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to it. They show that the apparent absence of reciprocity was in reality caused by my
not having taken sufficient notice of small differences in the position of the ear and the
bell, and they suggest that the apparent want of reciprocity in the experiments made at
Villejuif and Montlhery was due in the same way to the small differences in the positions
of the guns and the ears of the auditors, as pointed out in the text.



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

elevation the temperature was 2 F. greater than at Villejuif; so that after
the experiments just described there is nothing surprising in the fact that the
wind did not produce much effect on the sound.

A good reason (as I have previously stated) may be given in explanation
of these changes in the effects of the wind. The wind tends to lift the sound
proceeding against it and to bring down that which is travelling with it.
These effects are greatest near the earth and diminish as we proceed upwards
(for the simple reason that the retardation of the wind is greater near
the surface). The effect of the wind, therefore, will be to intensify the
sound proceeding against it at sufficiently high elevations (this was found to
be the case in my first experiments) and to weaken the sounds proceeding
with it at points at some height above the surface that is, when the sound
which is brought down is destroyed by the roughness of the surface, though
over a calm sea, the sound brought down would roll along the surface as in a
whispering-gallery. Now when the temperature diminishes upwards, as it
does generally during a calm day, the effect of the refraction thus caused will
be to increase the effect of the wind on sound moving against it, and to
diminish that on the sound moving with it. But when the diminution of
temperature is downwards, as it was at Villejuif and Montlhery, and as it
always is near the earth on a clear dewy night, it will directly diminish the
effect on sound moving against the wind, and increase it on the sound moving
with the wind. That is to say, it will prevent the wind lifting the sound in
one direction and will aid it in bringing it down in the other. Thus it will
prolong the distance to which sound can be heard against the wind, and
diminish that at which it can be heard with the wind (when the surface is
rough) ; and when the downward diminution of temperature bears a certain
relation to the strength of the wind, it is easy to see that it may neutralize or
even reverse its effect.

These facts, all taken together, appear to me to afford a satisfactory
explanation of the phenomenon observed by Arago. There was, however,
one other phenomenon observed during the same experiments on which I
will venture a word in explanation.

The reports of the guns at Montlhe'ry as heard at that station were
attended with prolonged echoes, but it was not so with those at Villejuif.
This phenomenon was not explained by the experimenters ; but I think it
admits of a simple explanation. The ground surrounding Villejuif towards
Montlhery is very flat with not a tree upon it for miles, and being all arable
would at that time of the year be covered with crops. Around Montlhery
the country is hilly, some of the hills rising 100 feet above Montlhery itself;
their sides are in many places precipitous, and are largely covered with trees.
From the flat country around Villejuif there would arise no echoes, but
from the hills and trees around Montlhery it is quite certain that there



22] ON THE REFRACTION OF SOUND BY THE ATMOSPHERE. 167

must arise very considerable echoes; and hence it seems to me that the
phenomenon becomes simple enough.

The Report of the American Lighthouse Board.

I may remark, in conclusion, that I have just received a copy of the
Report of the American Lighthouse Board, kindly sent me by Dr Henry,
the Chairman of the Board. In an appendix to this Report Dr Henry has
given an account of his experiments on the transmission of sound, undertaken
for the Board, and extending over the last thirty years. These experiments
have led him to the conclusion that the differences in the distances at
which the same sound can be heard at different times are in all cases to be
explained by refraction. He has ascribed the cause of the refraction to the
wind ; and to explain cases in which the refraction did not accord with the
direction of the wind, he points out that it is not sufficient to know the
direction of the wind at the surface, but that in order to say what would
be its effect upon sound we should know in what direction it is blowing
above ; for it is not the simple motion of the wind which affects sound,
but the difference between its motion above and below. This is very true ;
and I have met with instances at night which have led me to apply the
same explanation. Many of the phenomena, however, to which Dr Henry
has applied this explanation are, I feel sure, to be attributed to the effect
of the upward variation of temperature. Dr Henry does not appear to
have been aware of this cause of refraction of sound while making his
experiments or drawing up his Report; but in a note at the end he
expresses his general agreement with the views stated in my previous paper.

The Heterogeneity of the Atmosphere.

With respect to the stoppage of the sound by the heterogeneity of the
atmosphere, Dr Henry expressly states that through all his long experience
he has never met with a single phenomenon which he can fairly ascribe
to this cause ; and so far as my experience goes it agrees with that of
Dr Henry. I am far, however, from thinking that there is no such effect;
on the contrary, under circumstances such as those which Humboldt describes
as having led him to the idea, it seems to me that it must exist, but that
it must at all times be confined to a very small distance above the earth's
surface and be over land. That it is the principal cause, or even an im-
portant cause of the phenomena under discussion, appears to be more than
doubtful; for not only does the necessary effect of refraction appear to be
a sufficient cause for these phenomena, and therefore to afford a complete
explanation of them, but it is very difficult to conceive the existence of a
state of heterogeneity in a calm clear atmosphere at a considerable elevation
above the level of the sea.



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

In the first place such a state of heterogeneity could hardly fail to be
observed; for it would necessarily impart a flickering and unsteady ap-
pearance to objects seen through it an effect which may be observed any
hot summer's day when looking at objects low down over dry land. Over
the sea, however, such an appearance has not been recorded ; and although I
have often looked for it, I have been entirely unable to detect it. And in the
second place, even supposing the air to be in a heterogeneous state at any
given instant, such a state could not be maintained many minutes; for
different gases, or different portions of the same gas at different temperatures,
mix and diffuse very rapidly. It is true that the heterogeneity might be
maintained by upward streams of heated air or vapour, and this is doubtless
the cause of the heterogeneity of air over dry hot ground ; but this hetero-
geneity, although very apparent near the ground, is never observed at any
considerable height. Upward streams of heated air must tend to mix and
diffuse rapidly, and the air as it rises is cooled by expansion until it must
soon cease to be lighter than the surrounding air. That, as a rule, there
are no streams of heated air ascending to any considerable height over land,
is definitely proved by the fact that the light smoke from burning weeds
never, or very seldom, attains an elevation of anything like 100 feet. I
have often been struck with the way in which such smoke will creep along
the ground for the distance of half a mile, and even then not extend to an
elevation of more than 20 or 50 feet. Over the sea the cause of such
streamlets must be much less potent than over land, and their existence
still more unlikely.



23.



ON THE FORCES CAUSED BY THE COMMUNICATION OF HEAT
BETWEEN A SUE-FACE AND A GAS; AND ON A NEW
PHOTOMETER.

[From the "Philosophical Transactions of the Royal Society," Vol. 166,

part 2.]

(Bead March 23, 1876.)

IN a paper read before the Royal Society*, April 1874, I pointed out that
the communication of heat from a solid surface to a gas, whether accompanied
by evaporation or not, must, according to the kinetic theory, be attended by
a reactionary force equivalent to an increase in the pressure of the gas on
the surface, and, conversely, when heat is communicated from the gas to the
surface the pressure against the surface is diminished ; and I also suggested
that these forces are the probable cause of the motion, resulting in some way
from radiation, which Mr Crookes had brought into such prominent notice.

Since the publication of this paper neither my conclusions as to the
existence of these " heat reactions," nor the reasoning by which I supported
them, have been controverted or even questioned ; but, on the other hand,
they have received important confirmation. The results at which Professors
Tait and Dewar arrived after a careful investigation fully bear out my con-
clusions, not only as to the existence of the forces, but also as to the way in
which they explain Mr Crookes's experiments.

Still it seemed desirable, if possible, to settle the question by obtaining
such quantitive measurements of the effects produced as would show whether
or not they agreed with what might be expected from theoretical considera-
tions. I have accordingly been on the look-out for some means of making
these experimental verifications. Such a means I at length found in one of

* Proc. Eoij. Soc. 1874, vol. xxii. p. 401 (Paper 11).



23] ON THE FORCES CAUSED BY THE COMMUNICATION OF HEAT, ETC. 171

the beautiful little instruments constructed by Dr Geissler, of Bonn, after
the manner of Mr Crookes, and called by him " Light-Mills." As this
instrument has taken an important part in the experiments I have to describe,
I shall commence by giving a detailed description of it.

The Light-Mill

This consists of a glass envelope in the shape of a pear, about 2^- inches
through its thickest part ; standing up from its lower end is a steel needle,
coincident with its axis. On the top of this needle is balanced (after the
manner of a compass-card) the mill or wheel ; this consists of a small central
glass cup which rests on the point of the needle, and to which are fused fo in-
very thin platinum arms, which have their outer ends attached to four
square plates (which appear to be talc or mica-schist) inch square, fastened
so as to stand vertically with a corner at the top. The distance of the
centres of these plates from the axis is about f of an inch.
The plates are very thin, and are covered on one of their
sides (which sides are all turned the same way) with lamp-
black.

Descending from the top of the vessel is a small tube,
the function of which is to keep the wheel from falling
from its pivot when the instrument is turned over. The
air within the mill has been greatly rarefied ; electricity
will not pass ; but more than this I cannot say.

The Action of the Light- Mill.

When placed in the light the mill quickly arrives at its
maximum speed, and rotates continuously with a velocity
depending on the intensity of the light. It will rotate steadily at speeds
varying from 1 revolution in 6 minutes (in the light of the full moon)
to 240 revolutions in a minute (in the strongest light I have been able to
obtain).

When the mill is revolving, and the light is suddenly extinguished, it
rapidly comes to rest.

These two facts, namely (1) that the mill rapidly arrives at its
maximum velocity when the light is turned on, and (2) that it as rapidly
comes to rest when the light is turned off, are those to which I wish first to
direct attention, for they appear to me to prove conclusively that the air within
the envelope does exercise influence on the mill.

(1) If it were true, as has been supposed, that the best results are
obtained in a vacuum so perfect that there is not sufficient air to exercise
any influence on the vanes of the mill, then it follows that the mill would




172 ON THE FORCES CAUSED BY THE COMMUNICATION OF [23

move without experiencing any resistance from the air, and the only known
resistance would be the friction of the pivot. Now whether or not this is
the case is easily ascertained. The resistance of the pivot, whatever may be
its magnitude, does not increase with the speed of the mill, and hence does
not oppose a greater resistance to its motion when it is turning fast than
when it is turning slowly. The friction of the air, on the other hand,
increases rapidly with the velocity. There is therefore a difference in the
manner in which these two resistances will affect the motion of the mill.
If the mill were only subject to the resistance of the pivot, any force which
would start it would continue to turn it with increasing velocity as long as
it acted; whereas, when subject to the resistance of the air, the resistance
increasing with the speed, the mill would soon arrive at such a speed that
the resistance balanced the turning force ; after which the motion would be
steady. This difference in the action of the friction of a pivot and that of
the air is well known in mechanics, and utilized, as, for instance, in the
striking part of a clock. If prevented by nothing but the friction of the
spindles when the clock is striking 12 say, each stroke would follow after a
less interval than the previous one. Now the invariable means by which
this is prevented is by a fan like the wheel in the light-mill, which, by the
resistance it experiences in moving through the air, prevents the clock striking
at more than a certain rate.

Now, from the description of Mr Crookes's instruments which he has
published, it appears that they, like the one which I possess, arrive at a
constant velocity depending on the intensity of the light. Hence it may be
fairly inferred that in them the motion of the wheel is restrained by the same
resistance as in mine ; and that this resistance, as I have just shown, is not
the resistance of the pivot.

(2) The limited velocity of these mills is therefore exactly what would
be caused by the friction of the air, just as in the clock : but there is another
conceivable cause of the limit ; and this is, that the force which causes the
motion diminishes with the velocity. Fortunately, however, there is another
test by which the resistance may be examined, a test altogether independent
of the action of light or heat. This is the rate at which the mill comes to
rest when the light is turned off. If the pivot were the only source of
resistance the time required for the mill to come to rest would be as the
speed; that is to say, if it required 15 seconds for the mill to come to rest
when making 10 revolutions per minute, it would require 150 seconds to come
to rest from 100 turns per minute. In fact, however, my mill, which requires
15 seconds to come to rest from 10 revolutions, does not take 30 to come to
rest from 100 revolutions. In these experiments the wheel was set in motion
by turning the envelope, and not by the aid of light or heat. We have,
therefore, conclusive evidence that the resistance is not merely that of the



23]



HEAT BETWEEN A SURFACE AND A GAS, ETC.



173



pivot (which, in fact, is so small as to be inappreciable) ; and the only
other resistance of which we know* is that of the air. But this is not all.

The behaviour of the mill furnishes us with the exact law of the resist-
ance ; and this is identical with the law of the resistance of air in a highly
rarefied condition, a law distinctly special in its character.

The resistance which bodies experience in moving through the atmosphere
at considerable velocities is proportional to the square of the velocity ; but if
the velocity is very small, less than one-tenth of a foot per second, then, as
Prof. Stokes has shown, the resistance is nearly proportional to the velocity.
Now, so far as this latter resistance goes, Prof. Maxwell has shown the
singular fact that, although it depends on the nature, it is independent of the
density of the air or gas. A body moving at a very small velocity would
therefore experience the same resistance whether moving outside or within
the receiver of an air-pump in which the air was highly rarefied, the only
difference being that the speed for which the resistance continues pro-
portional to the velocity is higher in proportion as the tension of the air
is reduced.

If, therefore, the vanes of the light-mill were moving in air as dense as
the atmosphere, they would experience a resistance increasing with this speed
according to a law varying from the velocity at low speed to the square of the
velocity at high speeds ; but since they move in an exceedingly rare medium,
the resistance which, it offers is more nearly proportional to the velocity
throughout, and only at the highest speeds can there be any appreciable
deviation from this law.

The limit which this resistance would impose on the speed would, at low
speeds, be very simple ; the velocity would be proportional to the force
causing it.

If the light from each of two candles would cause the mill to turn with a
certain velocity, then the two candles acting together should cause the mill to
turn with double velocity ; and this is exactly what happens, as the following
Table shows :



Distance from the candles


Number of revolutions per minute.


in feet.






1 candle.


2 candles.


2


1-2


3


1


&i


11


i


23


36


*


65


120



* Ethereal friction, if it exists at all, must be too small to produce any appreciable
effect, and it is not probable that it would follow the same law as air.



174 ON THE FORCES CAUSED BY THE COMMUNICATION OF [23

It will be seen that at very small velocities the effect of two candles is
rather more than double that of one ; this is owing to the friction of the pivot,
which is constant.

Also at the higher velocities there is a falling off in the speed, exactly as
might be expected from the air. Hence we see that the force, which limits
the speed of the mill, follows the same complicated law as that of the resist-
ance which would result from the friction of the air ; and hence there cannot
be a doubt but that they are the same.

The Force which turns the Mill is not directly referable to Radiation.

With reference to the assumption that the force is radiant or in any way
directly referable to radiation, I pointed out at Bristol, before Section A (Brit.
Assoc.), that in any such supposition the results of the experiments are
directly opposed to one of the fundamental laws of motion, viz. that action
and reaction are equal. In these experiments a hot body causes a cold body
to recede, while a cold body causes the hot body to approach ; so that if both
the bodies were free to move, we should have the cold body running away
and the hot body running after it. This fact is, I take it, a conclusive proof
that the force does not act from body to body, but between each body and the
medium in which it is placed ; that each body, as it were, propels itself
through the surrounding medium in a direction opposite to its hottest side.

The truth of this reasoning has been set beyond all doubt by a very
beautiful experiment made by Dr Schuster. The results of this he is about
to communicate to the Royal Society ; and as his paper will contain a full
account of the experiment, it is only necessary here for me to refer to the
results and the way in which they bear on the subject in hand. Dr Schuster
suspended my light-mill by a double fibre, so that if undisturbed by any
torsional force it would hang with the vessel always turned in one direction,
but in such delicate equilibrium that the smallest torsional force would cause
it to take a fresh position. In this way he was enabled to ascertain whether
the action of light on the vanes of the mill was attended with any effect to
turn the envelope,

Some such effect must have been caused whatever had been the nature
of the force, either in the commencement or in the maintenance of the
motion.

For, in the first place, if the force acting on the vanes arose from an
external source, then the vanes in turning, owing to the friction of the pivot
and the friction of the air, must tend to drag the envelope round with the
mill ; consequently, on the light being turned on, the envelope would have
turned in the same direction as the vanes, and continued to do so until the
torsion of its suspension had restrained its further motion: it would then



23] HEAT BETWEEN A SURFACE AND A GAS, ETC. 175

have remained steady until the light was turned off, when it would have
come back to its former position.

Whereas, on the other hand, if the force on the vanes arises entirely
within the vessel, if the air is, as it were, the fulcrum against which the force
acts, then, in order to overcome the inertia of the vanes and set them in
motion, the air must itself move in the opposite direction, just as when a
steamboat starts it sends a stream of water backwards. This motion of the
air will be communicated, by friction, to the vessel, and the effect will be that
on the light being turned on the envelope must turn in the opposite direction
to the vanes ; that when the mill has acquired its full speed then, as in the
case of a steamboat, the backward motion given to the fluid by the propellers
will just balance the forward motion imparted by the resistance of the ship,
and the resultant force will be nothing. When, therefore, the mill has
acquired its full speed, the envelope will come back to its normal position,
where it will remain until the light is turned off, when the friction
acting will tend to drag the internal fluid and hence the envelope forward.

This was the view of the case which I took when Dr Schuster first
suggested his experiment to me ; and when it came to be performed, the
results, as may be seen, were in strict accordance with the second supposition,
namely, that the force acts entirely between the vanes and the air within the
mill.

This experiment of Dr Schuster's also afforded a means of arriving
approximately at

The Magnitude of the Force.

The weight of the mill and the envelope, considered in conjunction with
its manner of suspension, gave the moment of the torsional force necessary
to turn it through an angle of '06 as '0000000264 lb., or one forty-millionth
part of a pound acting on a lever a foot long. To cause this deviation the
light had to be such as would cause the vanes to make 240 revolutions per
minute. Hence, when making 240 revolutions per minute, we have a
measure of the force which causes the motion and the resistance which
opposes it. Now considering that the centres of the vanes are f inch
from the axis, the whole force acting on the vanes will be 16 x '0000000264
of a pound, that is '00000042, or one two-million-five-hundred-thousandth
part of a pound ; this distributed over the vanes (whose joint area is 1 sq. inch)
is '00000042 lb., or one two-million-five-hundred-thousandth part of a pound
on the square inch. And assuming that the tension of gas within the mill
is '0005 lb., or one two-thousandth part of a pound on the square inch (the
tension of a toricellian vacuum at 60 F.), then we see that the difference of



176 ON THE FORCES CAUSED BY THE COMMUNICATION OF [23

pressure on the two sides of the vanes is '0008 of the pressure within the mill,
or less than one-thousandth part.

These results, although they do not pretend to be more than approximate,
show how exceedingly small is the real effect, and they place these phenomena
of motion caused by heat in a light from which the exceeding delicacy and
sensitiveness of the instruments have altogether withdrawn them.



The Difference of Temperature.

Having obtained these measurements of the force, it remained to see what
difference of temperature would be necessary, according to the kinetic theory,
that the reaction from the communication of heat might equal these forces,
and then to ascertain how far such a difference of temperature actually
existed. To do this I have had to enter upon new and somewhat doubtful
ground: however, I venture to submit the following, which, although it con-
tains assumptions, contains none but what are legitimate and strictly in



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