Osborne Reynolds.

Papers on mechanical and physical subjects (Volume 1) online

. (page 27 of 40)
Online LibraryOsborne ReynoldsPapers on mechanical and physical subjects (Volume 1) → online text (page 27 of 40)
Font size
QR-code for this ebook

property of a certain quantity of gas which can be shown not to be possessed
by all the parts some property which is altered by a re-arrangement of the

Hitherto I believe that no such property has been recognised, or at all
events the conclusions to be drawn from such a property have not been
recognised. The phenomena of transpiration as well as those of the
radiometer depend on such properties, but these properties have not been
sufficiently understood to bring out the conclusion. This conclusion however
follows directly from the law indicated in Art. 4, viz. : that the results of
transpiration and impulsion depend on the relation between the size of the
internal objects and the density of the gas.

The force of this reasoning will be better seen after the results of the
experiments have been described, but it is introduced here to show the
importance which attaches to what otherwise might be considered secondary
properties of gases.

To these properties I must now return, not having yet indicated how
I was led to make the experiments, arid besides those already mentioned
there remains an important class of phenomena to be noticed.


The results deduced from theory.

7. Although the existence of the phenomena of thermal transpiration,
and the existence of the law of corresponding results at corresponding
densities have been verified by experiments, they were not so discovered.

They followed from what appeared to me to be a successful attempt to
complete the explanation I had previously given* of the forces which must
result when heat is communicated from a surface to a gas, and the phenomena
of the radiometer.

Having found, what I had not at first perceived, that according to the
kinetic theory the force resulting from the communication of heat to a gas
must depend on the surface from which it is communicated being of limited
extent, and must follow a law depending on some relation between the mean
path of a molecule and the size of the surface, it appeared that by using
vanes of comparatively small size the force should be perceived at com-
paratively greater pressures of gas (see Appendix, note 3).

On considering how this might be experimentally tested, it appeared that
to obtain any result at measurable pressures the vanes would have to be very
small indeed ; too small almost to admit of experiment. And it was while
thinking of some means to obviate this difficulty that I came to perceive that
if the vanes were fixed, then instead of the movement of the vanes we should
have the gas moving past the vanes a sort of inverse phenomenon and
then instead of having small vanes, small spaces might be allowed for the gas
to pass. Whence it was at once obvious that in porous plugs I should have
the means of verifying these conclusions. I followed up the idea, and by a
method which I devised of taking into account the forces, tangential and
normal, arising from a varying condition of molecular gas, I was able to
deduce what appears to me to be a complete theory of transpiration.

This theory appears to include all the results established by Graham, as
well as the known phenomena of the radiometer, which for the sake of
shortness I shall call the phenomena of impulsion. I was also able definitely
to deduce the results to be expected, both as regards thermal transpiration,
and the law of corresponding densities, both for transpiration and impulsion.

Having made these deductions, I then commenced the experiments on
transpiration, which so completely verified my theoretical deductions that I
have been able to produce the theory in its original form, with some additions,
but without any important modification.

Moreover, having succeeded (not without some trouble) in rendering

apparent the effect of differences of temperature in causing gas to move

through fine apertures, I recurred to the original problem, and by suspending

fibres of silk and spider lines to act as vanes, I have now succeeded in directly

* Proc. Roy. Soc., 1874, p. 402 (paper 11).


verifying the conclusion that the pressure of gas at which the force in the
radiometer becomes apparent varies inversely as the size of the vanes. With
the fibre of silk I obtained repulsion at pressures of half an atmosphere.

The arrangement of the paper.

8. My object is to describe the reasoning by which I was led to undertake
the experiments as well as the experiments themselves ; but as the theory will
be better understood after acquaintance with the facts, I have inverted the
natural order and given the experiments first. And in order that the reader
may not be at a disadvantage in reading the accounts of the experiments, I
include here a somewhat fuller account of the results to be expected as
deduced from the theory which is to follow.

The Laws established by the experiments.

9. Law I. When gas exists at equal pressures on either side of a porous
plate across which the temperature varies, the gas will transpire through the
plate from the colder to the hotter side, with velocities depending on the
absolute temperature and chemical nature of the gas, the relation between
the density of the gqis and the fineness of the pores, the thinness of the plug,
and the difference of temperature on the two sides of the plate.

Law II. In order to prevent transpiration through the plate, the pressure
on the hotter side must be greater than the pressure on the colder side.
This difference of pressure will depend on the chemical nature of the gas, the
mean pressure of the gas, the absolute temperature, the relation between the
size of the pores and the density of the gas, and the difference of temperature
on the two sides of the plate, but not on the thickness of the plate.

Law III. For the same plate and the same difference of temperature,
when the gas is sufficiently dense, the difference of pressure is approximately
proportional to the inverse density, but as rarefaction proceeds this law
gradually changes, the increase in the difference of pressure becomes less and
less until that difference reaches a maximum and begins to diminish, then on
further rarefaction this diminution increases until the difference of pressure
becomes approximately proportional to the density of the gas.

Law IV. After the rarefaction has reached that point at which the
difference in pressure is nearly proportional to the density, then the difference
in pressure will bear to the greatest pressure the ratio which the difference
in the square roots of the absolute temperature bears to the square root of
the greatest absolute temperature, or if A and B indicate the two sides of
the plate,


where P and r represent respectively the pressure and the absolute tem-
perature in the gas.

Respecting' the results depending on the relation between the density of
the gas and the fineness of the pores.

Law V. Both in the case of thermal transpiration and of transpiration
under pressure, similar results will respectively be obtained when the density
of the gas bears a fixed relation to the diameters of the apertures in the

Respecting the rate of transpiration arising from a difference of pressure
on the two sides of the plate.

Law VI. When gas exists at different pressures on the two sides of a
plate, and the difference of pressure bears a fixed ratio to the pressure on
either side ; then for a certain plate and a certain gas the time of transpiration
of equal volumes will, when the gas is sufficiently dense, be inversely pro-
portional to the density ; but as the rarefaction increases, the increase in the
time of transpiration becomes less and less, until the time becomes constant.

Law VII. When the rarefaction is so great that the time of transpira-
tion of equal volumes of the same gas is constant, the times of transpiration
of equal volumes of different gases will be proportional to the square root of
the atomic weights of the gases.

Respecting the results of impulsion, and the connection between these results
and the relation between the density of the gas and the size of the

Law VIII. When the gas is sufficiently dense, then the impulsive
force will be inversely proportional to the densities of the gas ; but as the
rarefaction proceeds the increase in the force becomes less and less until
the rarefaction has reached a point depending on the size of the vanes (the
larger the vanes the higher must be the rarefaction), after which the force
begins to diminish, and ultimately diminishes with the density.

These laws were reduced to the form in which they have been stated
in order to adapt them for experimental verification. Thus they do not
represent the simplest nor yet the fullest form in which the properties of
the gas can be expressed. This may be seen by reference to Sections X. and
XII. which treat of the theory of these properties. There definite expressions
will be found for the relations indefinitely indicated in Laws I. and II.
These definite expressions are not introduced here, because they have not
been definitely verified by experiment.


The definite relations expressed in Laws III., IV., V., VI., VII., and
VIII., although derived from theoretical considerations, have all been to a
greater or less extent verified by experiment as far as the possible range of
densities would admit and in all cases the experimental results within the
limits of error corresponded well with the theoretical deductions.


10. In commencing these experiments it was impossible to form any
estimate whatever of the magnitude of the results to be expected. The
laws just stated only showed what would be the comparative value of the
results under different circumstances ; so that until a result had been found
it was impossible to predict whether, with any particular plate, the result would
be appreciable or not.

Thus it happened that although the experiments commenced on Jan. 15,
1878, it was not until March that any definite results were obtained. This
delay was chiefly owing to several very subtle sources of disturbance, the
effect of which coi\ld only be distinguished from true results after a series of
tests extending in each case over several days.

The material first used for the plates was Wedgewood biscuit-ware, T 3 ^ths
inch thick ; and it was with this material after a long series of trials that
connected results were first obtained. These results were very minute. With
air at the pressure of the atmosphere, the greatest difference of pressure was
'1 of an inch (2'5 millims. of mercury).

Having, however, once obtained this result, it was seen to follow from
Law V., Art. 9, that greater results could be obtained with a finer plate. My
idea was to try graphite, such as that used by Graham ; but in the meantime it
occurred to me to try meerschaum, which proved to be a most convenient
material, as it could be obtained in any sizes and readily cut into plates of
any thickness.

With this material, first used on March 7, the later results were very
striking; the difference of pressure amounting to '25 of an inch with air
at the pressure of the atmosphere, and to nearly an inch with hydrogen at
the same pressure.

The description of the details of the earlier experiments, together with
the various difficulties which were met with and the means employed to
overcome them, would take too much room to admit of their being given at
length. I shall, therefore, proceed at once to the description of the apparatus
in its final form, and shall confine myself to noticing only such results as are
important to the subject.




Description of the apparatus.

11. This consisted principally of an instrument which may be called a

This instrument, as shown in Fig. 1, consists essentially of two chambers
separated by a plate of porous material, means being provided for keep-


Fig. 1.

ing the chambers at constant but different temperatures for many hours
at a time ; also for measuring the pressure of gas in the chambers, for ex-
hausting the chambers, and for bringing the chambers into direct communica-
tion when desired.




The chambers are formed by tin plates separated by rings of india-rubber,
between which is held the porous plate. The external diameter of the rings
is about 3| inches ; and the internal diameter, the diameter of the chambers,
is 1^ inches. The thickness of the rings, the depth of the chamber, is about
j^ths of an inch. The porous plates are 2 inches in diameter, so that the
edges are well covered by the rings of india-rubber which bound the
chambers; and outside the plate is fitted another ring of india-rubber of
the same thickness as the plate, so as to prevent any leak through the edges
of the plate.

Outside the tin plates which form the walls of the chamber, other chambers
are formed in the same manner by rings of india-rubber and tin plates.
These second chambers afford the means of regulating the temperature, steam
being continually passed through the one and cold water through the other.
The chambers are made air-tight by means of pressure, which is brought to
bear by means of a wooden press into which the rings and plates fit.

Figure 2 represents the plates and india-rubber rings somewhat

E. Is the porous plate with the ring of india-rubber outside it.

FF. The rings which form the two chambers for gas on each side of
the plate.


Fig. 2.

GG. The tin plates which close these chambers.

HH. The india-rubber rings which form the hot and cold chambers.

//. The tin plates which close these chambers.

KK. Tubes soldered to the tin plates GG to communicate with the
chambers FF, and

L M, LM. Are tubes soldered to the tin plates //, to allow of the
streams of steam or water through the chambers HH.




Figure 3 shows a section taken along
the axis of the rings and plates, showing
them in position, also the wooden press
by which they are held together.

Conduction of heat.

12. The circumstance which principally led to the selection of this form
of apparatus was the necessity of preventing, as far as possible, the conduction
of heat from the hot to the cold side, through the material bounding the
chambers. It will be seen that there is no metallic communication from the
hot to the cold side, and that all the heat which escapes across, besides what
passes through the porous plate, must pass through something like half an
inch of india-rubber, or through a considerably greater thickness of wood.

Communication with the chambers.

13. The communication with the gas chambers is effected by means of
the tubes KK, the outward ends of which are fitted with three and four
branches respectively.

By one of these branches the left chamber is connected with the open end
of a mercurial vacuum gauge V or barometer tube, which measures the
absolute pressure of this chamber.

Another branch from the left chamber, and a branch from the right, are
respectively connected with the two ends of a siphon tube S containing
mercury, which acts as a differential gauge for measuring the difference of
pressure in the two chambers.

By means of the third branch from the left, and a second from the right,
direct communication can be established between the chambers by turning a
tap D.

The third and fourth branches on the right are used to establish commu-
nication with a mercurial pump and to admit dry gas.

These various connections are shown in Fig. 1, page 265, which also shows
the general arrangement of the apparatus.


The connections between the metal and glass tubes are made with thick
india-rubber tubing, ^th inch bore and |th inch external diameter ; and the
two taps D and P shown in the sketch are both of glass.

The gauges.

14. The vacuum gauge is an ordinary barometer tube about 32 inches long
and 5 inch internal diameter, having its second limb sufficiently long to allow
of the mercury standing level when the chambers were exhausted.

The differential gauge is of glass tube about th inch internal diameter,
it is altogether 30 inches long, so as to prevent the mercury being driven out
of the tube by too great a difference of pressure.

Before the mercury was put into this tube it was wetted with sulphuric
acid. A small quantity of this remained and covered the mercury on either
side, by means of which sulphuric acid the free motion of the mercury was
secured, so that differences of pressure as small as Yo^?ro^ n ^ an ^ ncn ^
mercury caused it to move without the necessity of shaking.

Reading the gauges.

15. As far as the vacuum gauge was concerned, there was no point to be
gained by extreme accuracy in reading the absolute pressure of gas in both
chambers, so that a scale attached to the gauge was found to answer all

On the other hand the range of the experiments depended on the accuracy
with which the differential gauge could be read. A special means of reading
this gauge was devised. This consisted of a species of cathetometer almost
close to the gauge, in which, instead of a telescope, a microscope with an inch
object-glass and a semi-disc in the focus of the eye-piece was used, the screw
which moved the microscope had 50 threads to an inch, and the head had
200 divisions, so that one division corresponded to the -rdfin^ P ar ^ f an
inch. Owing to the high magnifying powers, the effect of a motion of one
division was visible, and several readings taken from the same position of the
mercury agreed to within one division.

Testing the apparatus.

16. The complicated character of the apparatus and the number of joints
rendered* it extremely difficult to make it perfectly tight. When working
at the pressure of the atmosphere this was of no great moment, but when
working with rarefied gas it was necessary that it should be so tight that the
leak might cause no appreciable disturbance.

At first india-rubber varnish was used to make the joints tight; but this
did not answer, as the vapour from the varnish produced very considerable


disturbance. After this the surfaces of the india-rubber were carefully
washed, and then considerable pressure applied by wrapping wire on the
tubes and screwing up the press. In this way, after a few days, the apparatus
became what may be called perfectly tight. There was a slight leak or pro-
bably slight diffusion through the india-rubber, for after the experiments were
concluded the apparatus was left full of hydrogen at the pressure of the
atmosphere, and the tap communicating with the pump closed. It was
then found that the pressure within the chambers steadily fell until it reached
9 inches of mercury. This point was reached after about one month. The
pressure then began to rise, and in another month the gauge showed 12 inches.
The entire volume of the chambers and tubes is only about 6 fluid ounces, so
that it might well be imagined that the hydrogen had been absorbed by, or
condensed on the india-rubber or the porous plate, but the fact that the
pressure again rose seemed to imply that the hydrogen had escaped ; but
whether through the india-rubber or not it is impossible to say.

Such a leak, however, was entirely without effect on the results. In fact,
a leak which admitted air at the rate of 1 inch of mercury in an hour into
one chamber did not cause any appreciable alteration in the differential

Drying the gas.

17. The presence of vapour in the gas was at first a source of great
trouble. The tendency of porous plates to absorb moisture is so great, and
the presence of vapour in the gas produces such a great disturbance even
when the pressure of vapour is a long way below that at which it would
condense on the cold surface, that for some time this threatened to prevent
any satisfactory result being obtained. At last, however, by having steam
on both sides, and repeatedly exhausting and refilling with air that had been
passed slowly through drying tubes, 40 inches long, containing first sulphuric
and then anhydrous phosphoric acid for which I am indebted to the kind-
ness of Dr Roscoe the effect of vapour was all but eliminated, and consistent
results were obtained over several trials, even when the sides of the steam and
water were reversed.

The differences of temperature.

18. The steam used for heating the apparatus was obtained by boiling
water in a glass flask which held about a gallon, enough to last for twelve
hours at a time. The glass was fitted with a water safety-valve ; so that the
pressure of steam could not exceed about 8 inches of water. The flask was
placed about 6 feet from the instrument, so that the heat from the gas flame
did not produce any material disturbance or materially affect the mercury in
the gauges.


The cold water was direct from the main, and was found to be very
constant in temperature, not varying throughout the experiments more than
23 from 47 F. in February to 70 F. in July.

In this way the tin plates (GG, Fig. 2) which bound the gas chambers
were respectively maintained at temperatures differing by less than 1F. from
the temperature of the steam (212) and that of the water.

The sides of the porous plate would not acquire the same temperatures as
the steam and water, because the conduction through the porous plates
would tend to equalise the temperature. Nor was there any means of
ascertaining the exact temperatures other than by comparing the results ob-
tained. But from these it appeared that there was considerable difference
between the temperature of the surfaces of the porous plate and that of the
opposite tin plate. A method of eliminating this difference has been found,
and this will be explained with the results themselves.

The porous plates.

19. These, whether of biscuit-ware, meerschaum, or stucco, were circular
discs 2 inches (53'0 millims.) in diameter. The rings FF which formed the
chamber had a diameter of 1^ inches (38 millims.), and these limited the
portion of the plate exposed to the passage of gas. The plates were of
different thicknesses, the thinnest being -j^th inch (1*5 millims.) and the
thickest '44 inch (14'2 millims.).

The results with air through porcelain plate No. 3 and meerschaum

Nos. 1 and 2.

20. After numerous experiments, commencing on January 23, with plates
Nos. 1, 2, and 3 of biscuit- ware, the results of which, although there appeared
to be a residual difference of pressure, were very much disturbed, the first
definite and consistent results were obtained with a porcelain plate, No. 3,
inch (2'5 millims.) thick, on February 22.

TABLE I. Thermal transpiration of air by biscuit-ware plate No. 3 ('1 inch or
2'5 millims. thick). Temperature of steam, 212" F. or 100 C. ; tempera-
ture of water, 47 F. or 8 C.

Mean pressure by vacuum

Difference of pressure by
siphon gauge, February 22

Ratio of mean pressure to
difference of pressure



inch millims.
1 2-54






This result was found to remain constant over a period of 8 hours, during
which the steam and water were kept constantly flowing. It was also found
to be the same whichever side of the diffusiometer was heated. During the
experiment the tap bringing the hot and cold chambers into direct commu-
nication was frequently opened, and the differential gauge then indicated
equal pressures. After each of these openings on the tap being again closed
the same difference was re-established in a few seconds.

The next experiments were made with a somewhat thinner plate of meer-
schaum No. 1.

TABLE II. Thermal transpiration of air by meerschaum plate No. 1 ('06 inch
or T5 millims.). Temperature of steam, 212 F. or 100 C. ; temperature
of water, 47 F. or 8 C.

Mean pressure by vacuum

Difference of pressure by
siphon gauge, March 12

Katio of mean pressure to
difference of pressure






As it seemed highly probable that the meerschaum plate was of finer
texture than the porcelain plate previously tried, the fact that the difference of
pressure with the meerschaum was not larger than with the porcelain was a

Online LibraryOsborne ReynoldsPapers on mechanical and physical subjects (Volume 1) → online text (page 27 of 40)