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and I have proved the impossibility of their existence ; but if he goes, as he
appears unwittingly to have done, to a higher order of small quantities, then
I have nothing to say, except that he has no inconsiderable task before

Lastly, as regards the charge of having changed my views and having
adopted a theory which is practically the same as that which I had been
previously combating, I can only say that against no theory have I said a


word of which I do not maintain the truth. I have never asserted that the
variation of pressure in the direction of the flow of heat, which I have
consistently maintained to be necessary to the production of the phenomena
of impulsion, may not be attended by a difference of pressure in different
directions ; and, of course, I have known that such must be the case since the
time that I have seen and proved by experiment that this direct variation of
the pressure depends on the convergence of the lines of flow, which was
before the letter referred to appeared in Nature. But what I have consistently
maintained is, that a difference of pressure in different directions (i.e. parallel
and normal to the hot and cold surface) will not explain the experimental
results ; and this was the theory advanced in opposition to mine, and which
Mr Fitzgerald still seems inclined to defend.

I am asked to mention the result which is referred to in Art. 54. I can
only point to every phenomenon of the radiometer ; for there the gas between
the hot and cold surfaces always maintains a greater pressure on the hot than
on the cold plate a result which is fully explained in Art. 129, as the con-
sequence of the divergence of the lines of flow from the hot plate and their
convergence on to the cold plate, shown in fig. 13. If Mr Fitzgerald will only
study the phenomena, he will see that it is he who has misapprehended the
entire problem. He says a difference of pressure in different directions might
tend to cause the plates to recede from each other. Obviously it would ; but
then there is not the slightest evidence that the plates do so tend to recede,
while they actually move in the same direction, the cold plate following the
hot. Hence no force merely causing them to separate can explain the
phenomena. I have pointed this out over and over again, and now, so far
from having changed my views, I have to go over the same ground again. I
will take a simple case a light mill with two equal radial vanes in the same
plane, and on opposite sides of the pivot, one black and one white. Let the
light be placed exactly opposite the vanes, and let the vanes be at rest. Also
let the surface of the vessel and the gas be generally at the mean temperature
of the vanes. If, then, the force were only such as tends to separate the hot
and cold surfaces, there would be exactly the same force between the com-
paratively hot black vane and the colder glass as between the comparatively
hotter glass and the colder white vane ; for there are the same differences of
temperature ; and therefore the forces on the two vanes would tend to turn
the mill in opposite directions, and the mill would remain at rest, instead of
whirling round as it actually does. That the flow of heat caused the surfaces
to follow each other was proved from the first by the experiments ; and that
there is no force causing the surfaces to separate of the same order of
magnitude as the force which causes them to follow is now proved by the
kinetic theory.

I think that now Mr Fitzgerald will reconsider his protest against 53 ;


for while maintaining, on the one hand, a theory fundamentally different
from that in my paper, he can hardly maintain, on the other, that there are
no such theories, and that they have not found supporters. But, in truth,
the remark in Art. 53 was not applied to the theory which Mr Fitzgerald
seems to be supporting ; and as I am sure that he is not prepared to maintain
that the phenomena of the radiometer take place in an absolute vacuum, or
are due to the same cause as gravitation, I am sure that he will not wish to
stand sponsor to all the theories set forth since 1874.

In conclusion, I would say one word in acknowledgment of those remarks
in Mr Fitzgerald's paper that were the reverse of critical, and to confess that
it is a matter of no small satisfaction to have found a reader of Mr Fitzgerald's
knowledge and acumen.

March 24, 1881.



(In a Letter to Professor STOKES, Sec. R.S. Communicated by
Professor G. G. STOKES.)

[From the " Proceedings of the Royal Society," No. 203, 1880.]
(deceived October 25, 1879.)

OWENS COLLEGE, 23?-o? October, 1879.

I have just received a copy of a paper by Professor Maxwell from
the Philosophical Transactions of the Royal Society, read April 11, 1878,
"On the Stresses in Rarefied Gases." To this paper I find that there is
an appendix added in May, 1879, in the course of which he refers to my
investigation in the following words :

" This phenomenon, to which Professor Reynolds has given the name of

Thermal Transpiration, was discovered entirely by him It was not till after

I had read Professor Reynolds's paper that I began to reconsider the surface
conditions of a gas, so that what I have done is simply to extend to the
surface phenomena the method which I think most suitable for treating the
interior of the gas. I think that this method is, in some respects, better
than that adopted by Professor Reynolds, while I admit that his method is
sufficient to establish the existence of the phenomena, though not to afford
an estimate of their amount."

As the abstract of my paper does not contain a sufficient account of what
is in the paper to enable a reader to form a fair judgment of the relative
merits of the two methods, I venture to request those interested in the
subject to withhold their opinion until they have an opportunity of reading


my paper. In the meantime I can only express my opinion that Professor
Maxwell is mistaken in supposing that the results which are obtained from
his method are more definite than those to be obtained by mine.

His method only applies to a particular case, and the equation which he
has given is identical with that which I have given for this particular case.

The particular case treated by Professor Maxwell is the extreme limit
when the tube is large as compared with the distances between the molecules ;
he does not deal at all with the other limit when the distances between the
molecules are large as compared with the tube. Whereas I have given
definite values for the coefficients in both limits, as well as indicating the
manner in which the coefficients vary between these limits.

It so happens that the case in which the tube is large as compared with
the molecular distances is one in which the results are too small to be
experimentally appreciable, and hence Professor Maxwell's method does not
explain any of the actual experimental results.

In order to explain the experimental results obtained with porous plates,
Professor Maxwell has reverted to Graham's assumption that fine plates act
as apertures in thin plates, while the coarse plates act like a tube, an
assumption which my experiments show conclusively to be unnecessary and
erroneous, the only sensible action in either case being that of tubes, and
hence the phenomena of porous plates is that of transpiration and not

I remain,

Yours truly,

Professor STOKES, F.R.S.,

Secretary to the Royal Society.

Note by the Communicator.

In communicating the above letter to the Royal Society, in accordance
with Professor Reynolds's wishes, I would beg permission to add a few

Professor Maxwell did not profess to treat more than the two extreme
cases, constituting what Graham called respectively transpiration and
diffusion. His statistical method applies, indeed, only to the first of these
limits ; but he has distinctly considered the second, following a suggestion of
Sir William Thomson's. It is true that at the first limit, as Professor
Reynolds remarks, the results are too small to be experimentally appreciable ;


but this was distinctly stated by Professor Maxwell himself, at the foot of
p. 256.

As to the second limit, I must remark, in the first place, that I cannot
find that Graham made any assumption that porous plates act as apertures
in thin plates. The result that the time of passage varies, cceteris paribus, as
the square root of the density in the case of fine porous plates, was obtained
by pure experiment ; and though he could not fail to notice the accordance
of this result with that of the mere hydrodynamical passage through a small
aperture, he has carefully distinguished between the two. Nor can I agree
with Professor Reynolds in regarding the explanation given by Professors
Thomson and Maxwell of the phenomenon of thermal transpiration or thermal
effusion, whichever it be called, afforded by assimilating a fine porous plate
to a thin plate pierced by apertures of ideal fineness as erroneous, even
though it should be shown that such assimilation is unnecessary. Professor
Maxwell did not profess to treat in his paper the intermediate cases between
the two extreme limits.

Perhaps I should mention, that the foot-note at p. 281 in Professor
Maxwell's paper was added as the paper passed through the press. I recollect
noticing the thing as, in my capacity of Secretary, I looked over the paper
before sending it to be printed off, and considering whether I should affix a
date. As, however, it seemed to me to contain merely an explanation of an
expression in the text, and as Maxwell, who had carefully added the dates of
fresh matter in other parts, did not seem to have thought it necessary to do
so in this case, I left it as it was. In a letter I received from him at the
time, he informed me that he ^felt very ill, and was hardly fit even to go
through his own paper ; though a subsequent letter, in which he entered into
some scientific matters, was written in his usual cheerful style. No one had,
I believe, at that time any notion of the very serious nature of his illness.


March 13, 1880.



[From the " Proceedings of the Literary and Philosophical Society of
Manchester." Session 1880-81.]

Two years ago I exhibited before this Society a vertical tube, 60 inches
long and ^-inch in diameter, in which mercury sustained itself by its internal
cohesion and adhesion to the glass, to a height of 60 inches, without any aid
from the pressure of the atmosphere*. This tube was subsequently shown
at the Royal Society, and was submitted to intermittent observation at the
College until about nine months ago, when one day, on being erected, it
either collapsed or was broken by the fall of the mercury. The fracture
taking place simultaneously with the fall of the mercury, it was impossible to
say which.

This tube was of common German glass, such as is used for chemical
purposes, and as it proved insufficiently strong I deferred further experiments
until I could obtain a tube of greater strength. This led to considerable
delay, but I have now a tube 90 inches long, in which mercury suspends
itself in a water vacuum, resisting a tension or negative pressure of three
atmospheres. Although this is probably still far short of the possible limit,
a certain amount of interest attaches to the probability that the tension in
this tube is the highest to which any fluid matter in the universe has been

Since my former communication, in working both with the old tube, and
particularly with the new and longer tube, further experience has been gained
of which it is my present object to give some account.

During the year and nine months before the old tube broke no great
change had been noticed in the water and mercury within the tube ; the
former became rather cloudy and the latter showed symptoms of a scum.

* Proceedings Lit. and Phil. Soc. 18778, p. 155.


These changes were but little noticed, as they did not apparently interfere
with the suspension of the mercury.

The most noticeable circumstance was that as time went on the difficulty
of getting rid of the air and getting the tube into such a condition that its
contents would sustain themselves diminished. In the first instance it had
been only after a fortnight's attempts that suspension was obtained. The
first successful suspension was obtained in the following manner : a little of
the water was allowed to pass up by the side of the mercury when the tube
was in an inclined position, the tube was then brought gently down so that
the water reached the top or closed end of the tube as nearly as the air,
generally a small bubble, would admit ; then further inclined until the closed
end was so low that the air bubble and water would float up to the open end
and pass out, leaving the straight portion of the tube and part of the bend
full of mercury. The tube was then left in this position for 24 hours, when
on being erected the mercury sustained itself. It was then again reversed
and left for some days, when on being erected not only was the mercury
sustained for the 30 inches above the barometer, but it remained suspended
when the pressure of the air on the lower end was reduced by the air-pump
to one or two inches of mercury.

No other method ever proved successful with this tube. It was always
necessary to leave the tube reversed for a longer or shorter interval.

As to what went on in this interval I changed my opinion. At first I
thought it must be that time was necessary to bring the mercury or water
into more intimate contact with the tube, but subsequent observation con-
vinced me that the interval was necessary to allow the water with such air as
it contained to drain up between the mercury and the glass that in this way
the surface of the glass was freed from air. After arriving at this view I
observed the tube carefully to see if after it had remained some days in the
reversed position any trace of water was left. I could find none either while
the tube was full or after the mercury had fallen ; but owing to the fact that
there was always water on the open end I could make no such comparison
with the barometer as would show that the vacuum in the tube was absolutely
free from vapour tension.

Having obtained from Messrs Webb of Manchester tubes 12 feet long,
-inch external and ^-inch internal diameter, one of these tubes was closed
at one end and bent so as to leave the closed branch 7 feet 6 inches long.
The bend is a curve of about 2 inches radius, and the two branches or limbs
are not quite parallel ; they straddle so that at 3 feet 6 inches from the bend
they are 7 inches apart. At this point the shorter or open limb was again
bent back through an angle of 160 degrees, so that when the main tube is
vertical the mouth points downwards. The bending of so large and thick a


tube was a matter of some difficulty, but was successfully accomplished by
Mr Haywood and Mr Foster of Owens College. The tube was then firmly
fastened on to a board by Mr Foster, and the board pivoted on to a stand so
that the tube can be turned round in a vertical plane.

The tube being placed so that there was a slight downward incline all the
way from the open to the closed end, some water was introduced into the
open end. This having passed down to the closed end arid filled all the tube,
mercury was introduced, which ran down, forcing out the water. As soon as
the long limb and the bend were full of mercury, the tube was turned into an
upright position, the mercury sinking down and forcing out the water in the
shorter limb. Having reduced the water until it only occupied about 9 inches
above the mercury, the tube was again brought into a somewhat horizontal
position, but this time it was turned so that the mouth was downwards, the
incline being from the closed to the open end. Before reaching that position
the pressure of the air had caused the mercury to fill the longer limb, leaving
only water in the shorter limb ; as the inclination continued, the mercury
and water began to change places, and the water passed up round the bend
into the longer limb ; when 5 or 6 inches of water had passed in, the tube
was erected and turned over the other way, so that the closed end was
lowest, the water and the bubble of air running up and passing out. The
tube was then further inclined until nearly vertical, the closed end down, and
the tube was left in this position for 24 hours.

This, it will be noticed, was the process by which, after the first trial, had
proved almost invariably successful with the former tube, and the only
circumstances likely to cause any difference in the new and old tube were
the comparatively short time the water and mercury had been together, in
the new tube, and the greater length, 90 inches, as against 60 with the old
tube. As regarded this latter difference, it would not affect a partial erection
of the tube, so that if the time was not an element of importance, it was to
be expected that at all events the mercury would sustain itself until the
closed end had reached a position 60 inches above the bend.

On examining the tube, however, after it had been standing 24 hours, it
presented a very different appearance from that usually presented by the old
tube ; instead of a polished column of mercury it was frosted with water
between itself and the glass ; it was clear that the upward draining of the
water had been very imperfect, a great deal remaining adhering to the

On slowly erecting the tube the mercury showed no symptom of sus-
pension, leaving the closed end quietly as erection proceeded.

The whole process of passing the water up the tube was again repeated
with the same result for three days.


The frosted appearance, however, gradually diminished, and on the fourth
day a partial suspension was obtained. The mercury remained up until the
tube was nearly erect.

Having obtained so much, and as it appeared by the turbid state of the
water that the mercury was impure, the tube was emptied, washed out
several times, both with water and a solution of nitrate of mercury, and was
then refilled as before with water and carefully purified mercury. At first it
presented much the same frosted appearance as before, and there was no

With a view to expedite matters the board carrying the tube was taken
off its pivot and laid flat on a table nearly horizontal ; in this position it was
so adjusted that the water and mercury both extended all along the tube.
The tube was then connected by an indiarubber tube with an air-pump, and
the air pumped off until, and so long as, the water boiled in the tube.

The board was then turned over on its edge so that the water might
come in contact with that part of the tube which had been previously below
the mercury.

Having been turned back into its first position and adjusted so that the
closed end and long limb were slightly lower than the rest, the pump was
kept working, and the end of the board at which was the closed end of the
tube was gently hit with the hand. At first this caused the mercury to
chatter all along the tube, and wherever the mercury broke, a minute bubble
of air or steam showed itself; these passed slowly along to the open end,
until, after this had been continued for some time, the chattering ceased, and
the last bubble had passed out.

Keeping the closed end lowest, and without breaking the connection
with the pump, the board was replaced on the pivot and the tube erected.
The mercury remained suspended until the tube was nearly erect, and this
without any assistance from the air on the open end, so that the tension was
nearly 90 inches.

The same process of tapping was then repeated, and the tube replaced
and left with the closed end downwards and the air pumped off, for 24 hours.
There was then no frost, but a bright column of mercury, which on erection
remained suspended, the pump having been worked so as to remove the last
trace of air. The tube was not left standing, but was inverted and erected
for a few minutes each day for 8 days, including this morning. When the pump
was again worked, and the tube sealed by clips on the indiarubber before
bringing it to the Society's rooms which somewhat difficult undertaking
has been accomplished by Mr Foster, who has assisted me throughout in
these experiments. (On being erected in the Society's rooms the mercury


remained suspended for about 15 minutes ; it then gave way with an audible
click and sank to such a level as showed that there had not been air pressure
of Lth of an inch on the lower end.)

This experiment shows that the cohesion of water and mercury, and their
adhesion to each other and glass, will withstand a tension of 3 atmospheres
or 90 inches of mercury, being one atmosphere more than was shown by the
former tube.

But as I have been of opinion from the first that the limit of cohesion,
whatever may be that of adhesion, is a much greater quantity, my object in
making and recounting these experiments has not been so much to prove a
somewhat higher cohesion as to throw light upon the circumstances on which
the successful suspension depends.

The fact that the frost on the glass, the imperfect draining up of the
water, and the non-suspension of the mercury all occur together, and may all
be removed by time or by the complete removal of the air from the glass,
seems to show that even when glass is completely wet or covered with water,
there may be and generally is a considerable quantity of air still adhering to
the glass.

As regards the limit of the cohesive or adhesive strength of water and
mercury, I conceive this to be beyond any test that can be applied by gravity.
Several feet more might be attained, but the difficulties increase with the
length of the tube. It has, however, occurred to me that by centrifugal force
the limit may be reached in tubes a few inches long, and I am at present
preparing some experiments for this purpose, of which I hope soon to be able
to give some account.



[From the eighteenth volume of the " Proceedings of the Literary and
Philosophical Society of Manchester." Session 1878-79.]

IN the interval which elapsed between the bursting of the gun and the
report of the Committee much thought and some trouble has been expended
in divining the possible causes which might, under one set of circumstances
or another, have led to such a result. It now appears however that different
as have been the various suggestions, they all resembled each other in one
particular, namely, that they were all wrong.

It is to be hoped, however, that all the ingenuity that has been expended
will not have been thrown away and that some improvement may result
from the pointing out of such numerous defects. That in some respects, such
as the increasing twist and the sudden steps or shoulders on the outside of
the gun, the present system is defective is shown quite apart from the recent
accident ; and although it now appears that the moving forward of the shot
as the rammer was withdrawn had probably nothing to do with this accident,
it cannot be considered satisfactory that this moving forward should be so
much the rule as it is shown to have been in the experiments recently

Although at first sight it may appear that the fact of the gun having
been loaded with two charges of powder and two shot is amply sufficient to
explain the bursting, it may not be useless to examine somewhat closely into
what would result under such circumstances. The bursting of a 38-ton
wrought-iron gun is an experiment of which we should make the most, as we
cannot expect to have it often repeated.

From the first accounts of the accident it appeared as though the gun
had simply broken in two, like a carrot, at the first step, and that the front


half had gone into the sea. Such a failure would not have implied an excess
of pressure. It might have been caused by a great end strain, such as would

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