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dv 2 /3gp



74 ON SURFACE-FORCES CAUSED BY EVAPORATION, ETC. [11

and

dv (v + 8v) z - v 2 dv 2 8v

c ^ '

~~%" ~%~

dv



. f-'-'J

J v V 3gp



Therefore, in the case of steam at a temperature of 60,

f= '

J 2000 '

and in the case of air

e



1400'



It must be remembered that e depends on the rate at which cold particles
will come up to the hot surface, which is very slow when it depends only on
the diffusion of the particles of the gas inter se and the diffusion of the heat
amongst them.

It will be much increased by convection-currents ; but these will (as has
been already explained), to a certain extent, produce an opposite effect. It
would also seem that this action cannot have had much to do with Mr Crookes's
experiments, as one can hardly conceive that much heat could be communicated
to the gas or vapour in such a perfect vacuum as that he obtained, unless,
indeed, the rate of diffusion varies inversely as the density of a gas *. It will
be interesting, however, to see what light experiments will throw on the
question^.

* June 10. Professor Maxwell has shown that the diffusion both of heat and of the gas varies
inversely as the density ; therefore, excepting for convection-currents, the amount of heat com-
municated from a surface to a gas would be independent of the density of the gas, and hence the
force / would be independent of the density ; that is to say, this force would remain constant as
the vacuum improved, while the convection-currents and counteracting forces would gradually
diminish. It seems probable, therefore, that Mr Crookes's results are, at least in part, due to
this force.

t For continuation see papers 24 and 35.



12.



ON THE SURFACE-FORCES CAUSED BY THE COMMUNI-
CATION OF HEAT.

[From the "Philosophical Magazine " for November, 1874.]

IN a paper read before the Royal Society, June 18, I pointed out, as it
seemed to me, that whenever evaporation or condensation takes place on a
surface, they are attended with certain forces tending respectively to drive
the surface back and urge it forward, these forces arising, according to the
kinetic theory, from the momentum which is imparted from the surface
to the particles driven off, and vice versa. I also pointed out at the end
of the paper that similar effects will be produced whenever heat is com-
municated from a surface to a gas, and vice versa. The possibility of this
latter effect only occurred to me as I was on the point of sending off the
paper, and consequently was added by way of an appendix. The first part
of the paper contains a description of some experiments undertaken to
verify my conclusions respecting the forces of evaporation and condensation,
the results of which seem to me to be fully explained by these forces; so
that had I rewritten the paper after becoming aware of the possible existence
of the other force, I should have had nothing to add in connexion with these
experiments. I had, however, also endeavoured to show that the first class
of forces afforded an explanation of Mr Crookes's experiments; and had
this part of the paper been rewritten it would have been somewhat altered,
as the last class of forces (those arising from the simple communication
of heat) seem to afford a simpler explanation of some of the phenomena
observed by Mr Crookes. I regret that this was not done, as, from some
remarks in a paper published in the August Number of the Philosophical
Magazine, I fear that Mr Crookes has not understood my meaning, and has
coosequently been at the trouble of making further experiments, which,



76 ON THE SURFACE-FORCES CAUSED BY [12

however valuable from other considerations, throw no fresh light on the
case in point. However, before proceeding to discuss the subject further,
I would set myself straight with Mr Crook es in one or two particulars.

Mr Crookes appears to complain that I did not give him credit for
having obtained evidence of repulsion by heat in a medium as dense as
that which I used, viz. from to f inch of mercury. Now the only
account of his experiments which I had seen was the abstract published
in the ' Proceedings of the Royal Society,' December 1 ; and in this the
highest pressure at which he definitely states he obtained repulsion is 3
millimetres, or one-tenth of an inch : but this in truth was not the point.
In Art. 44 of his paper he describes an experiment in which he did not
obtain repulsion until the Sprengel pump had been at work for a long
time after the gauge showed half a millimetre. It was the results of this
experiment which I was endeavouring to explain, and consequently it was
to this experiment that my remarks applied ; and I had not the least
intention of implying that these were the only results which Mr Crookes
obtained. However, had it not been so, had I misread Mr Crook es's paper
as he supposed, I think that he would have forgiven me when he sees that
he has committed a similar offence against me. He commences his remarks
on my paper by saying, " In my exhausted receiver he assumes the presence
of aqueous vapour " ; whereas nowhere in my paper do I mention any such
assumption, nor did it enter into my head to make it. Nay, further, I think
I have shown, however darkly, that, under the conditions under which
Mr Crookes's experiments were made, aqueous vapour would not be sufficient
to explain the results, since it would be to all intents a non-condensable gas.
However, enough of this.

So far as I can see, the case now stands thus :

1. Whenever a body is surrounded by a condensable medium (that is,
vapour at its point of saturation), heating or cooling of the body will be
respectively attended with evaporation and condensation, and hence with
forces over the surface.

2. The amount of evaporation or condensation will not depend on the
density of the vapour with which the surface is surrounded, provided only
that it be at its point of saturation, but will depend on the amount of
heat available ; that is to say, it will depend on the amount of heat imparted
to or taken from the body. Thus the evaporation of mercury would take
place as readily, in a medium of too small density to be measured, as the
evaporation of water under the pressure of f of an inch.

3. The presence of a non-condensable gas will greatly retard the rate
of evaporation and condensation.



12] THE COMMUNICATION OF HEAT. 77

4. That under the conditions (1), there will be forces arising from
convection-currents in the surrounding medium, which will generally act
in opposition to the forces (1), but which will diminish with the density
of the medium, while the other forces remain constant and therefore must
ultimately prevail. ^,

5. That there is yet another set of forces, which act when the medium
is not in a state of saturation, i.e. is not condensable. These forces arise from
the communication of heat to or from the surface from or to the gas. These
forces will be directly proportional to the rate at which the heat is com-
municated; and since this rate has been shown by Professor Maxwell to
be independent of the density of the gas, these forces, like those arising
from condensation and evaporation, will be independent of the density of
the surrounding medium, and their effect will increase as the density and
convection-currents diminish.

These forces would appear, if their magnitude is sufficient, to afford an
explanation of all Mr Crookes's results if the medium is not in a state of
saturation; but when, as in my experiments, the medium is steam, and
water is present in the receiver, or, as I suppose in Mr Crookes's experiments,
mercury was present, and the medium was vapour of mercury, or at any rate
sulphuric acid, then it would be impossible for the medium to communicate
heat to the ball or surface without condensation ; and hence in such cases
it seems to me that the effects must be due to the forces of condensation.



13.



ON THE EFFECT OF IMMERSION ON SCREW PROPELLERS.

[From the " Transactions of the Institution of Naval Architects," 1874.]
(Read March 27th, 1874.)



IN a paper read before this Institution last year (see paper 9), I showed
that the phenomena of screw propulsion called "racing" is due to the
difference between the conditions under which a screw works when so far
buried below the surface that it does not break the surface, and when by
breaking the surface it is able to draw air down behind its blades. The
present communication contains the results of some experiments which
bear on the same subject, and which are of a somewhat different kind to
those previously described.

In these experiments my object was to determine how far the depth
of immersion affected the resistance which a screw encounters when not
travelling forward when the boat is stationary.

It has been stated by several writers and it seems to be a very
general impression that the resistance which the water offers to the
turning of a screw is greater at greater depths. This certainly is shown
to be the case by the experiments of Messrs Rennie and Maudslay.

Now, neither the friction nor action of liquids against a moving vane
is affected by pressure in ordinary circumstances, consequently, this increase
of resistance in the case of the screw requires explanation. This explanation
is to be found in the action of the air drawn in from the surface ; or, rather,
I should say, is due to the atmospheric pressure acting when the air is
excluded.



13]



ON THE EFFECT OF IMMERSION ON SCREW PROPELLERS.



79



When the screw is sufficiently near the surface to draw air down, then
it will only be working on a partial stream of water, and the quantity of
water which it will be able to draw within its range will depend, not upon
the velocity of the screw, but upon the velocity with which fresh water from
behind will replace that which the screw removes, and this will obviously
depend on the head of water above the cavity, or its depth below the
surface. When, however, the screw is once sufficiently below the surface
not to draw air, then, owing to the pressure of the atmosphere being added
to the head of water, the total will be greater than necessary, and it will
be acting on a full stream of water, and no further immersion will affect
its action; unless, indeed, it be drawn with sufficient velocity to cause
a vacuum behind its blades. Such cases, however, do not come within
the range of ordinary experience, for the exclusion of the air has the same
effect as an extra immersion of 30 feet.

This explanation is fully established by the following experiments,
which also confirm the results of my previous experiments on racing. For
in this case the action of racing was invariably attended with frothing, and
vice versa.

The screw used in these experiments was 2 inches in diameter ; and was
connected with a spring, which, in running down, made the screw turn two
hundred and forty times. The resistance which the screw encountered was
shown by the time taken in running down.

FIRST SERIES OF EXPERIMENTS, DURING WHICH THE SAME STRENGTH OF

SPRING WAS USED.



Number of
Experiment


Depth of
Immersion


Time taken
to run down


Remarks






Seconds




1


1


19


Did not race


2


2


19


11


3


3


20




4


2


20




5


1


20


n


6


|


20




7


|


20


Raced a little at starting


8


J


12


Raced


9


A


12




10


i


12


11


11





12


11


12





12




13


1


10


J}


14


- J


7






80



ON THE EFFECT OF IMMERSION ON SCREW PROPELLERS.



[13



SECOND SET OF EXPERIMENTS, DURING WHICH THE SAME SPRING WAS
USED, BUT WHICH WAS STRONGER THAN THAT USED IN THE PREVIOUS

CASE.



Number of
Experiment


Depth of
Immersion


Time taken
to run down


Remarks






Seconds




1


3


10


Did not race


2


1


10


5>


3


|


11


Raced at starting


4


I


11


M


5


7


9


Raced intermittently


6


To


9





7


!


6


Raced


8


-1


4


M


9





4


>5



From these experiments we must conclude, that so long as the screw is
not frothing (is working in solid water*), the resistance is independent of
the depth of immersion. Hence it follows that it is probable that in
Mr Rennie's and Mr Maudslay's experiments the screw was frothing all
the time. It must be remembered that, when the screw or boat is
stationary, there is a much greater chance of drawing down air than when
it is under way. While on one of Me Ivor's boats the Palmyra last
summer, I observed that whenever we made a start the screw frothed the
water, although at the time the tips of its blades did 'not come within 8 feet
of the surface-; and when we were under way in calm water there was no
froth whatever.

* The term " solid water" is used to express unbroken water, i.e., water without air, not, as
is sometimes assumed, undisturbed water. This latter condition is not apparent, for the water is
just as clear whatever may be its natural motion, so long as there are no bubbles of air.



14.



ON THE EXTENT AND ACTION OF THE HEATING SURFACE

OF STEAM BOILERS.

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

(Read October 6, 1874.)

THE rapidity with which heat will pass from one fluid to another, through
an intervening plate of metal, is a matter of such practical importance that
I need not apologise for introducing it here. Besides its practical value, it
also forms a subject of very great philosophical interest, being intimately
connected with, if it does not form part of, molecular philosophy.

In addition to the great amount of empirical and practical knowledge
which has been acquired from steam boilers, the transmission of heat has
been made the subject of direct inquiry by Newton, Dulong and Petit,
Peclet, Joule, and Rankine, and considerable efforts have been made to
reduce it to a system. But as yet the advance in this direction has not
been very great ; and the discrepancy in the results of the various experi-
ments is such, that one cannot avoid the conclusion that the circumstances
of the problem have not been all taken into account.

Newton appears to have assumed that the rate at which heat is trans-
mitted from a surface to a gas, and vice versa, is, ceteris paribus, directly
proportional to the difference in temperature between the surface and the
gas, whereas Dulong and Petit, followed by Pe'clet, came to the conclusion
from their experiments that it followed altogether a different law*.

These philosophers do not seem to have advanced any theoretical reasons

* Traite lie la Clialeur, P6clet, Vol. i., p. 365.
O. R. 6



82 ON THE EXTENT AND ACTION [14

for the law which they have taken, but have deduced it entirely from
their experiments, "a chercher par tatonnement la loi que suivent ces
resultats*."

In reducing these results, however, so many things had to be taken into
account, and so many assumptions have been made, that it can hardly be a
matter of surprise if they have been misled. And there is one assumption
which upon the face of it seems to be contrary to general experience, this
is, that the quantity of heat imparted by a given extent of surface to the
adjacent fluid is independent of the motion of that fluid or of the nature of
the surface f ; whereas the cooling effect of a wind compared with still air is
so evident that it must cast doubt upon the truth of any hypothesis which
does not take it into account.

In this paper I approach the problem in another manner from that in
which it has been approached before. Starting with the laws, recently
discovered, of the internal diffusion of fluids, I have endeavoured to deduce
from theoretical considerations the laws for the transmission of heat, and then
verify these laws by experiment. In the latter respect I can only offer a
few preliminary results ; which, however, seem to agree so well with general
experience, as to warrant a further investigation of the subject, to promote
which is my object in bringing it forward in the present incomplete form.

The heat carried off by air, or any fluid, from a surface, apart from the
effect of radiation, is proportional to the internal diffusion of the fluid at
and near the surface, i.e., is proportional to the rate at which particles or
molecules pass backwards and forwards from the surface to any given depth
within the fluid, thus, if AB be the surface and ab an ideal line in the fluid
parallel to AB then the heat carried off from the surface in a given time
will be proportional to the number of molecules which in that time pass
from ab to AB that is for a given difference of temperature between the
fluid and the surface.

This assumption is fundamental to what I have to say, and is based on
the molecular theory of fluids.

Now the rate of this diffusion has been shown from various considerations
to depend on two things :

1. The natural internal diffusion of the fluid when at rest.

2. The eddies caused by visible motion which mixes the fluid up and
continually brings fresh particles into contact with the surface.

The first of these causes is independent of the velocity of the fluid, and,
if it be a gas, is independent of its density, so that it may be said to depend
only on the nature of the fluid J.

* Traits de la Chaleur, Peclet, Vol. i., p. 363. t Ibid., p. 383.

J Maxwell's Theory of Heat, Chap. xix.



14] OF THE HEATING SURFACE OF STEAM BOILERS. 83

The second cause, the effect of eddies, arises entirely from the motion of
the fluid, and is proportional both to the density of the fluid, if gas, and
the velocity with which it flows past the surface.

The combined effect of these two causes may be expressed in a formula
as follows :

H = At + Bpvt ......................... ..... (I),

where t is the difference of temperature between the surface and the fluid,
p is the density of the fluid, v its velocity, A and B constants depending on
the nature of the fluid, and H the heat transmitted per unit area of the
surface in a unit of time.

If, therefore, a fluid were forced along a fixed length of pipe, which was
maintained at a uniform temperature greater or less than the initial tempera-
ture of the gas, we should expect the following results.

1. Starting with a velocity zero, the gas would then acquire the same
temperature as the tube. 2. As the velocity increased the temperature at
which the gas would emerge would gradually diminish, rapidly at first, but
in a decreasing ratio until it would become sensibly constant and inde-
pendent of the velocity. The velocity after which the temperature of the
emerging gas would be sensibly constant can only be found for each
particular gas by experiment ; but it would seem reasonable to suppose that
it would be the same as that at which the resistance offered by friction to
the motion of the fluid would be sensibly proportional to the square of the
velocity. It having been found both theoretically and by experiment that
this resistance is connected with the diffusion of the gas by a formula :

(II),



And various considerations lead to the supposition that A and B in (I)
are proportional to A' and B' in (II).

The value of v which this gives is very small, and hence it follows that
for considerable velocities the gas should emerge from the tube at a nearly
constant temperature whatever may be its velocity.

This, as I am about to point out, is in accordance with what has been
observed in tubular boilers, as well as in more definite experiments.

In the Locomotive the length of the boiler is limited by the length of
tube necessary to cool the air from the fire down to a certain temperature,
say 500. Now there does not seem to be any general rule in practice for
determining this length, the length varying from 16 ft. to as little as 6, but
whatever the proportions may be, each engine furnishes a means of comparing
the efficiency of the tubes for high and low velocities of the air through
them. It has been a matter of surprise how completely the steam-producing

62



84 ON THE EXTENT AND ACTION [14

power of a boiler appears to rise with the strength of blast or the work
required from it. And as the boilers are as economical when working with
a high blast as with a low, the air going up the chimmey cannot have a
much higher temperature in the one case than in the other. That it should
be somewhat higher is strictly in accordance with the theory as stated
above.

It must, however, be noticed that the foregoing conclusion is based on
the assumption that the surface of the tube is kept at the same constant
temperature, a condition which it is easy to see can hardly be fulfilled in
practice.

The method by which this is usually attempted is by surrounding the
tube on the outside with some fluid the temperature of which is kept
constant by some natural means, such as boiling or freezing, for instance the
tube is surrounded with boiling water. Now although it may be possible to
keep the water at a constant temperature, it does not at all follow that the
tube will be kept at the same temperature ; but on the other hand, since
heat has to pass from the water to the tube, there must be a difference of
temperature between them, and this difference will be proportional to the
quantity of heat which has to pass. And again, the heat will have to pass
through the material of the tube, and the rate at which it will do this will
depend on the difference of the temperature at its two surfaces. Hence if
air be forced through a tube surrounded with boiling water, the temperature
of the inner surface of the tube will not be constant, but will diminish with
the quantity of heat carried off by the air. It may be imagined that the
difference will not be great : a variety of experiments lead me to suppose
that it is much greater than is generally supposed. It is obvious that, if the
previous conclusions be correct, this difference would be diminished by
keeping the water in motion, and the more rapid the motion the less would
be the difference. Taking these things into consideration the following
experiments may, I think, be looked upon, if not as conclusive evidence of
the truth of the above reasoning, yet as bearing directly upon it.

One" end of a brass tube was connected with a reservoir of compressed
air, the tube itself was immersed in boiling water, and the other end was
connected with a small non-conducting chamber, formed of concentric
cylinders of paper with intervals between them, in which was inserted the
bulb of a thermometer. The air was then allowed to pass through the tube
and paper chamber, the pressure in the reservoir being maintained by
bellows, and measured by a mercury gauge; the thermometer then indicated
the temperature of the emerging air. One experiment gave the following
results: With the smallest possible pressure the thermometer rose to
96 F., and as the pressure increased fell until with ^ inch it was 87, with



14] OF THE HEATING SURFACE OF STEAM BOILERS. 85

inch it was 70, with 1 inch it was 64, with 2 inches 60, beyond this point
the bellows would not raise the pressure.

It appears, therefore, (1) that the temperature of the air never rose to
212, the temperature of the tube, even when moving slowest; but the
difference was clearly accounted for by the loss of heat in the chamber from
radiation, the small quantity of air passing through it not being sufficient
to maintain the full temperature, an effect which must obviously vanish as
the velocity of the air increased ; (2) as the velocity increased the tempera-
ture diminished, at first rapidly, and then in a more steady manner. The
first diminution might be expected, from the fact that the velocity was not
as yet equal to that at which the resistance of friction is sensibly equal to
the square of the velocity, as previously explained. The steady diminution,
which continued when the velocity was greater, was due to the cooling o'f the
tube. This was proved to be the case, for at any stage of the operation the
temperature of the emerging air could be slightly raised by increasing the
heat under the water, so as to make it boil faster, and produce greater agita-
tion in the water surrounding the tube. This experiment was repeated with
several tubes of different lengths and characters, some of copper and some
of brass, with practically the same results. I have not however as yet been
able to complete the investigation, and I hope to be able before long to bring
forward another communication before the Society.

I may state that should these conclusions be established, and the constant



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