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although far from complete, throw some light on the subject, besides revealing
some remarkable facts. I hope to be able to continue the investigation ; but
since its nature is such as to render the chance of bringing it to anything
like a final conclusion very uncertain, it seems to me that it may be well to
publish an account of what has been already done ; and this is the object of
the present communication.

In order to render the object of the various experiments clear, it may be
well to recapitulate here some of the theoretical considerations previously
explained. It will be remembered that the idea that the variations of tem-
perature would cause refraction of sound occurred to me while making
experiments on the effect of wind upon sound, from which it was shown that
when sound proceeds in a direction contrary to that of the wind, it is not, as
had been thought, destroyed or stopped by the wind, but that it is lifted,



158 ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. [22

and that at sufficiently high elevations it can be heard to as great distances
as in other directions, or as when there is no wind thus confirming the
hypothesis first propounded by Professor Stokes and afterwards by myself,
that the effect is owing to the retardation of the velocity of the wind near
the earth, which allows the sound moving against the wind to move faster
below than above, and thus causes the fronts of the waves to incline upwards,
and consequently to move in that direction. Having clearly shown that this
was the case, it became apparent that anything which would cause an
upward diminution in the velocity at which sound proceeds would cause a
similar effect to that of the wind and lift the sound, and that since the
speed of the sound depends on the temperature of the air in which it is
moving, an upward diminution in the temperature must cause such an effect.
That such a diminution of temperature does very often exist was proved by
Mr Glaisher's balloon ascents in 1862, in which he found that when cloudy
the mean rate of diminution for the first 300 feet was 0'5 for each 100 feet,
and that when clear it was 1, and that on some occasions it was greater and
on others less than this. A variation of 1 in the temperature of the air
alters the velocity of sound nearly 1 foot per second, so that with a clear
sky the sound instead of moving horizontally would move upwards on a
circle of 110,000 feet radius, and with a cloudy sky on a scale of 220,000 feet
radius. This rate of refraction is very small compared with that caused
even by a very moderate wind ; and consequently in order to verify it by ex-
periment it is necessary to observe sounds at much greater distances. This
renders the experiment very difficult to carry out ; and to make it worse we
have no means of determining what the upward variation of temperature is,
which therefore can only be surmised by the behaviour of the sound.

The method of experimenting which first suggested itself was the same
as that which I had previously employed for wind namely, to obtain a
means of producing a sound of certain intensity, and proceeding to such a
distance that it could no longer be heard at the ground or on the level, and
then ascertaining whether the range was extended by attaining a greater
elevation or elevating the source of sound.

The difficulty in every item of the experiments was greatly enhanced by
the increased distance. For the wind an electric bell had answered very
well, the range on the level being always less than a quarter of a mile ; but
where the range was to be measured in miles, something in the nature of
an explosion was the only sound available. A place in which to make the
experiments was also difficult to find; for it involved a range of several
miles of level and unobstructed country, and thus the time occupied in
moving from place to place became a matter of serious inconvenience. The
greatest difficulty of all, however, was the effect of the wind ; since this was
much greater than anything to be expected from the temperature, it was



22] ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. 159

absolutely necessary that the air should be quite calm, a circumstance which
no precaution will insure, and for which, as I know from experience, one may
have to wait a long while. These various circumstances rendered the results
of the first series of experiments less conclusive than I had hoped they might
prove.

Experiments with rockets.

I obtained a quantity of rockets capable of rising to a height of 1000 feet
and exploding a charge of 12 ounces of powder. The first experiments with
these rockets were made at Debach, a village lying between Ipswich and
Framlingham, where the country is tolerably flat and traversed by roads in
all directions.

I. On the 14th of July, at about 3 P.M., three rockets and three cartridges
were fired from the same spot, observers being stationed at three-quarters of
a mile and a mile and a half respectively. There was no wind, but the sky
was covered with a thick haze, the day being very hot. All six discharges
were heard at the nearer station, but only the rockets the distance of a mile
and a half, although these were heard very distinctly, even their hiss as they
ascended.

II. On the 16th of July, at 3 P.M., the day being very hot with no wind,
a single rocket was sent up, an observer being stationed at four miles and a
half on the Woodbridge road. The explosion was very distinct, but the hiss
was not heard.

III. On the 18th a series of rockets were compared with the discharges
of a gun capable of firing \ Ib. of powder, and which made a much louder
report than the rockets. The observers drove along the Framlingham road,
the times of the discharges having been determined beforehand. This road
was chosen because at the commencement of the experiments the wind
was blowing almost at right angles to it. The wind was very light when
the start was made, but before the first gun was fired it had considerably
strengthened and changed in direction so as to blow against the sound. It
was to this cause I attribute the fact that the first two guns were not
heard at a distance of a mile and a half and two miles respectively. After
this the direction of the wind again changed, and the two next guns were
heard distinctly, although at greater distances; but, strange to say, the
rockets at the same distance were not heard. The wind remained constant
in this direction until the end of the experiments, and a rocket was heard
at four miles. Owing to the changes in the wind the results of these last
experiments have shown nothing as regards the refraction of sound, although
they show (what was, indeed, shown by the previous ones) that it is possible
on a very hot day when there is little or no wind to hear the discharge of a



160 ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. [22

small cartridge, such as that carried by the rockets, distinctly for a distance
of four or five miles, and this when the lower stratum of the atmosphere
was so heterogeneous that all distant objects near the ground appeared to
waver and twinkle as they do when seen over the top of a furnace.

In the hope of improving the conditions of the experiments, I accepted
the invitation of my friend Major Hare, of Docking, in West Norfolk, to
accompany him in his yacht the ' Feronia ' during a cruise on the east coast,
taking rockets with me. Here I spent three weeks without having a single
calm day.

Experiments in Lynn Deeps.

On the evening of the 18th of August, however, the weather improved ;
and being then in Lynn Deeps, I made some preliminary experiments so as
to get the men into the way of firing the rockets. The yacht was at anchor
in what is called the Upper Road, and at 9.50 P.M. I rowed with two men in
a direction slightly to leeward of the yacht. The wind was very light : at a
distance of two miles they fired a large pistol; the interval between the
flash and the report was eleven seconds (which gave us our distance); the
report was loud and accompanied with prolonged reverberation; a rocket
was also heard distinctly, but was not so loud as the pistol, and was not ac-
companied with any echoes or reverberation. The hails from the yacht were
heard by us in the boat quite distinctly, but our answers were not heard on
board the yacht. As there was a light mist it was not thought safe to go
further away from the yacht, so we returned and waited in hope of being
able to do something the next day. In this we were not disappointed ; for
on this day we observed what I have no doubt will be thought an extra-
ordinary phenomenon, although not of the kind anticipated.

The morning was perfectly calm, with only a few local breaths, which,
measured with the anemometer, never registered more than two miles an
hour, and came first from the east and then from the west, but not from the
north. Up to 12 o'clock the sky was completely covered with a white cloud,
which did not show the least sign of movement. The land from four to
eight miles distant was hazy; the thermometer stood at 65 in the cabin
with all the lights open. The Upper Road, in which the 'Feronia' was
anchored, is two miles below the ends of the stone banks which terminate
the Lynn Cut, and five miles from Lynn (see accompanying chart, page 169).
From this station sounds in Lynn were distinctly heard. Steamers could be
heard leaving the dock.

About 12 o'clock the sky cleared, and a slight breeze (four miles) sprang
up. We then weighed anchor and proceeded down the Bull-dog Channel.
Soon after the sky became perfectly clear, and the breeze died away until



22] ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. 161

the yacht had not steering-way. I then had a boat lowered (with the same
two men), and. proceeded to row to the Roaring Middle Buoy, while the
yacht still continued her course as well as she could down the Bull-dog
Channel ; she was going north by east in a curve, while we were going
north-west. Before leaving the yacht I arranged that on our showing two
flags they should send up a rocket, and when one they should fire a pistol,
and that whenever they heard us call they should answer. When about
half a mile distant I commenced calling, and the answers came back quite
distinct; when a little further some one on the yacht commenced tapping
the anchor, and we heard this quite distinctly until we were nearly two
miles off them; then the tapping was discontinued, and I commenced
calling again. Each time the answer came back quite distinct at the
instant it was expected, and afforded a good means of checking our distance,
which we also knew from the buoys. At two miles, although the calls were
quite distinct, I signalled for a pistol ; the report was loud. The sun was
very hot to us in the boat so hot, indeed, that it blistered the skin on my
hands and face.

The next time I called, the answer was doubtful ; but on my calling
again, it came quite distinct in thirty seconds. I then signalled for a pistol,
and heard a report which we took to be a pistol, but afterwards found to be
a rocket, we being too far off for them to distinguish our signals. I then
asked for a rocket, and had one, of which we heard the hiss as well as the
report. We now proceeded up to the Roaring Middle Buoy and signalled for
rockets and pistols, but could get neither, so we judged that they could not
see our signals. Although it seemed hopeless, I called from this point, and
to my surprise we all heard the answer faint but quite distinct after an
interval of thirty-five seconds. It was now about 3 P.M., so that we had
been rowing about two hours and a half. We waited at the buoy and kept
calling; but as there were now a number of fishing-boats which answered
our calls we could not be certain of an answer. At this time our calls
appear to have been heard on the yacht but not answered. When we heard
the last call, to be sure of it, the yacht was close by the Sunk Buoy ; she
was now approaching the Well light-ship, which is six miles from the Roaring
Middle Buoy. There was now a very light breeze again, so we set up our
sail to get steering-way on, and fell down with the tide. We presently
heard a rocket go up and explode, but we could make no impression with
our signals: we found on returning that they had completely lost sight of
us; nor was this surprising considering that we were in a small boat and
the sun was directly behind us. A breeze sprang up, so we returned to the
yacht, where on comparing notes we found that we had heard every call as
well as report. During the interval in which we had no answers, Major
Hare, who had been answering my calls, having completely lost sight of us,

o. R, 11



162 ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. [22

had gone below to get some lunch ; in the mean time the men on deck had
heard our calls, but not having instructions had not answered them.

To sum up the results of our excursion : We had called and been
answered up to three miles and a half, and our calls, as well as the re-
ports of the rockets, had been heard to more than five miles.

Incidentally, I noticed that we could occasionally hear the reports of guns
from the shore, which was more than eight miles distant; and once while
listening for an answer to one of my calls, I distinctly heard a dog bark, which
must have been on shore, as there was no boat between us and it except the
yacht. All the time we could distinctly hear the paddles of a steamer, which
at the time we were at the Roaring Middle was in the Wisbech Channel, or
nine miles from us and fifteen from the yacht, on which her paddles were also
distinctly heard.

It appears to me that the distances at which sounds of such comparative
low intensity were heard over the water this day is beyond anything definitely
on record. One hears casually, however, of remarkable instances : once in
this district I heard of a clergyman who from the Hunstanton side of the
Wash heard a man hammering a boat on the Wisbech side. When one
thinks, however, of the extreme difficulty of identifying a sound with its
source at three or four miles distance, it is no matter of surprise that such
phenomena should for the most part escape notice. On this day, had we not
been purposely on the look-out, I do not think anything we heard would have
attracted our attention. I have often heard the rifles of volunteers over
tolerably flat country seven miles ; and, as I have previously stated, the guns
of the naval review at Portsmouth were heard by many persons, including
myself, in Suffolk, over a distance of 170 miles*.

With regard to the cause of the exceptional distances over which we heard
the sounds on the 19th of August, 1874; as was only natural, my attention
was all the while directed to this. For the sake of my experiments, . what I
had been in hope of was a state of the atmosphere which would cause great
upward refraction of the sound, and I was naturally on the qui-vive for any
indications of such a state. All the morning I had been watching the distant
objects to see whether they were lifted or depressed by the refraction of light.
They loomed to a remarkable degree, which showed that the upward variation
of temperature was the reverse of what I wanted; and before leaving the
yacht I had my doubts of our finding much upward refraction of sound of
our being able to hear the rockets further than the guns. I was in hopes,
however, that as the sun came out matters might change, and while in the
boat I kept looking out for signs of depression in the distant objects. These,

* They were also heard by Sir William Thomson, who was on board his yacht about
10 or 15 miles to the west of Portland, and therefore 180 miles from Dover.



22] ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. 163

however, never came ; they loomed all the time, and very considerably. From
the boat we could see the water for five or six miles. The yacht's hull was
visible to us all the time. On one occasion we had two buoys and a ship in a
line, the nearest buoy being two miles from us ; we could see the water
between this and the second, and again between this and the ship.

It seems to me, therefore, that although in a manner the reverse of what
was expected, our observations this day prove the very great effect which
upward refraction has on the distances at which sounds can be heard. The
looming of the distant objects showed that the air was colder below than above.
This would tend to bring the sound down and intensify it at the surface of the
water in fact convert the sea into a whispering-gallery.

No other explanation appears to hold good. The conditions were exactly
those which have been described as favourable to acoustic opacity; the sea
was calm, there was no wind, and an August sun was shining with its full
power, and, having evaporated the clouds, must have been raising vapour from
the sea.

During the experiment I particularly noticed the echoes. Except the first
and only pistol, none of the reports were attended with echoes or reverbera-
tion. But in most cases, though not in all, after calling I could hear the ring
of my voice for ten or eleven seconds ; and on one or two occasions when there
were boats within half a mile of us, I could distinctly hear the echoes from
them. Without attempting to explain the reverberation and echoes which
have been observed, I will merely call attention to the fact that in no case
have I heard any attending the reports of the rockets, although they seem to
have been invariable with the guns and pistols. This fact suggests that these
echoes are in some way connected with the direction given to the sound.
They are caused by the voice, trumpets, and the siren, all of which give
direction to the sound ; but I am not aware that they have ever been observed
in the case of a sound which has no direction of greatest intensity.

Arago s Experiments.

These observations in Lynn Deeps were the last I made in 1874. In the
spring of this year my attention was called to a phenomenon recorded by
Arago, which was noticed during the celebrated experiments on the velocity
of sound made by Humboldt, Arago, Prony, Gay-Lussac, and others, on the
nights of the 21st and 22nd of June, 1822, between Villejuif and Montlhe'ry.
On both these nights the sounds from Montlhe'ry were heard more distinctly
at Villejuif than the sounds from Villejuif at Montlhery, although the wind
was blowing (very lightly) from Villejuif to Montlhery, the speed of the
wind being about one foot per second, or, roughly, three-quarters of a mile an
hour. This remarkable want of reciprocity was much commented on by the

112



164 ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. [22

observers, although they appear to have been entirely at a loss to account
for it.

On reading M. Arago's report*, I noticed that the observations on the
barometer showed Montlhery to be about 80 feet above Villejuif, and it
occurred to me that this difference of elevation might afford a clue to the
mystery. I had observed, in my observations of the effect of wind upon
sound, that a difference of a few feet in the height of the observer or in the
source of sound, especially when near the ground, often made all the
difference between hearing distinctly and not hearing at all. It appeared to
me probable, therefore, that there might be something advantageous in the
situations of the gun at Monti beVy, and the observers at Villejuif, over the
situations of the gun at Villejuif and the observers at Montlhery. I was
confirmed in this impression by a fact mentioned by Arago, viz. that on the
first night the gun at Villejuif had been pointed upwards at a considerable
angle, but that thinking this might have had something to do with its not
being heard so well as the other, on the second night it was brought down to
the horizontal. The result, however, was that the gun was not heard so well
on the second night as it had been on the first. This remark concerning the
gun at Villejuif seemed to imply that it was fired from level ground and at no
great elevation, whereas at Montlhery it seemed possible that the gun might
have been fired over a parapet. To settle this question I took an opportunity
last Easter of walking over the ground from Villejuif to Montlhery, and by the
aid of a map made a section of it.

The two stations are visible from each other ; that at Villejuif is on the
top of a gently rising hill, whereas that at Montlhery is on the top of a very
steep sugar-loaf hill, terminating in the mound of an old castle, which is
supported on the side facing Villejuif by a wall some 20 feet vertical, and
then so steep that Villejuif can be seen over the tops of the trees surrounding
the castle. Part of the old parapet wall is left, and it is impossible to believe
but that anyone firing a gun from that spot would place it with its muzzle
over the parapet. It seems very probable, therefore, that the gun at Montlhery
was fired over the parapet, which would be the most favourable position for
being heard, as the direct sound would be strengthened by that reflected from
the wall below it, while the observers, standing somewhat behind the parapet,
would not have the advantage of any reflected sound, and would therefore be
in a disadvantageous position as compared with the muzzle of the gun. At
Villejuif the case would be different ; the gun, as fired on level ground, would
be at a disadvantage compared with the observers, whose ears would be con-
siderably above it. That this difference was sufficient to affect the results

* Annales de Chimie, 1822, p. 211.



22] ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. 165

seems to have been proved by the evil effect of lowering the muzzle of the
gun*.

These differences in the conditions of the guns and the observers would
seem to afford good reason why the guns from Montlhery should have been
better heard than those at Villejuif, supposing other conditions for the trans-
mission of sound to be equally favourable both ways ; but the wind was
blowing from Villejuif to Montlhery, and that this should not have reversed
the effect is the most remarkable part of the phenomenon. This is remark-
able, however, only on the supposition that the effect of the wind upon sound
is invariable. As it seemed to me that there were several good reasons for
supposing that this is not the case, I thought it might be worth while trying
a few observations. I accordingly made some experiments with my electric
bell on some very calm nights in May and June, with the following
results :

When the sky was cloudy and there was no dew, the sound could in-
variably be heard much further with the wind than against it, even when
the wind was not more than one foot per second.

But when the sky was clear and there was a heavy dew, the sound could
be heard as far against a light wind as with it, and sometimes much further.
On one occasion, when the wind was very light (about 1 foot per second at
6 feet above the ground) and the thermometer showed 39 degrees at 1 foot
above the grass and 47 at 8 feet, the sound was heard at 440 yards against the
wind, and 270 yards with it.

Now the nights on which Arago made his experiments were clear ; there
was a heavy dew, and the thermometer at Montlhery showed that at that

* From my previous experiments on the effect of wind upon sound, I had been led to
the conclusion that under certain circumstances there may be an absence of reciprocity in
the passage of sound backwards and forwards between two points. Lord Eayleigh, however,
pointed out to me that there are strong reasons for believing that this is not the case.
To prove the force of these reasons, I made some observations behind a large wheat-stack
standing alone on level ground, experience having shown me that a wheat-stack from its
rough surface is a most effectual barrier to sound sound produced close to one side of the
stack being quite inaudible on the other side. On this occasion, however, I found the most
perfect reciprocity ; sounds produced close behind the stack could be heard at a distance
just as well, and no better, than similar sounds at a distance could be heard behind the
stack, provided always that great care was taken to bring the ear behind the stack into
exactly the same position as that previously occupied by the source of sound. It appears,
however, that a few inches difference in the position of the ear or the source of sound
was sufficient to make all the difference as to the audibility of the sound. These experi-
ments therefore, although they confirmed Lord Eayleigh and showed my previous idea to
have been wrong, suggested another explanation of the phenomenon which had led me



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