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B for different fluids be determined, we should then be able to determine,
as regards length and extent, the best proportion for the tubes and flues of
boilers.



15.



ON THE ACTION OF RAIN TO CALM THE SEA.

[From, the Fourteenth Volume of the " Proceedings of the Literary and
Philosophical Society of Manchester." Session 1874-5.]

(Head January 12, 1875.)



THERE appears to be a very general belief amongst sailors that rain tends
to calm the sea, or as I have often heard it expressed, that rain soon knocks
down the sea.

Without attaching very much weight to this general impression,^ my
object in this paper is to point out an effect of rain on falling into water
which I believe has not been hitherto noticed, and which would certainly
tend to destroy any wave motion there might be in the water.

When a drop of rain falls on to water the splash or rebound is visible
enough, as are also the waves which diverge from the point of contact ;
but the effect caused by the drop under the surface is not apparent, because
the water being all of the same colour there is nothing to show the inter-
change of place which may be going on. There is however a very con-
siderable effect produced. If instead of a drop of rain we let fall a drop
of coloured water, or better still if we colour the topmost layer of the water,
this effect becomes apparent. We then see that each drop sends down
one or more masses of coloured water in the form of vortex rings. These
rings descend, with a gradually diminishing velocity and with increasing
size, to a distance of several inches, generally as much as 18, below the
surface.

Each drop sends in general more than one ring, but the first ring is
much more definite and descends much quicker than those which follow it.



15]



ON THE ACTION OF RAIN TO CALM THE SEA.



87



If the surface of the water be not coloured, this first ring is hardly apparent,
for it appears to contain very little of the water of the drop which causes it.
The actual size of these rings depends on the size and speed of the drops.
They steadily increase as they descend, and before they stop they have
generally attained a diameter of from 1 to 2 inches, or even more. The
annexed cut shows the effect which may be produced in a glass vessel.




It is not that the drop merely forces itself down under the surface, but in
descending carries down with it a mass of water, which, when the ring is

1 inch in diameter, would be an oblate spheroid having a larger axis of

2 inches and a lesser of about 1 inches. For it is well known that the
vortex ring is merely the core of the mass of fluid which accompanies it,
the shape of which is much the same as that which would be formed by
winding string through and through a curtain ring until it was full.

It is probable that the momentum of these rings corresponds very nearly
with that of the drops before impact, so that when rain is falling on to water,
there is as much motion immediately beneath the surface as above it, only
the drops, so to speak, are much larger and their motion is slower.

Thus besides the splash and surface effect, which the drops produce,
they cause the water at the surface rapidly to change places with that at
some distance below.

Such a transposition of water from one place to another must tend to
destroy wave motion. This may be seen as follows. Imagine a layer of
water, adjacent to the surface and a few inches thick, to be flowing in any
direction over the lower water, which is to be supposed at rest. The effect
of a drop would be to knock some of the moving water into that which is



88 ON THE ACTION OF RAIN TO CALM THE SEA. [15

at rest, and a corresponding quantity of water would have to rise up into
the moving layer, so that the upper layer would lose its motion by com-
municating it to the water below. Now when the surface of water is
disturbed by waves, besides the vertical motion, the particles move back-
wards and forwards in a horizontal direction, and this motion diminishes
as we proceed downwards from the surface. Therefore in this case, the effect
of rain-drops will be the same as in the case considered above, namely, to
convey the motion, which belongs to the water at the surface, down into
the lower water, where it has no effect so far as the waves are concerned ;
hence the rain would diminish the motion at the surface, which is essential
to the continuance of the waves, and thus destroy the waves.



16.

ON THE REFRACTION OF SOUND BY THE ATMOSPHERE.

[From the " Proceedings of the Royal Society," No. 155, 1874.]

>

(Read April 23, 1874.)

MY object in this paper is to offer explanations of some of the more
common phenomena of the transmission of sound, and to describe the
results of experiments in support of these explanations. The first part of
the paper is devoted to the action of wind upon sound. In this part of the
subject I find that I have been preceded by Professor Stokes, who in
1857 gave precisely the same explanation as that which occurred to me.
1 have, however, succeeded in placing the truth of this explanation upon
an experimental basis ; and this, together with the fact that my work upon
this part of the subject is the cause and foundation of what I have to say
on the second part, must be my excuse for introducing it here. In the
second part of the subject I have dealt with the effect of the atmosphere
to refract sound upwards, an effect which is due to the variation of tem-
perature, and which I believe has not hitherto been noticed. I have been
able to show that this refraction explains the well-known difference which
exists in the distinctness of sounds by day and by night, as well as other
differences in the transmission of sound arising out of circumstances such
as temperature; and I have applied it in particular to explain the very
definite results obtained by Professor Tyndall in his experiments off the
South Foreland.

The Effect of Wind upon Sound

is a matter of common observation. Cases have been known in which,
against a high wind, guns could not be heard at a distance of 550 yards*,

* Proc. Roy. Soc., 1874, p. 62.



90 ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. [16

although on a quiet day the same guns might be heard from ten to twenty
miles. And it is not only with high winds that the effect upon sound is
apparent ; every sportsman knows how important it is to enter the field on
the lee side even when the wind is very light. In light winds, however,
the effect is not so certain as in high winds ; and (at any rate so far as our
ears are concerned) sounds from a small distance seem at times to be rather
intensified than diminished against very light winds. On all occasions the
effect of wind seems to be rather against distance than against distinctness.
Sounds heard to windward are for the most part heard with their full dis-
tinctness; and there is only a comparatively small margin between that
point at which the sound is perceptibly diminished and that at which it
ceases to be audible.

That sound should be blown back by a high wind does not at first sight
appear to be unreasonable. Sound is known to travel forward through or
on the air; and if the air is itself in motion, moving backwards, it will
carry the sound with it, and so retard its forward motion just as the
current of a river retards the motion of ships moving up the stream. A
little consideration, however, serves to show that the effect of wind on
sound cannot be explained in this way. The velocity of sound (1100 feet
per second) is so great compared with that of the highest wind (50 to 100
feet per second), that the mere retardation of the velocity, if that were all,
would not be apparent. The sound would proceed against the wind with a
slightly diminished velocity, at least 1000 feet per second, and with a but
very slightly diminished intensity.

Neither can the effect of wind be solely due to its effect on our hearing.
There can be no doubt that during a high wind our power of hearing is
damaged; but this is the same from whatever direction the sound may
come ; and hence from this cause the wind would diminish the distance at
which sounds could be heard, whether they moved with it or against it,
whereas this is most distinctly not the case. Sounds at right angles to the
wind are but little affected by it; and in moderate winds sounds can be
heard further with the wind than when there is none.

The same may be said against theories which would explain the effect of
wind as causing a heterogeneous nature in the air so that it might reflect
the sound. All such effects must apply with equal force with and against
the wind.

This question has baffled investigators for so long a time, because they
have looked for the cause in some direct effect of the motion of the air,
whereas it seems to be but incidentally due to this. The effect appears,
after all, not to be due simply to the wind, but to the difference in the
velocity with which the air travels at the surface of the ground and at a



16] ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. 91

height above it ; that is to say, if we could have a perfectly smooth surface
which would not retard the wind at all, then the wind would not obstruct
sound in the way it does, for it would all be moving with an equal velocity ;
but, owing to the roughness of the surface and the obstructions upon it,
there is a gradual diminution in the velocity of the wind as it approaches
the surface. The rate of this diminution will depend on the nature of the
surface ; for instance, in a meadow the velocity at 1 foot above the surface
is only half what it is at an elevation of 8 feet, and smaller still compared
with what it is at greater heights.

To understand the way in which this variation in the velocity affects the
sound, it is necessary to consider that the velocity of the waves of sound
does depend on the velocity of the wind, although not in a great degree.
To find the velocity of the sound with the wind we must add that of the
wind to the normal velocity of sound, and against the wind we must subtract
the velocity of the wind from the 1100 feet per second (or whatever may be
the normal velocity of the sound) to find the actual velocity. Now if the
wind is moving at 10 feet per second at the surface of a meadow, and at
20 feet per second at a height of 8 feet, the velocity of the sound against
the wind will be 1090 feet per second at the surface, and 1080 feet per
second at 8 feet above the surface ; so that in a second the same wave of
sound will have travelled 10 feet further at the surface than at a height of
8 feet. This difference of velocity would cause the wave to tip up and
proceed in an upward direction instead of horizontally. For if we imagine
the front of a wave of sound to be vertical to start with, it will, after
proceeding for one second against the wind, be inclined at an angle of more
than 45, or half a right angle ; and since sound-waves always move in a
direction perpendicular to the direction of the front (that is to say, if the
waves are vertical they will move horizontally, and not otherwise), after one
second the wave would be moving upwards at an angle of 45 or more. Of
course, in reality, it would not have to proceed for one second before it
began to move upwards: the least forward motion would be followed by
an inclination of the front backwards, and by an upward motion of the
wave. A similar effect would be produced in a direction opposite to that
of the wind, only as the top of the wave would then be moving faster
than the bottom, the waves would incline forwards and move downwards.
In this way the effect of the wind is to lift the waves which proceeded to
windward, and to bring those down which move with it.

Thus the effect of wind is not to destroy the sound, but to raise the ends
of the wave, which would otherwise move along the ground, to such a height
that they pass over our heads.

When the ends of the waves are raised from the ground they will tend



92 ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. [16

to diverge down to it, and throw off secondary waves, or, as I shall call them,
diverging waves, so as to reconstitute the gap that is thus made. These
secondary waves will be heard as a continuation of the sound, more or
less faint, after the primary waves are altogether above our heads. [This
phenomenon of divergence presents many difficulties, and has only as yet
been dealt with for particular cases. It may, however, be assumed, from
what is known respecting it, that in the case of sound being lifted up from
the ground by refraction, or, what is nearly the same thing, passing directly
over the crest of a hill so that the ground falls away from the rays of sound,
diverging waves would be thrown off very rapidly at first and for a con-
siderable distance, depending on the wave-length of the sound; but as
the sound proceeds further the diverging rays, would gradually become
fainter and more nearly parallel to the direct rays, until at a sufficient
distance they would practically cease to exist, or, at any rate, be no greater
than those which cause the diffraction-bands in a pencil of light*. The
divergence would introduce bands of diffraction or interference within the
direct or geometrical path of the sound, as in the case of light. These
effects would also be complicated by the reflection of the diverging waves
from the ground, which, crossing the others at a small angle, would also
cause bands of interference. The results of all these causes would be very
complicated, but their general effect would be to cause a rapid weakening
of the sound at the ground from the point at which it was first lifted ; and
as the sound became weaker it would be crossed by bands of still fainter
sound, after which, the diverging rays, as well as the direct rays, would be
lifted, and at the ground nothing would be heard. September 1874.]

If we leave out of consideration the divergence, then we may form some
idea as to the path which the bottom of the sound, or the rays of sound
(considered as the rays of light), would follow. If the variation in the speed
of the wind were uniform from the surface upwards, then the rays of sound
would at first move upwards, very nearly in circles. The radii of these

circles may be shown to be 1100 x , where v, and v* are the velocities

Vi~V 2

of the wind in feet per second at elevations differing by h feet. In fact,
however, the variation is greatest at the ground, and diminishes as we
proceed upwards, so that the actual path would be more nearly that of a
parabola.

Also, owing to this unequal variation in the velocity, those parts of the
waves immediately adjacent to the ground will rise more rapidly than the

* Taking sound of 1 foot wave-length, and comparing it with light whose wave-length is the
50,000th part of an inch, then the divergence of the sound at a mile from the point at which it
left the ground would be comparatively the same as that of the light at T V of an inch from the
aperture at which the pencil was formed.



16] ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. 93

part immediately above them ; hence there will be a crowding of the waves
at a few feet from the ground, and this will lead to an intensifying of the
sound at this point. Hence, notwithstanding the divergence, we might
expect the waves to windward to preserve their full intensity so long as they
were low enough to be heard. And this is in accordance with the fact, often
observed, that sounds at short distances are not diminished but rather
intensified when proceeding against the wind.

It will at once be perceived that by this action of the wind the distance
to which sounds can be heard to windward must depend on the elevation
of the observer and the sound-producing body. This does not appear to be a
fact of general observation. It is difficult to conceive how it can have been
overlooked, except that, in nine cases out of ten, sounds are not continuous,
and thus do not afford an opportunity of comparing their distinctness at
different places. It has often astonished me, however, when shooting, that
a wind which did riot appear to me to make the least difference to the
direction in which I could hear small sounds most distinctly, should yet be
sufficient to cover one's approach to partridges, and more particularly to rabbits,
even until one was within a few feet of them a fact which shows how much
more effectively the wind obstructs sound near the ground than even a few
feet above it.

Elevation, however, clearly offered a crucial test whether such an action
as that I have described was the cause of the effect of wind upon sound.
Having once entertained the idea, it was clearly possible to put it to the
test in this way. Also, if the principles hold in sound, something analogous
must hold in the case of waves on the surface of a running stream of water
for instance, waves made near the bank of a river.

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*. Of course, after such a discovery, it seemed almost unnecessary
for me to pursue the matter further ; but as there were one or two points
about which I was not then quite certain, and as Prof. Stokes's paper does
not appear to be so well known as it might be (I do not know of one writer on
sound who has adopted this explanation), it still seemed that it might
be well, if possible, to put the subject on an experimental basis. I therefore
made the experiments I am about to describe ; and I am glad that I did
not rest content without them, for they led me to what I believe to be the
discovery of refraction of sound by the atmosphere.

The results of my first observation are shown in Fig. 1. This represents
the shape of the waves as they proceeded outwards from a point near the

* Prit. Assoc. Report, 1857, Trans, of Sect. p. 22,



94



ON THE REFRACTION OF SOUND BY THE ATMOSPHERE.



[16



bank of a stream about 12 feet wide. Had the water been at rest there
would have been semicircular rings ; as it was, the front of the waves up the




Fig. i.

stream made an obtuse angle with the wall, which they gradually left. The
ends of the waves, it will be observed, gradually died out, showing the effect
of divergence. The waves proceeding down the stream were, on the other
hand, inclined to the wall, which they approached.

I was able to make a somewhat better observation in the Medlock, near
the Oxford Road Bridge, Manchester. A pipe sent a succession of drops
into the water at a few inches from the wall, which, falling from a consider-
able height, made very definite waves. Fig. 2 represents a sketch of these




Fig. 2.

waves, made on the spot : the diverging waves from the ends of the direct
waves, and also the bands of interference, are very clearly seen. Both these
figures agree with what has been explained as the effect of wind on sound.

In the next place I endeavoured to ascertain the effect which elevation
has on the distance to which sound can be heard against a wind. In
making these experiments I discovered some facts relating to the transmission
of sound over a rough surface, which, although somewhat obvious, appear
hitherto to have escaped attention.



16] ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. 95

My apparatus consisted of an electrical bell, mounted on a case containing
a battery. The bell was placed horizontally on the top of the case, so that
it could be heard equally well in all directions ; and when standing on the
ground the bell was 1 foot above the surface. I also used an anemometer.

These experiments were made on four different days, the 6th, 9th, 10th,
and llth of March. On the first of these the wind was very light, on the
others it was moderately strong, strongest on the second and fourth ; on all
four the direction was the same, viz. north. On the two last davs the
ground was covered with snow, which gave additional interest to the ex-
periments, inasmuch as it enabled me to compare the effect of different
surfaces. On the first two days I was alone, but on the last two I had
the assistance of Mr J. B. Millar, of Owens College, whose ears were rather
better than mine, although I am not aware of any deficiency in this respect.
The experiments were all made in the same place, a flat meadow of con-
siderable extent.

The General Results of the Experiments.

De La Roche*, in his experiment, found that the wind produced least
effect on the sound at right angles to its direction, i.e. sounds could be
heard furthest in this direction. His method of experimenting, however,
was not the same as mine. He compared the sounds from two equal bells,
and in all cases placed the bells at such distances that the sounds were
equally distinct. I, on the other hand, measured the extreme distance at
which the sounds could be heard, the test being whether or not the observer
noticed a break in the continuity of sound, a stoppage of the bell. The
difference in our method of experimenting accounts for the difference in
our results. I found in every case that the sound could be heard further
with the wind than at right angles to its direction ; and when the wind was
at all strong, the range with the wind was more than double that at right
angles. It does not follow, however, nor was the fact observed, that at com-
paratively short distances the sound with the wind was more intense than at
right angles.

The explanation of this fact, which was fully borne out by all the ex-
periments, is that the sound which comes in immediate contact with the
ground is continually destroyed by the rough surface, and the sound from
above is continually diverging down to replace that which has been
destroyed. These diverging waves are in their turn destroyed ; so that
there is a gradual weakening of the intensity of the waves near the ground,
and this weakening extends upwards as the waves proceed. Therefore,
under ordinary circumstances, when there is no wind the distant sounds

* Annales de Chimie, Vol. i. p. 177 (1816).



96 ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. [16

which pass above us are more intense than those which we hear. Of this
fact I have abundant evidence. On the 6th, when the wind was light, at
all distances greater than 20 yards from the bell the sound was much less
at the ground than a few feet above it; and I was able to recover the
sound after it had been lost in every direction by mounting on to a tree,
and even more definitely by raising the bell on to a post 4 feet high,
which had the effect of doubling the range of the sound in every direction
except with the wind, although even in this the range was materially
increased.

It is obvious that the rate at which the sound is destroyed by the
ground will depend on the roughness of its surface. Over grass we might
expect the sound at the ground to be annihilated, whereas over water it
would hardly be affected. This was shown to be the case by the difference
in the range at right angles to the wind over grass, and over the same
ground when completely covered with snow. In the latter case I could
hear the sound at 200 yards, whereas I could only hear it at 70 or 80 in the
former.

Now, owing to the fact that the sound is greater over our heads than
at the ground, any thing which slowly brings down the sound will increase
the range. Hence, assuming that the action of the wind is to bring down
the sound in the direction in which it is blowing, we see that it must
increase its range in this direction. And it must also be seen that in this
direction there will be less difference in the intensity of the sound from
the ground upwards than in other directions. This was observed to be
the case on all occasions. In the direction of the wind, when it was strong,
the sound could be heard as well with the head on the ground as when
raised, even when in a hollow with the bell hidden from view by the slope
of the ground ; and no advantage whatever was gained either by ascending
to an elevation or raising the bell. Thus, with the wind over the grass
the sound could be heard 140 yards, and over snow 360 yards, either with
the head lifted or on the ground; whereas at right angles to the wind on
all occasions the range was extended by raising either the observer or
the bell.

It has been necessary to notice these points ; for, as will be seen, they
bear directly on the question of the effect of elevation on the range of sound
against the wind.

Elevation was found to affect the range of sound against the wind in
a much more marked manner than at right angles.



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