as shown in Fig. 2. The wave of 
sound, on entering the convex surface c, would be accelerated (com- 
mencing at the middle) so as to acquire a continuously convex front, as 
shown at 5, 6, &c. Passing through the second surface, d, and being 
retarded in a reverse order, the wave-front would advance with an in- 
creased convexity, as seen at 8, 9, 10, &c., giving a general divergence 
of the sound-rays, the focus being negative. 209 
THE REFRACTION OF SOUND. 
It follows that to obtain a focal convergence by means of a hydrogen 
lens, we should have to employ a concave form, as shown in Fig. 3. In 
Fig. 2.—Hydrogen lens, (a.) 
this case, the outer annulus of the wave on euteriug the projecting sur- 
face of the lens g, as at 4 and 5, would be hurried forward into a con- 
cave form, as shown at 5 and G, having a general center of convergence 
at about e. On emerging from the second surface, h, (supposed here to 
Fig. 3.—Hydrogen lens, (b.) 
be a plane,) the wave, by oblique retardation, as shown at 7, would be 
somewhat flattened, as at 8, 9,10, &c., extending the focal point of con- 
vergence to/. The effect of a double concave surface to the lens would 
be to shorten the focal distance according to the degree of concavity. 
2.—REFRACTION FROM INEQUALITY OF WIND. 
In 1S57, Prof. G. G. Stokes showed that differences of motion in the 
air must exert a bending influence on the beams of sound, and that this 
s. Mis. 115 14 210 
THE REFRACTION OF SOUND. 
deflection presented the only satisfactory explanation of the familiar 
fact of observation that sound is usually heard many times farther in 
the direction of a wind than in a direction opposed to its action. His. 
explanation of this phenomenon is as follows : 
“If we imagine4the whole massof air in the neighbourhood of the source 
of disturbance divided into horizontal strata, these strata do not all 
move with the same velocity. The lower strata are retarded by friction 
against the earth, and by various obstacles they meet with ; the upper 
by friction against the lower, and so on. Hence the velocity increases 
from the ground upward, conformably with observation. This difference 
of velocity disturbs the spherical form of the sound-wave, tending to 
make it somewhat of the form of an ellipsoid, the section of which, by a 
vertical diametrical plane parallel to the direction of the wind, is an 
ellipse meeting the ground at an obtuse angle on the side toward which 
the wind is blowing, and an acute angle on the opposite side. Now sound 
tends to propagate itself in a direction perpendicular to the sound-wave 
and if a portion of the wave is intercepted by an obstacle of large size,, 
the space behind is left in a sort of sound-shadow, and the only sound 
there heard is what diverges from the general wave after passing- 
the obstacle. Hence, near the earth, in a direction contrary to 
the wind, the sound continually tends to be propagated upward, 
and consequently there is a continual tendency for an observer in 
that direction to be left in a sort of sound-shadow. Hence, at a 
sufficient distance, the sound ought to be very much enfeebled ; but 
near the source of disturbance this cause has not yet had time to oper- 
ate, and therefore the wind produces no sensible effect, except what 
arises from the augmentation in the radius of the sound-wave, and this 
is too small to be perceptible. In the contrary direction—that is, in the 
direction toward which the wind is blowing—the sound tends to propa- 
gate itself downward, and to be reflected from the surface of the earth 
and both the direct and reflected waves contribute to the effect per- 
ceived.”—{Rep. Brit. Assoc., 1857, xxvii, p. 23 of Abstracts.) 
Fig. 4.—Yental refraction. 
This action may be illustrated by Fig. 4, in which the larger arrow THE REFRACTION OF SOUND. 
211 
above indicates the direction and force of the wind, and the two smaller 
arrows below the diminished force of the wind in the same direction, by 
reason of the increasing resistance and retardation toward the surface 
of the earth. The result is a flattening of the waves at the left side 
and a swaying of the waves forward on the right side, thus giving the 
radial lines or sound-beams a curved form, (as shown by the lower lines 
l i and i fc,) these being always perpendicular to the wave-faces. As 
this curvature or refraction is necessarily upward against the unequal 
wind and downward in the direction of the wind, an observer at Jc will 
hear with great distinctness the sound emanating from i, while an ob- 
server on the other side at j will hear nothing, by reason of the sound- 
beams being tilted above his head. By rising to an elevation, as at l, 
the observer will hear the sound as well against the wind as with it. 
It is not a little surprising that an explanation of a well-marked and 
puzzling phenomenon, so elegant and so conclusive as that promulgated 
b}* Professor Stokes, should have remained for fifteen years unnoticed 
and unthought-of by the scientific world. When in 1865 Professor 
Henry discovered that “ a sound moving against the wind, inaudible to 
the ear on the deck of a schooner, was heard by ascending to the mast- 
head, this remarkable fact at first suggested the idea that sound was 
more readily conveyed by the upper current of air than the lower.” 
And this general idea seemed confirmed by the observation that with 
the upper and lower currents at variance the upper wind appeared to 
most favor the sound. Nor was it till early in 1872 that the full signifi- 
cance of all this became apparent on first learning of the explanation 
given by Professor Stokes. And yet during the same series of obser- 
vations, Professor Henry discovered that the velocity of wind in the 
higher regions of the air was much greater than in the lower regions. 
In like manner, Professor Reynolds having, in the spring of 1874, 
independently arrived at the same theory, and undertaken a series of 
experiments and observations in this direction, remarks: “I had just 
reached the point of making such tests, when I discovered that the 
same views had been propounded by Professor Stokes so long ago as 
1857.”—(Proc. R. $., 1874.) Professor Reynolds made the decisive 
observations thar in the direction of the wind, the sound of a bell could 
be as well heard at a distance, with the head depressed as when stand- 
ing ; while against the wind, the sound at no great distance ceased to 
be heard, passing over the head, and could be regained in full force by 
elevation. It was found also that the elevation required to reach the 
lowest sound-beam increased with the distance. 
If we suppose the wind near the surface of the earth (or at C feet 
above it) to be moving at the rate of six miles per hour, (one mile in 10 
minutes, or 8.8 feet per second,) aud at the elevation of 1,000 feet to be 
moving in the same direction with just double the velocity, then a ver- 
tical wave-front of sound in moving 4.7 seconds, or one mile, against 
such wind would be retarded 41 feet near the ground, and 82 feet at 
the height of 1,000 feet. This difference of 41 feet would so tilt the 212 
THE REFRACTION OF SOUND. 
wave-face backward that a line perpendicular to it would have an up- 
ward direction of about 2° 21/; or, an arc described with a radius of 
24.39 miles would represent approximately the upward curvature of a 
horizontal sound-beam, whereby at the distance of a mile it would be 
lifted up about 108 feet. A wave-front of sound moving in the direction 
of the wind would, of course, be correspondingly accelerated above, 
and the beam bent downward in a similar arc. 
A wind blowing along the face of an extended bluff or cliff, being re- 
tarded near the same by friction, would, in a similar manner, cause a 
sound originating near it to be laterally refracted toward the wall in 
the direction of the wiud, and from it in the opposite direction. 
When, from any cause, the upper wind should move more sluggishly 
than the lower wind, as sometimes occurs, the lines of refraction above 
indicated would be reversed, and we should have the exceptional case 
of sound being favored by an opposing wind, and vice versa. 
This very simple principle of vental refraction has thus a wide prac- 
tical range, and the variety of its applications is limited only by that 
of the actual differences in force and direction of the winds. In short, 
in the case of any divergence between the upper and lower currents, in 
whatever direction, there will be but two lines of no refraction. In all. 
other directions, a positive or a negative resultant must to some degree 
disturb the direction of the acoustic ray. 
In consequence of the slight internal friction (or “viscosity”) of air, 
the shadow-line is not usually very sharply defined. Wave-impulses act- 
ing laterally on the adjacent air cause the sound to be feebly heard within 
the shadow-line; and the sound-beam is thus practically diffracted 
around an obstacle to an extent which is probably some function of its 
intensity or energy. The effect of this, in the case of a refracted beam, 
is to diminish somewhat its apparent curvature, and thus to render an 
uplifted sound sensible to a greater distance than it would be on a merely 
geometrical theory, or without such marginal diffusion. 
From the same cause the following practical results follow : 1st. A 
continuous sound, as of a horn or steam-whistle, requires at a distance 
a short but appreciable interval (a second or more) to be heard with its 
full power; 2d. Hence, with adverse winds, sounds of single impulse, 
as those of bells and guns, are more refracted than continuous sounds, 
whose initial impulses are re-enforced by rhythmic successions, giving 
them greater persistence of force and direction ; 3d. It is unnecessary to 
add that sounds under such circumstances (with beams of convex cur- 
vature) can be heard to a greater distance when originating from an ele- 
vation, and also when observed from an elevation ; 4th. It is probable 
that sounds of high pitch are more refracted than medium tones and 
those of lower pitch. 
3.—REFRACTION FROM INEQUALITY OF TEMPERATURE. 
In 1874, Prof. Osborne Eeynolds pointed out a third practical cause of 
acoustic refraction in the differences of temperature to which advancing THE REFRACTION OF SOUND. 
213 
waves of sound are frequently subjected. He remarks: “Although 
barometric pressure does uot affect the velocity of sound, yet, as is well 
known, the velocity of sound depends on the temperature, and every 
degree of temperature between 32° and 70° adds approximately one foot 
per second to the velocity of sound. This velocity also increases with 
the quantity of moisture in the air; but the quantity is at all times too 
small to produce au appreciable result. This vapor nevertheless plays 
an important partin the phenomena under consideration; for it gives 
to the air a much greater power of radiating and absorbing heat, and 
thus renders it much more susceptible of changes in the action of the 
sun. ... It is a well-known fact that the temperature of the air 
diminishes as we proceed upward, and that it also coutaius less vapor. 
Hence it follows that, as a rule, the waves of sound must travel faster 
below than they do above, and thus be refracted or turned upward.”— 
(Proc. E. S., 1874.) 
Professor Reynolds cites observations showing that on a calm clear 
day in July, 1873, while the sun was shining with great power, loud 
sounds which could be heard but two or three miles \yere heard several 
times this distance toward evening after the sun had become obscured 
with clouds. “ Here we see that the very conditions which actually 
diminished the range of sound were precisely those which would cause 
the greatest lifting of the waves.” 
This furnishes a satisfactory explanation of the familiar fact that 
sounds heard during the day-time to comparatively short distances (es- 
pecially in summer and with still air) are audible many times as far in 
the night. “ Humboldt could hear the falls of Orinoco three times as 
loud by night as by day at a distance of one league; and he states that 
the same phenomenon lias been observed near every waterfall in 
Europe.” Humboldt also remarked that the heating effect of the sun 
was so great that “ all distant objects had wavy undulating outlines, 
the optical effect of the mirage. Not a breath of air moved the dust- 
like sand. The sun stood in the zenith.”—(Views of Nature, Bohn’s ed., 
p. 200.) Dr. Gregory, in his experiments on sound, undertaken in 1824, 
observed that, on January 9, in the evening, with no wind stirring, 
“ the sound of the same charge fired from the same musket was heard 
much more intensely on this clear frosty night than in the day-time of 
January 3, at the same distance, 3,600 feet.”—{Phil. Mag., 1824, lxiii, 
404.) 
Fig. 5 illustrates this effect of heated lower strata of air in tilting 
up the beams of sound in all directions. If we suppose the horizontal 
lines to mark spaces upward, of 100 yards each, into which the air is 
arranged by strata of diminishing temperatures of 3 degrees each, but 
increasing more rapidly near the surface, (75°, 70°, 67°, 64°,) then near 
the ground (at 75°) the horizontal sound-beams will travel 5 feet per 
second (or 23.5 feet per mile) faster than at the line n of 70°, or the 
height of 300 feet; at this line, 3 feet per second (or 14 feet per mile) 214 
THE REFRACTION OF SOUND. 
faster than at the line o of 67°, or the height of GOO feet; and at this line- 
the same quantity faster than at the of G4°, or the height of 900 
feet. The result is that a vertical wave-front 900 feet deep would, at 
the distance of one mile, be advauced at its lower part more than 51 feet 
beyond its upper part, making an angle of about 3£°; and the corres- 
ponding upward curvature of the lower sound-beams emanating from 
tn (the versed sine of this arc) would amount to about 150 feet. 
Fig. 5.—Thermal refraction. 
If the temperature of the lower strata of air were found to increase 
only at half the rate above assumed, the lower sound-beams from m 
would be lifted one hundred and fifty feet in about two miles. If the 
differences of temperature were reduced to one-fourth, this amount of 
upward tilt would be reached in about four miles, &c. 
From this it is apparent that temperature-refraction—the upward 
“ dishing ” of the lower sheet of sound by the overheating of the lower 
air—is not only a real phenomenon, but that in quantity it introduces 
a very considerable amount of disturbance in the direction of sound, 
and thus impairs seriously its audibility at any great distance on the 
surface of the earth. 
In further illustration of the same principle, no less notable is the 
converse effect of an excess of cooling in the lower strata, occasionally 
noticed. Professor Reynolds, continuing his researches “ On the re- 
fraction of sound,” during the summer of 1875, found that, on the 19th 
of August, “ after three weeks of cold and windy weather,” the sea 
and the adjacent air being chilled considerably below the average or 
upper temperature, sound passing over the water reached the observers 
in a boat with such remarkable clearness that “ guns, and on one occa- 
sion the barking of a dog, on the shore, eight miles distant, were dis- 
tinctly heard, as were also the paddles of a steamer fifteen miles dis- 
tant. The day was perfectly calm; there was no wind; the sky was 
quite clear, and the sun shining with great power.” The significant 
circumstance is recorded that “ all the time distant objects loomed con- 
siderably, i. e., appeared lifted.” In this case, “ the diminution in the 
temperature of the air being downward, the sound instead of being THE REFRACTION OF SOUND. 
215 
lifted as it usually is, was brought down, and thus intensified at the 
surface of the water, which, being perfectly smooth, was thus converted 
iuto a sort of whispering-gallery.”—(Proc. E. $., 1876.) 
This action is illustrated by Fig. 6, in which the temperature of the 
air below the horizontal line q r, being gradually less toward the earth 
than above the line, the sound-waves originating at s are shortened lat- 
Fig. 6.—Refraction by cold. 
erally (or in the direction of the lower rays) about one foot per second 
for each degree of refrigeration, and the sound-beams (always perpen- 
dicular to the waves) are thus gradually bent downward. 
The remarkable distances to which sounds have sometimes been 
heard in Arctic regions receive here a satisfactory explanation. “ Lieu- 
tenant Foster, in the third polar expedition of Captain Parry, found 
that he could hold a conversation with a man across the harbour of Port 
Bowen, a distance of G,G9G feet, or about a mile and a quarter.”—(Sir J. 
Herschel, Sound, sect. 21.) The same author remarks of the polar 
regions: In consequence of the intense cold of the icy surface, con- 
trasted, as it sometimes is in summer, with the warmth of the air, the 
phenomena of atmospheric refraction are exaggerated in these regions 
in a most extraordinary manner; the forms of ice-bergs, rocks, etc., are 
seen drawn up in vertical altitude, and spread out at their apparent 
summits laterally, so as to present no resemblauce to their real form.”— 
(Sir J. Herschel, Physical Geography, sect. 98.) From which we learn 
that the optical deportment of the air may very often be accepted as an 
index of its acoustic condition. 
In the play and interaction of these two great and prevalent modes 
of acoustic refraction—that resulting from co-existent differences of 
wind in varying directions and that from co-existent differences of tem- 
perature—whether re-enforcing or checking each other, or leaving a dif- 
ferential resultant, we have abundant opportunities to exercise the 
judgment and discrimination of the most diligent observers. Professor 
Reynolds noticed that on some clear nights in May and June, 1875, 
when a heavy dew indicated considerable refrigeration at the surface, 
“ the sound could invariably be heard as far against a light wind as 
with it,” showing that the upward refraction from wind was completely 216 
THE REFRACTION OF SOUND. 
counteracted by the downward refraction from diminution of tempera- 
ture. This was observed not to be the case when the cloudiness of the 
night prevented terrestrial radiation and the deposition of dew.—(Prof 
R. 8., 1876.) 
It has thus been shown in the course of this discussion, that while 
the refraction of sound as illustrated by gas lenses, still retains its 
original interest as a striking class-experiment, the far more important 
examples of acoustic refraction constantly presented by the infinitely 
varied conditions of differing air-currents and of differing air-tempera- 
tures, have until very recently, attracted no attention, and their prac- 
tical significance has been strangely overlooked.