Over the grass no sound could be heard with the head on the ground
at 20 yards from the bell, and at 30 yards it was lost with the head 3 feet
from the ground, and its full intensity was lost when standing erect at
16] ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. ' 97
30 yards. At 70 yards, when standing erect, the sound was lost at long
intervals, and was only faintly heard even then; but it became continuous
again when the ear was raised 9 feet from the ground, and it reached its full
intensity at an elevation of 12 feet.
Over the snow similar effects were observed at very nearly equal
distances. There was this difference, however, the sound was not entirely
lost when the head was lowered or -even on the ground. Thus at 30 yards
I could still hear a faint sound. Mr Millar could hear this better than
I could; he, however, experienced the same increase on raising his head.
At 90 yards I lost the sound entirely when standing on the ground, but
recovered it again when the ear was 9 feet from the ground. Mr Millar,
however, could hear the sound very faintly, and at intervals, at 160 yards ;
but not with his head on the ground. At this point I was utterly unable
to hear it ; and even at an elevation of 25 feet I gave it up as hopeless.
However, as Mr Millar by mounting 10 feet higher seemed to hear it very
much better, I again ascended; and at an elevation of 33 feet from the
ground I could hear it as distinctly as I had previously heard it when
standing at 90 yards from the bell. I could not hear it 5 feet lower down ;
so that it was the last 5 feet which had brought me into the foot of the
wave. Mr Millar experienced the same change in this 5 feet. As the
sound could now be heard as strong as at a corresponding distance with
the wind, we thought we had reached the full intensity of the waves. This,
however, was not the case ; for the least raising of the bell was followed by
a considerable intensifying of the sound ; and when it was raised 6 feet
I could hear each blow of the hammer distinctly, although just at that time
a brass band was playing in the distance. It seemed to me that I could
hear it as distinctly as at 30 yards to leeward of the bell. All these results
were repeated on both days with great uniformity.
When more than 30 yards to the windward of the bell, the raising of
the bell was always accompanied by a marked intensifying of the sound, and
particularly over the grass. I could only hear the bell at 70 yards when
on the ground; yet when set on a post 5 feet high I heard it at 160 yards,
or more than twice the distance. This is a proof of what I previously
pointed out, that the waves rise faster at the ground than they do high up,
and crowding together they intensify. In all cases there was an unmistakable
greater distinctness of the sound from short distances to windward than to
leeward or at right angles.
Except when the sound was heard with, full force it was not uniform.
The bell gave two sounds (the beats of the hammer and the ring) which
could be easily distinguished ; and at times we could hear only the ring, and
at others the beats. The ring seemed to preserve itself the longest above the
o. R. 7
98 ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. [16
ground ; whereas near the ground at short distances the ring was lost first.
This is explained by the fact that the rate at which sound-waves diverge
depends upon their note: the lower the note the more will they diverge.
Thus the beats diverge more rapidly than the ring, and consequently die
out sooner ; whereas when the head is on the ground near the bell it is
only the diverging waves that are heard, and here the beats have the best
chance. The intensity of the sound invariably seemed to waver ; and as one
approached the bell from the windward side, the sound did not intensify
uniformly or gradually, but by fits or jerks; this was the result of crossing
the rays' interference, such as those shown in fig. 2.
During the observations the velocity of the wind was observed from time
to time at points 1 foot and 8 feet above the surface.
On the 9th, that is over grass, it varied from 4 feet per second at 1 foot
and 8 feet per second at 8 feet, to 10 feet per second at 1 foot and 20 feet
per second at 8 feet, always having about twice the velocity at 8 feet that it
had at 1 foot above the ground.
Over the snow there was not quite so much variation above and below.
On the 10th the wind varied from 3 feet per second at 1 foot to 4 feet per
second at 8 feet*. On the llth the variation was from 12 at 1 foot and 19
at 8 feet to 6 at 1 foot and 10 at 8 feet. Thus over snow the variation in the
velocity was only about one-third instead of half.
Since the foregoing account was written, I have had an opportunity of
experimenting on a strong west wind (on the 14th of March) ; and the results
of these experiments are, if anything, more definite than those of the previous
ones. The wind on this occasion had a velocity of 37 feet per second at an
elevation of 12 feet, and of 33 at 8 feet, and 17 at 1 foot. The experiments
were made in the same meadows as before, the snow having melted, so that
the grass was bare.
With the wind I could hear the bell at 120 yards, either with the bell
on the ground or raised 4 feet above it. At right angles to the direction
of the wind it ranged about 60 yards with the bell on the ground, and
80 yards when the bell was elevated.
To windward, with the bell standing on the ground (which, it must be
remembered, means that the bell was actually 1 foot above the surface), the
sound was heard as follows :
With the head close to the ground... At 10 yards. At 20 yards.
Standing ; H 30 n n 40
At an elevation of 25 feet Not heard at 90 yards.
* The wind fell rapidly towards the close of the observations on this day.
16] ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. 99
With the bell at an elevation of 4 feet 6 inches :
Head to the ground At 18 yards. At 30 yards.
Standing up 40 60
At an elevation of 12 feet 90
At. an elevation of 18 feet 90
These results entirely confirm those of the previous experiments; and
the intensifying of the sounds to windward by the raising of the bell was
even more marked than before ; for at 90 yards to windward, with the bell
raised, I could hear it much more distinctly than at a corresponding distance
to leeward. This fact calls for a word of special explanation ; it is clearly due
to the fact that the variation in the velocity of the air is much greater near
the ground than at a few feet above it. When the bell is on the ground all
the sound must pass near the ground, and will all be turned up to a nearly
equal extent ; but when the bell is raised, the rays of sound which proceed
horizontally will be much less bent or turned up than those which go down
to the ground ; and consequently, after proceeding some distance, these rays
will meet or cross, and if the head be at this point they will both fall on the
ear together, causing a sound of double . intensity. It is this crossing of the
rays also which for the most part causes the interference seen in fig. 2.
These experiments establish three things with regard to the transmission
of sound :
1. That when there is no wind, sound proceeding over a rough surface is
more intense above than below.
2. That as long as the velocity of the wind is greater above than below,
sound is lifted up to windward and is not destroyed.
3. That under the same circumstances it is brought down to leeward,
and hence its range extended at the surface of the ground.
These experiments also show that there is less variation in the velocity of
the wind over a smooth surface than over a rough one.
It seems to me that these facts fully confirm the hypotheses propounded
by Prof. Stokes, that they place the action of wind beyond question, and
that they afford explanations of many of the anomalous cases that have been
observed ; for instance, that sounds can be heard much further over water
than over land, and also that a light wind at sea does not appear to affect
sound at all, the fact being that the smooth water does not destroy either the
sound or the motion of the air in contact with it. When the wind and sea
are rough the case is different.
100 ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. [16
The Effect of Variations of Temperature.
Having observed how the wind acts to lift the waves of sound, by
diminishing their velocity above compared with what it is below, it was evident
to me that any other atmospheric cause which would diminish the velocity
above, or increase that below, would produce the same effect, viz. would cause
the waves to rise.
Such a cause must at certain times exist in the variation in the condition
of the air as we proceed upwards from the surface.
Although barometric pressure does not 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
1 foot per second to the velocity of sound. The velocity also increases with
the quantity of moisture in the air; but the quantity is at all times too
small to produce an appreciable result. This vapour nevertheless plays an
important part in 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.
If, then, the air were all at the same temperature and equally saturated
with moisture, the velocity of sound would be the same at all elevations ;
but if the temperature is greater, or if it contains more water below than
above, then the wave of sound will proceed quicker below than above, and
will be turned up in the same way as against a wind. This action of the
atmosphere is, strictly speaking, analogous to the refraction of light. In light,
however, it is density which retards motion : temperature and pressure have
little or nothing to do with it ; and since the density increases downwards,
the rays of light move slower below than they do above, and are therefore
bent downwards, and thus the distance at which we can see objects is
increased. With sound, however, since it is temperature which affects the
velocity, the reverse is the case ; the rays are bent upwards, and the distance
from which we can hear is reduced.
It is a well-known fact that the temperature of the air diminishes as
we proceed upwards, and that it also contains less vapour. 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.
* It varies as the square root of ^^^ , and consequently as the square root of the absolute
16] ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. 101
The variation of temperature is, however, by no means constant, and a
little consideration serves to show that it will be greatest in a quiet atmo-
sphere when the sun is shining. The sun's rays, acting most powerfully on
that air which contains the most vapour, warms the lower strata more than
those above them ; and besides this, they warm the surface of the earth, and
this warmth is taken up by the air in contact with it. It is not, however,
only on such considerations as these that we are in a position to assert the
law of variation of atmospheric temperature. Mr Glaisher has furnished us
with information on the subject which places it beyond the region of surmise.
I extract the following from his " Report on Eight Balloon Ascents in
1862 " (Brit. Assoc. Rep. 1862, p. 462) :
" From these results the decline of temperature when the sky was
For the first 300 feet was 0'5 for every 100 feet.
From 300 to 3400 0'4
3400 to 5000 0-3
"Therefore in cloudy states of the sky the temperature of the air
decreased nearly uniformly with the height above the surface of the earth
nearly up to the cloud.
" When the sky was partially cloudy the decline of temperature
In the first 100 feet was 0'9
* * * *
From 2900 to 5000 0'3 for every 100 feet.
" The decline of temperature near the earth with a partially clear sky is
nearly double that with a cloudy sky.
" In some cases, as on July 30th, the decline of temperature in the first
100 feet was as large as l'l."
We may say, therefore, that when the sky is clear the variation of
temperature, as we proceed upwards from 1 to 3000 feet, will be more
than double what it is when the sky is cloudy. And since for such small
variations the variation in the velocity of sound, that is the refraction, is
proportional to the temperature, this refraction will be twice as great with
a clear sky as when the sky is cloudy.
This is the mean difference, and there are doubtless exceptional cases in
which the variations are both greater and less than those given; during the
night the variations are less than during the day, and again in winter than
This reasoning at once suggested an explanation of the well-known fact
that sounds are less intense during the day than at night. This is a matter
102 ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. [16
of common observation, and has been the subject of scientific inquiry. F. De
La. Roche discusses the subject, and exposes the fallacies of several theories
advanced to account for it. Amongst others there are some remarks by
Humboldt, in which he says that the difference is not due to the quietness
of the night, for he had observed the same thing near the torrid zone, where
the day seemed quieter than the night, which was rendered noisy with
It is, however, by the experiments of Prof. Tyndall that this fact has
been fully brought to light; and from their definite character they afford
an opportunity of applying the explanation, and furnish a test of its
Neglecting the divergence of the bottom of the waves, a difference of
1 degree in the 100 feet would cause the rays of sound, otherwise horizontal,
to move on a circle, the radius of which by the previous rule is :
1100 . iq* or 110,000 feet.
A variation of one-half this would cause them to move on a circle of
220,000 feet radius. From the radii of these circles we can calculate the
range of the sound from different elevations.
With a clear sky, i.e. with a radius 110,000 feet, from an elevation of
235 feet the sound would be audible with full force to T36 mile; the direct
sound would then be lifted above the surface, and only the diverging sound
would be audible. From an elevation of 15 feet, however, the direct sound
might be heard to a distance of '36, or mile further, so that in all it could
be heard 1'72 (If) mile.
With a cloudy sky, i.e. with a radius 220,000 feet, the direct sound would
be heard to 2 '4 miles from an elevation of 15 feet, or T4 times what it is
with the clear sky. These results have been obtained by taking the extreme
variations of temperature at the surface of the earth. At certain times,
however, in the evening, or when it was raining, the variation would be
much less than this, in which case the direct sound would be heard to much
[So far I have only spoken of the direct or geometrical rays of sound,
that is, I have supposed the edge of the sound to be definite, and not
fringed with diverging rays; but, as has been already explained, the sound
would diverge downwards, and from this cause would be heard to a con-
siderable distance beyond the point at which the direct rays first left the
ground. From this point, however, the sound would become rapidly fainter
until it was lost. The extension which divergence would thus add to the
range of the sound would obviously depend on the refraction that is to say,
when the direct rays were last refracted upwards, the extension of the range
16] ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. 103
due to divergence would be greatest. It is difficult to say what the precise
effect of this divergence would be; but we may assume that it would be
similar to that which was found in the case of wind, only the refraction
being so much smaller the extension of the range by divergence would be
greater. On the whole the results calculated from the data furnished by
Mr Glaisher agree in a remarkable manner with those observed ; for if we
add ^ mile for the extension of the range by divergence, the calculated
distance with a clear sky would be two miles from a cliff 235 feet high.
Now Prof. Tyndall found that from the cliffs at the South Foreland,
235 feet high, the minimum range of sound was a little more than 2 miles,
and that this occurred on a quiet July day with hot sunshine. The ordinary
range seemed to be from 3 to 5 miles when the weather was dull, although
sometimes, particularly in the evening, the sounds were heard as far as
15 miles. This was, however, only under very exceptional circumstances.
Prof. Tyndall also found that the interposition of a cloud was followed by
an almost immediate extension of the range of the sound. I extract the
following passages from Prof. Tyndall's Report :
" On June 2 the maximum range, at first only 3 miles, afterwards ran up
to about 6 miles.
" Optically, June 3 was not at all a promising day ; the clouds were dark
and threatening, and the air filled with a faint haze ; nevertheless the horns
were fairly audible at 9 miles. An exceedingly heavy rain-shower ap-
proached us at a galloping speed. The sound was not sensibly impaired
during the continuance of the rain.
" July 3 was a lovely morning : the sky was of a stainless blue, the air
calm, and the sea smooth. I thought we should be able to hear a long way
off. We steamed beyond the pier and listened. The steam-clouds were
there, showing the whistles to be active ; the smoke-puffs were there, attest-
ing the activity of the guns. Nothing was heard. We went nearer; but
at two miles horns and whistles and guns were equally inaudible. This,
however, being near the limit of the sound-shadow,. I thought that might
have something to do with the effect, so we steamed right in front of the
station, and halted at 3| miles from it. Not a ripple nor a breath of air
disturbed the stillness on board, but we heard nothing. There were the
steam-puffs from the whistles, and we knew that between every two puffs
the horn-sounds were embraced, but we heard nothing. We signalled for
the guns ; there were the smoke-puffs apparently close at hand, but not the
slightest sound. It was mere dumb-show on the Foreland. We steamed in
to 3 miles, halted, and listened with all attention. Neither the horns nor
the whistles sent us the slightest hint of a sound. The guns were again
104 ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. [16
signalled for ; five of them were fired, some elevated, some fired point-blank
at us. Not one of them was heard. We steamed in to two miles, and had
the guns again fired : the howitzer and mortar with 3-lb. charges yielded
the faintest thud, and the 18-pounder was quite unheard.
"In the presence of these facts I stood amazed and confounded; for it
had been assumed and affirmed by distinguished men who had given special
attention to this subject, that a clear, calm atmosphere was the best vehicle
of sound : optical clearness and acoustic clearness were supposed to go hand
in hand * * *.
"As I stood upon the deck of the 'Irene" pondering this question, I
became conscious of the exceeding power of the sun beating against my
back and heating the objects near me. Beams of equal power were falling
on the sea, and must have produced copious evaporation. That the vapour
generated should so rise and mingle with the air as to form an absolutely
homogeneous mixture I considered in the highest degree improbable. It
would be sure, I thought, to streak and mottle the atmosphere with spaces,
in which the air would be in different degrees saturated, or it might be
displaced by the vapour. At the limiting surfaces of these spaces, though
invisible, we should have the conditions necessary to the production of
partial echoes, and the consequent waste of sound.
"Curiously enough, the conditions necessary for the testing of this
explanation immediately set in. At 3.15 P.M. a cloud threw itself athwart
the sun, and shaded the entire space between us and the South Foreland.
The production of vapour was checked by the interposition of this screen,
that already in the air being at the same time allowed to mix with it more
perfectly; hence the probability of improved transmission. To test this
inference the steamer was turned and urged back to our last position of
inaudibility. The sounds, as I expected, were distinctly though faintly
heard. This was at 3 miles distance. At 3f miles we had the guns fired,
both point-blank and elevated. The faintest thud was all that we heard;
but we did hear a thud, whereas we had previously heard nothing, either
here or three-quarters of a mile nearer. We steamed out to 4^ miles, when
the sounds were for a moment faintly heard, but they fell away as we waited ;
and though the greatest quietness reigned on board, and though the sea
was without a ripple, we could hear nothing. We could plainly see the
steam-puffs which announced the beginning and the end of a series of
trumpet-blasts, but the blasts themselves were quite inaudible.
" It was now 4 P.M., and my intention at first was to halt at this distance,
which was beyond the sound range, but not far beyond it, and see whether
the lowering of the sun would not restore the power of the atmosphere to
transmit the sound. But after waiting a little, the anchoring of a boat was
16] ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. 105
suggested; and though loth to lose the anticipated revival of the sounds
myself, I agreed to this arrangement. Two men were placed in the boat,
and requested to give all attention, so as to hear the sound if possible.
With perfect stillness around them, they heard nothing. They were then
instructed to hoist a signal if they should hear the sounds, and to keep it
hoisted as long as the sounds continued.
" At 4.45 we quitted them and steamed towards the South Sand Head
light-ship. Precisely fifteen minutes after we had separated from them the
flag was hoisted. The sound, as anticipated, had at length succeeded in
piercing the body of air between the boat and the shore.
" On returning to our anchored boat, we learned that when the flag was
hoisted the horn-sounds were heard, that they were succeeded after a little
time by the whistle-sounds, and that both increased in intensity as the
evening advanced. On our arrival of course we heard the sounds ourselves.
"The conjectured explanation of the stoppage of the sounds appeared
to be thus reduced to demonstration ; but we pushed the proof still further
by steaming further out. At 5f miles we halted and heard the sounds. At
6 miles we heard them distinctly, but so feebly that we thought we had
reached the limit of the sound range ; but while we waited the sound rose
in power. We steamed to the Varne buoy, which is 7f miles from the
signal-station, and heard the sounds there better than at 6 miles distance.
" Steaming on to the Varne light-ship, which is situated at the other end
of the Vame shoal, we hailed the master, and were informed by him that
up to 5 P.M. nothing had been heard. At that hour the sounds began to be
audible. He described one of them as ' very gross, resembling the bellowing
of a bull,' which very accurately characterizes the sound of the large American
steam-whistle. At the Varne light-ship, therefore, the sounds had been heard
towards the close of the day, though it is 12f miles from the signal station."
Here we see that the very conditions which actually diminished the range
of the sound were precisely those which would cause the greatest lifting of
the waves. And it may be noticed that these facts were observed and
recorded by Prof. Tyndall with his mind altogether unbiassed with any
thought of establishing this hypothesis. He was looking for an explanation
in quite another direction. Had it not been so he would probably have
ascended the mast, and thus found whether or not the sound was all the
time passing over his head. On the worst day an ascent of 30 feet should
have extended the range nearly J mile.
The height of the sound-producing instruments is apparently treated as
a subordinate question by Prof. Tyndall. At the commencement of his
lecture he stated that the instruments were mounted on the top and at
106 ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. [16
the bottom of the cliff; and he subsequently speaks of their being 235 feet