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562


0017


24


3'4


80


100





...


756


159


596


0016


26


3'2



TABLE II.
= 457, / = 500.











Drops per








Pz


Drops


Drops




'o


*i


ft,


minute


Pi


Pz


Pa


Ps


Pa


Pa





27


66


567


100


190





190




53


42-4


2'5


24




572


84


185


4-5


180


022


45


36


5


20




582


59


175


9


166


055


35


27


10


13




582


21


175


19


156


12


14


11-2


27


10




582


10


175


48


127


39


76


6-0


37


10




579


10


177


66


111


66


9


7-2


50


9




572


8


184


90


94


10


8


6'4



ON THE CONDENSATION OF A MIXTURE OF AIR



[10



TABLE III.
= 748, t =ll, /=500.





|


j.


Drops per








P?


Drops


a


l i


*l


minute


Pi


Pa


Pa


Ps


Pa





6


741




1





7


o







47


663


106


85





85


o


125


3-2


66


557


106


191


6


185


032


60


5




))


56





9


182


050


30


10







21





18


173


104


11


15







17





27


164


163


10


20




)>


12





36


155


23


8


30




552


10


196


54


142


39


7


40




557


8


191


72


119


60


6*


50




562


7


186


90


96


93


7



12. Table I. shows the result of an experiment after the first method,
during which the flame and condensation remained constant, whilst the
pressure within the flask increased with the quantity of air.

Table II. shows the result of an experiment after the second method, in
which the pressure within the flask remained constant, whilst the flame and
condensation were reduced as the air was admitted. In this experiment
the rate at which the water passed through the condenser was constant from
first to last, and consequently the temperature of the effluent water varied
with the condensation.

Table III. shows the result of an experiment, also made according to
the second method, but in which the quantity of water flowing through the
condenser was so varied that the temperature of the effluent water remained
constant.

13. Each of these Tables shows the effect of air on the condensation in
a very definite manner ; but the results as given in the column p 3 in Table I.

cannot be compared with the - - in Tables II. and III. as they stand ;

P3

for these show the effect of the air in a series of increasing figures. If,
however, these figures show the power of the air to diminish condensation,
then they will be inversely proportional to the quantity of water con-
densed, i.e. what would have been condensed if the pressure and other

things had remained constant. Hence the numbers in the column

PB

should be proportional to the numbers in the column r ^ s in Tables

PB
II. and III.



10]



AND STEAM UPON COLD SURFACES.



65



In order to compare the results of these experiments, the results in each
Table have been multiplied by a common factor, so that they may be the
same when the pressure of air is one-tenth that of the steam. Thus the

numbers in the column in Table I. have been multiplied by 2000, and



numbers under



Drops .



in Table II. by 7. The results of the experiments thus



reduced are shown in the curves 1, 2, 3.

The point of no air might have been chosen as the point in which the
curves should coincide; but, as has been previously explained, the results
under such circumstances are to be taken as indicating the power of the
condenser to carry off the heat. Had it been possible to keep the condenser
cool, there is reason to believe that there would have been no limit to the
condensation of pure steam, and that the true form of the curves is like
that shown by the dots.



130 r

120

no I

100
90
80
70
60



20




10 20 30 40 50 60 70 80 90 100
Eatio of the pressure of air to that of steam.

Although the curves do not coincide, yet they are all of the same form,

and the difference between them is not greater than can be accounted for

by the disturbing causes already mentioned. They all show that the effect

of air begins to fall off rapidly when its pressure amounts to one- tenth that

o. R. 5



66 ON THE CONDENSATION OF A MIXTURE OF AIR, ETC. [10

of the steam, and that when it amounts to about one-fourth that of the steam
the admission of more air produces scarcely any effect.

14. Conclusions. The conclusions to be drawn from these experiments
are as follows :

1. That a small quantity of air in steam does very much retard its con-
densation upon a cold surface ; that, in fact, there is no limit to the rate
at which pure steam will condense but the power of the surface to carry off
the heat.

2. That the rate of condensation diminishes rapidly and nearly uniformly
as the pressure of air increases from two to ten per cent, that of the steam,
and then less and less rapidly until thirty per cent, is reached, after which
the rate of condensation remains nearly constant.

3. That in consequence of this effect of air the necessary size of a surface-
condenser for a steam-engine increases very rapidly with the quantity of air
allowed to be present within it.

4. That by mixing air with the steam before it is used, the condensation
at the surface of a cylinder may be greatly diminished, and consequently the
efficiency of the engine increased.

5. That the maximum effect, or nearly so, will be obtained when the
pressure of the air is one-tenth that of the steam, or when about two cubic
feet of air, at the pressure of the atmosphere and the temperature 60 F., are
mixed with each pound of steam.

15. Remarks. As this investigation was nearly completed my attention
was called to a statement by Sir W. Armstrong, to the effect that Mr Siemens
had suggested as an explanation of the otherwise anomalous advantage of
forcing air into the boiler of a steam-engine, that the air may prevent, in
a great measure, the condensation at the surface of the cylinder. It would
thus seem that Mr Siemens has already suggested the probability of the fact
which is proved in this investigation. I am not aware, however, that any
previous experiments have been made on the subject, and therefore I offer
these results as independent testimony of the correctness of Mr Siemens's
views as well as of my own.



11.



ON THE FORCES CAUSED BY EVAPORATION FROM, AND
CONDENSATION AT, A SURFACE.



[From the "Proceedings of the Royal Society," No. 153, 1874.]
(Read June 18th, 1874.)

IT has been noticed by several philosophers, and particularly by Mr Crookes,
that, under certain circumstances, hot bodies appear to repel and cold ones
to attract other bodies. It is my object in this paper to point out, and to
describe experiments to prove, that these effects are the results of evaporation
and condensation, and that they are valuable evidence of the truth of the
kinetic theory of gas, viz. that gas consists of separate molecules moving at
great velocities.

The experiments of which the explanation will be given were as follows :

A Ijght stem of glass, with pith-balls on its ends, was suspended by a silk
thread in a glass flask, so that the balls were nearly at the same level.
Some water was then put in the flask and boiled until all the air was driven
out of the flask, which was then corked and allowed to cool. When cold there
was a partial vacuum in it, the gauge showing from ^ to f of an inch pressure.

It was now found that when the flame of a lamp was brought near to the
flask, the pith-ball which was nearest the flame was driven away, and that
with a piece of ice the pith was attracted.

This experiment was repeated under a variety of circumstances, in
different flasks and with different balances, the stem being sometimes of glass
and sometimes of platinum ; the results, however, were the same in all cases,
except such variations as I am about to describe.

The pith-balls were more sensitive to the heat and cold when the flask
was cold and the tension within it low ; but the effect was perceptible until

52



68 ON SURFACE-FORCES CAUSED BY [11

the gauge showed about an inch, and even after that the ice would attract
the ball.

The reason why the repulsion from heat was not apparent at greater
tensions, was clearly due to the convection-currents which the heat generated
within the flask. When there was enough vapour, these currents carried
the pith with them ; they were, in fact, then sufficient to overcome the forces
which otherwise moved the pith. This was shown by the fact that when the
bar was not quite level, so that one ball was higher than the other, the
currents affected them in different degrees ; also that a different effect could
be produced by raising or lowering the position of the flame.

The condition of the pith also perceptibly affected the sensitiveness of
the balls. When a piece of ice was placed against the side of the glass, the
nearest of the pith-balls would be drawn towards the ice, and would eventually
stop opposite to it. If allowed to remain in this condition for some time, the
vapour would condense on the ball near the ice, while the other ball would
become dry (this would be seen to be the case, and was also shown, by the
tipping of the balance, that ball against the ice gradually getting lower). It
was then found, when the ice was removed, that the dry ball was insensitive
to the heat, or nearly so, while that ball which had been opposite to the ice
was more than ordinarily sensitive.

If the flask were dry and the tension of the vapour reduced with the
pump until the gauge showed f of an inch, then, although purely steam, the
vapour was not in a saturated condition, and the pith-balls which were dry
were no longer sensitive to the lamp, although they would still approach
the ice.

From these last two facts it appears as though a certain amount of
moisture on the balls was necessary to render them sensitive to the heat.

In order that these results might be obtained, it was necessary that the
vapour should be free from air. If a small quantity of air was present,
although not enough to appear in the gauge, the effects rapidly diminished,
particularly that of the ice, until the convection-currents had it all their own
way. This agrees with the fact that the presence of a small quantity of air
in steam greatly retards condensation and even evaporation.

With a dry flask and an air-vacuum, neither the lamp nor the ice produced
their effects ; the convection-currents reigned supreme even when the gauge
was as low as { inch. Under these circumstances the lamp generally attracted
the balls and the ice repelled them, i.e. the currents carried them towards the
lamp and from the ice ; but, by placing the lamp or ice very low, the reverse
effects could be obtained, which goes to prove that they were the effects of
the currents of air.



11] EVAPORATION AND CONDENSATION. 69

These experiments appear to show that evaporation from a surface is
attended with a force tending to drive the surface back, and condensation
with a force tending to draw the surface forward. These effects admit
of explanation, although not quite as simply as may at first sight appear.

It seems easy to conceive that when vapour is driven off from a body
there must be a certain reaction or recoil on the part of the body ; Hero's
engine acts on this principle. If a sheet of damp paper be held before
the fire, from that side which is opposite to the fire a stream of vapour
will be thrown off towards the fire with a perceptible velocity ; and therefore
we can readily conceive that there must be a corresponding reaction, and that
the paper will be forced back with a force equal to that which urges the
vapour forwards. And, in a similar way, whenever condensation goes on at a
surface it must diminish the pressure at the surface, and thus draw the
surface forwards.

It is not, however, wholly, or even chiefly, such visible motions as these
that afford an explanation of the phenomena just described. If the only
forces were those which result from the perceptible motion, they would
be insensible, except when the heat on the surface was sufficiently intense to
drive the vapour off with considerable velocity. This, indeed, might be the
case if vapour had no particles and were, what it appears to be, a homogeneous
elastic medium, and if, in changing from liquid into gas, the expansion took
place gradually, so that the only velocity acquired by the vapour was that
necessary to allow its replacing that which it forces before it and its giving
place to that which follows.

But, although it appears to have escaped notice so far, it follows, as a
direct consequence of the kinetic theory of gases, that, whenever evaporation
takes place from the surface of a solid body or a liquid, it must be attended
with a reactionary force equivalent fco an increase of pressure on the surface,
which force is quite independent of the perceptible motion of the vapour.
Also, condensation must be attended with a force equivalent to a diminution
of the gaseous pressure over the condensing surface, and likewise independent
of the visible motion of the vapour. This may be shown to be the case as
follows :

According to the kinetic theory, the molecules which constitute the
gas are in rapid motion, and the pressure which the gas exerts against
the bounding surfaces is due to the successive impulses of these molecules,
whose course directs them against the surface, from which they rebound with
unimpaired velocity. According to this theory, therefore, whenever a molecule
of liquid leaves the surface henceforth to become a molecule of gas, it must
leave it with a velocity equal to that with which the other particles of gas
rebound that is to say, instead of being just detached and quietly passing



70 ON SURFACE-FORCES CAUSED BY [11

off into the gas, it must be shot off with a velocity greater than that of a
cannon-ball. Whatever may be the nature of the forces which give it the
velocity, and which consume the latent heat in doing so, it is certain, from the
principle of conservation of momentum, that they must react on the surface
with a force equal to that exerted on the molecule, just as in a gun the
pressure of the powder on the breech is the same as on the shot.

The impulse on the surface from each molecule which is driven off
by evaporation must therefore be equal to that caused by the rebound
of one of the reflected molecules, supposing all the molecules to be of the
same size ; that is to say, since the force of rebound will be equal to that of
stopping, the impulse from a particle driven off by evaporation will be half the
impulse received from the stopping and reflection of a particle of the gas.
Thus the effect of evaporation will be to increase the number of impulses on
the surface ; and although each of the new impulses will only be half as
effective as the ordinary ones, they will add to the pressure.

In the same way, whenever a molecule of gas comes up to a surface and,
instead of rebounding, is caught and retained by the surface, and is thus
condensed into a molecule of liquid, the impulse which it will thus impart to
the surface will only be one-half as great as if it had rebounded. Hence
condensation will reduce the magnitude of some of the impulses, and therefore
will reduce the pressure on the condensing surface.

For instance, if there were two surfaces in the same vapour, one of which
was dry and the other evaporating, then the pressure would be greater on the
moist surface than on that which was dry. And, again, if one of the surfaces
was dry and the other condensing, then the pressure would be greater on the
dry surface than on that which was condensing. Hence, if the opposite sides
of a pith-ball in vapour were in such different conditions, the ball would be
forced towards the colder side.

These effects may be expressed more definitely as follows :
Let v be the velocity with which the molecules of the vapour move,
p the pressure on a unit of surface,
d the weight of a unit of volume of the vapour,
w the weight of liquid evaporated or condensed in a second ;

then the weight of vapour which actually strikes the unit of dry surface in a
second will be

_ dv

= '
and the pressure p will be given by

= 2^*
6(7

* See Maxwell, Theory of Heat, p. 294.



11] EVAPORATION AND CONDENSATION. 71

and f (the force arising from evaporation) will be given by

f wv

y ~7 ;

therefore




Thus we have an expression for the force in terms of the quantity of
water evaporated and the ratio of the pressure to the density of the vapour ;
and if the heat necessary to evaporate the liquid (the latent heat) is known,
we can find the force which would result from a given expenditure of heat.

Applying these results to steam, we find that, at a temperature of 60,
the evaporation of 1 Ib. of water from a surface would be sufficient to maintain
a force of 65 Ibs. for one second.

It is also important to notice that this force will be proportional to the
square root of the absolute temperature, and, consequently, will be approxi-
mately constant between temperatures of 32 and 212.

If we take mercury instead of water, we find that the force is only 6 Ibs.
instead of 65 Ibs. ; but the latent heat of mercury is only ^ that of water,
so that the same expenditure of heat would maintain nearly three times
as great a force.

It seems, therefore, that in this way we can give a satisfactory explanation
of the experiments previously described. When the radiated heat from the
lamp falls on the pith, its temperature will rise, and any moisture on it will
begin to evaporate and to drive the pith from the lamp. The evaporation
will be greatest on that ball which is nearest to the lamp ; therefore this ball
will be driven away until the force on the other becomes equal, after which
the balls will come to rest, unless momentum carries them further. On the
other hand, when a piece of ice is brought near, the temperature, of the pith
will be reduced, and it will condense the vapour aud be drawn towards
the ice.

It seems to me that the same explanation may be given of Mr Crookes's
experiments ; for, although my experiments were made on water and at
comparatively high pressures, they were in reality undertaken to verify
the explanation as I have given it. I used water in the hope of finding
(as I have found) that, in a condensable vapour, the results could be obtained
with a greater density of vapour (that is to say, with a much less perfect
vacuum), the effect being a consequence of the saturated condition of the
vapour rather than of the perfection of the vacuum.

Mr Crookes only obtained his results when his vacuum was nearly as
perfect as the Sprengel pump would make it. Up to this point he had



72 ON SURFACE-FORCES CAUSED BY [11

nothing but the inverse effects, viz. attraction with heat and repulsion with
cold. About the cause of these he seems to be doubtful; but I venture
to think that they may be entirely explained by the expansion of the
surrounding gas or vapour, and the consequent convection-currents. It
must be remembered that whenever the air about a ball is expanded, and
thus rendered lighter by heat, it will exercise less supporting or floating
power on the ball, which will therefore tend to sink. This tendency will be
in opposition to the lifting of the ascending current, and it will depend on the
shape and thickness of the ball whether it will rise or fall when in an ascend-
ing current of heated gas.

The reason why Mr Crookes did not obtain the same results with a
less perfect vacuum was because he had then too large a proportion of
air, or non-condensing gas, mixed with the vapour, which also was not in a
state of saturation. In his experiments the condensable vapour was that of
mercury, or something which required a still higher temperature, and it was
necessary that the vacuum should be very perfect for such vapour to be any-
thing like pure and in a saturated condition. As soon, however, as this state
of perfection was reached, then the effects were more apparent than in the
corresponding case of water. This agrees well with the explanation ; for, as
previously shown, the effect of mercury would, for the same quantity of heat,
be three times as great as that of water ; and, besides this, the perfect state
of the vacuum would allow the pith (or whatever the ball might be) to move
much more freely than when in the vapour of water at a considerable tension.

Of course this reasoning is not confined to mercury and water ; any gas
which is condensed or absorbed by the balls when cold in greater quantities
than when warm would give the same results ; and, as this property appears
to belong to all gases, it is only a question of bringing the vacuum to the
right degree of tension.

There was one fact connected with Mr Crookes's experiments which,
independently of the previous considerations, led me to the conclusion that
the result was due to the heating of the pith, and was not a direct result of
the radiated heat.

In one of the experiments exhibited at the Soire'e of the Royal Society,
a candle was placed close to a flask containing a bar of pith suspended from
the middle : at first, the only thing to notice was that the pith was oscillating
considerably under the action of the candle ; each end of the bar alternately
approached and receded, showing that the candle exercised an influence
similar to that which might have been exercised by the torsion of the thread
had this been stiff. After a few minutes' observation, however, it became
evident that the oscillations, instead of gradually diminishing, as one naturally
expected them to do, continued; and, more than this, they actually increased,



11] EVAPORATION AND CONDENSATION. 73

until one end of the bar passed the light, after which it seemed quieter for a
little, though the oscillations again increased until it again passed the light.
As a great many people and lights were moving about, it seemed possible that
this might be due to external disturbance, and so its full importance did not
strike me. Afterwards, however, I saw that it was only to be explained on
the ground of the force being connected with the temperature of the pith.
During part of its swing one end of the pith must be increasing in tem-
perature, and during the other part it must be cooling. And it is easily seen
that the ends will not be hottest when nearest the light, or coldest when
furthest away ; they will acquire heat for some time after they have begun
to recede, and lose it after they have begun to approach. There will, in
fact, be a certain lagging in the effect of the heat on the pith, like that which
is apparent in the action of the sun on a comet, which causes the comet to
be grandest after it has passed its perihelion. From this cause it is easy to
see that the mean temperature of the ends will be greater during the time
they are retiring than while approaching, and hence the driving force on that
end which is leaving will, on the whole, more than balance the retarding force
on that which is approaching ; and the result will be an acceleration, so that
the bar will swing further each time until it passes the candle, after which
the hot side of the bar will be opposite to the light, and will for a time tend
to counteract its effect, so that the bar will for a time be quieter. This fact
is independent evidence as to the nature of the force ; and although it does
not show it to be evaporation, it shows that it is a force depending on the
temperature of the pith, and that it is not a direct result of radiation from
the candle.

Since writing the above paper, it has occurred to me that, according to
the kinetic theory, a somewhat similar effect to that of evaporation must
result whenever heat is communicated from a hot surface to gas.

The particles which impinge on the surface will rebound with a greater
velocity than that with which they approached ; and consequently the effect
of the blow must be greater than it would have been had the surface been of
the same temperature as the gas.

And, in the same way, whenever heat is communicated from a gas to a
surface, the force on the surface will be less than it otherwise would be, for the
particles will rebound with a less velocity than that of which they approach.

Mathematically the result may be expressed as follows the symbols
having the same meaning as before, e representing the energy communicated
in the form of heat, and &v the alteration which the velocity of the molecule
undergoes on impact. As before,



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