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definite capacity about 3 oz. on each side of the plate.

The vacuum gauge was cut off during these experiments, so that the
movement of the mercury in the siphon gauge constituted the only source of
variation in capacity, and this was small.

This constancy in the capacity of the several parts of the apparatus, if not
absolutely essential for these experiments, was very important, as it did away

192



292 ON CERTAIN DIMENSIONAL PROPERTIES OF MATTER [33

with the necessity of any process of reduction in comparing the results of the
experiments at different pressures. This may be seen as follows.

Equal volumes.

35. Starting with the pump full of mercury, and the taps open so that
the pressure, whatever it might be, is the same throughout the instrument,
both taps being then closed, one stroke of the pump draws a definite pro-
portion of the entire air in the instrument out of the right-hand flask,
lowering the pressure in this flask in a definite ratio. Or in other words,
one stroke of the pump withdraws from the flask on the right a definite
volume of gas as measured at the pressure in the instrument.

This condition would be maintained until the tap P, between the right-
hand flask and the instrument, was opened. Then the pressure on the right-
hand side of the porous plate would fall in a definite ratio. Transpiration
would commence, and by the time the pressure on the two sides of the plate
had again become equal, a definite volume of air, about half that withdrawn
by the pump, must have passed through the porous plate.

The time from the opening of the tap before complete equalisation is
effected, is then seen to be the time of transpiration of a definite volume of
gas measured at either the initial or the final pressures in the instrument,
under differences of pressure which, although varying, are at corresponding
stages proportional to the initial or final pressures in the instrument.

This time, which is called by Graham the time of transpiration of equal
volumes, is directly measured in these experiments.

/Measurement of the time.

36. The time at which transpiration commenced was the time at which
the tap was opened, the tap and the tubes being sufficiently large to allow
almost instantaneous adjustment of the pressures on the right of the porous
plate. On first opening the tap P, the mercury in the siphon gauge was
displaced, and as equalisation was re-established the mercury re-assumed its
level position, the instant of complete transpiration being that at which the
mercury became level.

The final adjustment of the mercury, however, was very slow, and it was
not found possible, even with the cathetometer, to ascertain definitely the
instant of complete equalisation. This threatened to be a difficulty, but it
was finally overcome in a very simple manner.

Instead of waiting for complete equalisation, the time was taken at which
the equalisation had proceeded, until the residual excess of pressure to the
left of the plate bore a certain relation to the initial absolute pressure '002
was the proportion allowed.

It will be seen that in this way the volume which passed, instead of being
the volume for complete equalisation, was some definite proportion of this,



33] IN THE GASEOUS STATE. 293

and that the differences of pressure under which it passed were proportional
to the initial difference of pressure, and hence the time occupied was the
time of transpiration of equal volumes according to the previous definition.

The manner of experimenting.

37. The temperature of the room in which the diffusiometer was, having
been read, the pump being full of mercury, and the taps D and P open so as
to allow of complete equalisation through all the chambers of the instrument,
the experiment commenced. The vacuum gauge was read ; this gave the
initial pressure in the instrument. The position of the mercury on the left
side of the differential gauge was then read with the cathetometer.

From this reading was subtracted '001 of the reading on the vacuum
gauge, i.e., the micrometer screw was turned through ten divisions for every
inch pressure in the instrument.

The vacuum gauge was then cut off by pinching the india-rubber tubing ;
the taps P and D closed; one stroke of the pump was taken; a definite
volume of air being thus drawn out of the flask, the pump was replaced so as
to be full of mercury. Then at a given second, marked by a chronometer, the
tap P was opened. A watch was then kept through the cathetometer, until
the mercury in the differential gauge descended to line in the cathetometer.
As the mercury was still in motion, this instant was well marked by merely
raising the eyes to the chronometer.

The small losses of time (personal equations) between reading the
chronometer and opening the tap, and reading the cathetometer and the
chronometer, were determined as approximately equal to one second, which
was accordingly subtracted from the time noticed.

In one set of experiments, that of hydrogen through stucco, the time of
equalisation was so small (between 20 and 30 seconds) that a fraction of a
second became a matter of some importance, and as the instant at which the
eye reached the chronometer did not always correspond with the complete
second or half second, there was a liability to this error; but this was to
some extent obviated by making successive experiments for such small
differences of pressure, that the differences in the reading were much less
than a second, and passing over all the observations except those which
corresponded with the beat of the chronometer.

With the stucco plates, both for air and hydrogen, three series of readings
were taken, and the agreement was found to be very close.

With the meerschaum, the interval of transpiration was so long, about
12 minutes for air and about 3 minutes for hydrogen, that one series of
experiments was considered to be sufficient.

It is important to notice here, that while making these experiments I
had not the least idea as to how the results would come out when they came



294



ON CERTAIN DIMENSIONAL PROPERTIES OF MATTER



[33



to be compared. This comparison was not made for several weeks, as the
logarithmic method of comparing them had not occurred to me at the time
the experiments were made.

The very remarkable agreement which has been found in the results
cannot, therefore, be owing to any bias in my mind, but must be entirely
attributed to the accuracy of the means of observation.

Purity of gases.

38. The greatest care was taken to get the gas pure and dry. And as it
had been found in the previous experiments that when the pressure in the
instrument was low, the gas, particularly the hydrogen, was liable to become
contaminated by infusion through the india-rubber, the experiments were not
continued to very low pressures and were made as rapidly as possible.

The results of the experiments.

39. Two plates were tried, meerschaum No. 3 and stucco No. 2, which
were both in their respective diffusiometers just as they had been used for
thermal transpiration. The results are given in the following tables :

TABLE XIV. Time of transpiration of equal volumes of air at different
pressures through stucco plate No. 2.



Initial
pressure


Time of
transpiration
in seconds,
July, 1878
[


Log of
pressure


Log of time


inches








30-10


54-5


1-478


1-7364


29-95


55


1-476


1-7404


26-25


58


1-418


1-7634


26-15


60


1-416


1-7781


22-95


62


1-36


1-7924


20-50


65


1-31


1-8129


19-90


66


1-30


1-8195


17-75


68


1-25


1-8325


15-40


72


1-19


1-8573


13-45


75


1-13


1-8750


11-60


79


1-06


1-8976


10-05


82


1-00


1-9138


8-75


85


94


1-9294


5-90


90


77


1-9542


5-35


93


73


1-9684


5-20


92


72


1-9638


4-75


95


68


1-9777


4-50


95


65


1-9777


3-90


97


59


1-9867


3-85


97


58


1-9867


3-40


98


53


1-9912


2-95


100


47


2-0000


2-50


101


40


2-0040


95


102


98-1


2-0128



33]



IN THE GASEOUS STATE.



295



TABLE XV. Time of transpiration of equal volumes of hydrogen at different
pressures through stucco plate No. 2.



Pressures
before
transpiration


Time of
transpiration
in seconds


Log of
pressure


Log of time


inches








30-10


19


1-48


1-2787


26-30


20


1-42


1-3010


18-6


21


1-27


1-3222


7-35


25


0-87


1-3979


5-50


26


0-74


1-4149


4-15


27


0-61


1-4313


3-75


28


0-57


1-4471


1-35


28-5


0-13


1-4540


1-20


28-5


0-08


1-4540



TABLE XVI. Time of transpiration of equal volumes of air at different
pressures through meerschaum plate No. 2.



Initial
pressure


Time of
transpiration
in seconds


Log of
pressure


Log of time


inches








30-


674


1-477


2-8286


15-10


716


1-179


2-8549


12-75


720


1-105


2-8573


11-25


724


1-051


2-8579


6-40


725


1-806


2-8600


6-00


725


1-792


2-8603



TABLE XVII. Time of transpiration of equal volumes of hydrogen at
different pressures through meerschaum plate No. 3.



Initial
pressure


Time of
transpiration
in seconds


Log of pressure


Log of time


inches








32-5


187


1-5118


2-27184


13-25


198


1-1222


2-29665


12-40


198


1-0934


2-29666


4-05


200


1-6074


2-30103


3-85


200


1-5854


2-30103



From these tables it appears that the transpiration times at pressures
nearly equal to that of the atmosphere are for air and hydrogen, through



296 ON CERTAIN DIMENSIONAL PROPERTIES OF MATTER [33

stucco, as 55 to 19, or 2'9 to 1, while through meerschaum they are as
3'6 to 1.

Graham found the ratio for stucco 2 '8 to 1, and for graphite 3'8 to 1.

The small difference between these numbers may be well explained by
supposing, as is quite probable, that the stucco used by Graham was rather
coarser than plate No. 2, also that the graphite was finer than the meer-
schaum ; but even allowing the difference, the present results are in very fair
accord with Graham's as far as the conditions of pressure corresponded.

When, however, we come to compare the times for air and hydrogen at
lower pressures, we see that not only does this ratio differ very greatly from
that obtained by Graham for stucco, but that it approaches what he obtained
with graphite. Thus at a pressure of 4 inches the ratio of the times are as
96 to 27, or 3*56 to 1, or they are the same as with the meerschaum at the
pressure of the atmosphere. For lower pressures we have indications of a
still higher ratio. Thus at 1 inch the ratio is 103 to 28'5, or 3'62 to 1.

In the same way we see that with the meerschaum, as the pressure falls,
we have an increase in the difference of the times for air and hydrogen.

This variation in the comparative times for air and hydrogen is strictly in
accordance with Law VI., Art. 9, as is also the manner of variation, as the
pressure falls, of the times for each particular gas. These variations indicate
that there are certain pressures for the stucco plate corresponding with
certain other pressures for t,ne meerschaum, at which the relation between
the times for hydrogen arvfl air are equal, and the variation of these times
with the pressure similar.

Logarithmic homologues.

40. To test this, the logarithms of the pressures and times are plotted,
and curves drawn, as explained in Art. 28. These are shown in fig. 11.

ab and cd are the curves for air and hydrogen through meerschaum, ef
and gh are the curves for air and hydrogen through stucco. The figure con-
sisting of the two curves ef and gh is found to fit on to the figure consisting
of ab and cd, the displacement being from ef and gh to e'f'g'h'. The scale of
the figure is too small to allow of the position of the points marking the
experiments being shown, but these are shown in figure 12, page 298.

The agreement is there seen to be very close the very considerable
portions of the curves which overlap coming into actual coincidence.

As previously explained with reference to the log. curves for thermal
transpiration, the displacement O'M in the direction of the abscissae repre-
sents the logarithm of the ratio of corresponding pressures, while the
displacement O'N in the ordinates represents the log. of the ratio of the



33]



IN THE GASEOUS STATE.



297



corresponding times for the two plates. This latter ratio cannot be made
use of for the sake of comparison, as it involves the number of openings
through the plate as well as their diameters.




N Inches of Mercury
Fig. 11.

The relative coarseness of the plates.

41. The ratio of the corresponding pressures, as given by the difference
in the abscissae, is of the greatest importance. This ratio, according to Law
V., Art. 9, corresponds with the ratio for the coarseness of the plates, and as
these were the same plates as were used in thermal transpiration, it was to
be expected that the results should agree ; that is to say, the displacement
O'M, fig. 11, should be equal to the displacement O'M, fig. 7. The actual
measures give

For thermal transpiration, O'M = '748 = log 5'6,

transpiration under pressure, O'M = "819 = log 6'5.

By this comparison the two independent and distinct experimental results
check one another.

The difference in the results, although too small to cast a doubt upon
their agreement, is too large to be attributed to experimental inaccuracy.
But it must be remembered that the conditions under which the plates are
compared differs in an important particular. In the experiments on thermal



298



ON CERTAIN DIMENSIONAL PROPERTIES OF MATTER



[33



transpiration the plates were heated, whereas in the experiments on transpi-
ration under pressure they were at the normal temperatures, and it appears



Air



CM CM >- -



Hydrogen




0.'5o'ed-76-8d-9 1 2 3 4 5678910 15 202530

PRESSURES WITH STUCCO



o Meerschaum
,x Stucco



Fig. 12.



only natural to suppose that such a difference of temperature would somewhat
alter the condition of the plate (see Appendix, note 3).

Small densities.

42. It appears very clearly from the curves, that as the pressure of the
gas diminishes, the time of transpiration of equal volumes tends to become
constant ; approximate constancy having been reached in the experiments.

The ultimate ratio of the times of different gases was found by Graham
to be as the square roots of the atomic weights of the gases, and the same
ratio is obtained for air and hydrogen in these experiments. The square
roots of the densities of dry air and hydrogen are 3'8 (379) to 1. The ratio
of the times for air and hydrogen at the smallest pressures tried is 3*624,
and as this is the result for both stucco and meerschaum the approximation



33] IN THE GASEOUS STATE. 299

is too close to be questioned, particularly when it is remembered that the
smallest trace of impurity in the gases might cause the difference.

Large densities.

43. As the density of the gas increases, the times of transpiration
diminish, at first slowly, and then more rapidly. According to Law VII.,
ultimately the time of transpiration becomes inversely proportional to the
density ; this rate was not reached in the present experiments, the nearest
approach being with air through stucco. The shape of the curves, however,
shows that the limit has not been reached.

In order, however, to show that the rate of variation of the times of
transpiration of equal volumes reaches but does not pass beyond the rate of
variation of the inverse density, we have Graham's experiments on capillary
tubes, this being the exact law which was found to hold with all the gases
and all the tubes. These tubes may be considered as corresponding with an
extremely coarse plate.

Grahams results reconciled.

44. It is thus seen how the apparently different laws obtained by
Graham for capillary tubes and plates of different coarseness, which led him
to suppose that the passage of the gas through the finer plates more nearly
resembled effusion than transpiration, are all reconciled and brought under
one general law, involving, besides the nature of the gas, nothing but the
ratio which the density of the gas bears to the fineness of the plate.

The verification of Law I.

45. The deduction of the comparative rates of thermal transpiration
which would have ensued if the tap D in the thermo-diffusiometer had been
open, is now only a matter of calculation. We have only to calculate by
Law VI. the comparative rates of transpiration that would have resulted
from the thermal differences of pressure. Hence it will be seen that Law I.
follows from Laws II. and VI., Art. 9, and as these have both been verified,
Law I. has also been verified.



SECTION IV. EXPERIMENTS WITH VERY SMALL VANES.

First experiments.

46. Before commencing the experiments on thermal transpiration
described in Section II., I made an attempt to ascertain how far were borne
out the theoretical conclusions that the necessity for extremely small
pressures in the radiometer was owing to the comparatively large size of the



300 ON CERTAIN DIMENSIONAL PROPERTIES OF MATTER [33

vanes, and that with smaller vanes similar results would be obtained at pro-
portionally higher pressures.

The pressure, at which the impulsive force in the radiometer first
becomes sensible, is so extremely small that it may be increased several
hundred fold without becoming what may be called sensible measurable
by a mercurial gauge. So that on the assumption that the pressure, at
which the effect would be apparent, increases proportionally as the size of
the vanes diminishes, it was clear that in order to obtain the repulsive
effect at the pressure of the atmosphere the size of the vanes must be
reduced several thousand times.

The only means of obtaining such small vanes was to suspend a fibre of
silk or a spider line. A single fibre of silk has a diameter of ^oo^h f an
inch (about), which is less than j^oth the breadth of the vanes of the light
mill on which my previous experiments had been made. But in order that
the pressures at which the results would be sensible might be inversely
proportional to the size of the vanes, the vanes should preserve the same
shape ; whereas the vanes in the light mill were square, while the fibre of
silk was only narrow in one direction, which would be considerably to the
disadvantage of the fibre of silk. More than this : it appeared probable that
the thinness and transparency of the fibre, together with the cooling action
of the air, would only allow an extremely small difference of temperature to
be maintained on its Apposite faces by radiant heat falling on one side ;
whereas air currents in the tubes, which would tend to carry the fibre with
them, would be caused by the greater temperature of the glass on that side
of the tube on which was the hot body, and these, which .would be quite
independent of the size of the fibre or vane, would exercise, proportionally,
as great an effect on the fibre as on the larger vanes.

For the foregoing reasons a result was hardly probable, but as a pre-
liminary step I suspended a fibre in a test tube 7 inch in diameter and
5 inches long ; I then brought a gas flame near to the tube to see if it would
cause any motion in the fibre, the pressure of the air within the tube being
that of the atmosphere.

The result was that the hair moved very slightly and somewhat uncer-
tainly towards the flame.

As I had more than suspected that such would be the result at the
pressure of the atmosphere, and as I had no means at hand for exhausting
the tube, I postponed further experiments in this direction in order to take
up the more promising investigation with the porous plates. When, however,
I had concluded this, and succeeded almost beyond my expectation, I returned
to the experiments on the fibre with the intention of exhausting the tube
and using hydrogen as well as air.



33]



IN THE GASEOUS STATE.



301



Subsequent experiments.
47. These experiments were commenced on July 24, 1878.

A single fibre of unspun silk, having a thickness of '0005 of an inch, was
suspended in a test tube 1 inch in diameter and 7 inches long. The tube
was closed with an india-rubber cork, through which passed a small glass tube
to allow of exhaustion ; this tube was connected with the vacuum gauge and
the mercury pump, also with drying tubes for admitting dry air or hydrogen.
A microscope with micrometer eye-piece reading 10 ^ o0 th of an inch (the
same as had formed the cathetometer in the previous experiments) was
arranged for the observation of the motion of the fibre.




Fig. 13.
The apparatus as arranged is shown in fig. 13.

The tube having been dried was filled with dry air at the pressure of the
atmosphere. A hot body was then brought near it. .

In order to secure uniformity in the hot body, a test tube filled with
boiling water was placed on a stand, which stand remained in the same
position throughout the experiment, the water in the test tube being boiled
the instant before the tube was placed on the stand.

The motion of the fibre was then watched through the microscope and
measured.



302



ON CERTAIN DIMENSIONAL PROPERTIES OF MATTER



[33



Having ascertained the motion, the heater was removed and the fibre allowed
to return to its normal position, which it always did with more or less exactness.

The tube was then exhausted to a limited extent and the operations
repeated.

48. In this way were obtained a series of observations both for air and
hydrogen at various pressures. These are shown in the following tables.

TABLE XVIII. Impulsion of fibre of silk in air, August 1, 1878.



Pressure by
vacuum gauge


Motion of
the fibre


inches


inches


30


- -0930


16


-0300


8


+ 00


4


+ 0150


2


+ 0210


1


+ -0230


5


+ -0390


2


+ 0700


1


+ 0830


05


+ 0930


025


+ 1005



TABLE XIX. Impulsion of fibre of silk in hydrogen, August 1, 1878.



Pressure by
vacuum gauge


Motion of
the fibre


inches


inches


30


+ 0040


16


+ 0070


8


+ 0100


5


+ '0160


2


+ '0310


1


+ '0490


40


+ 0710


2


+ -0880


1


+ 1070



Table XVIII. shows that with air the result was negative until a pressure
of less than 8 inches was obtained, it then became positive, and it was
measurable at a pressure of 4 inches, and then steadily increased as the
pressure fell, until for very small pressures the fibre moved through about
1,000 divisions on the micrometer.

With hydrogen, Table XIX. shows that the results were positive from the
pressure of the atmosphere and for small pressures were somewhat larger
than with air.



33] IN THE GASEOUS STATE. 303

Although only one series of such observations is recorded in the table,
the experiments were repeated several times with each gas. Also a flame
was used instead of a heater, and the results were consistent throughout.

Elevation of the heater.

49. The effect of having the heater at different elevations was carefully
studied, for it was obvious that this would atfect the air currents in the tube.
It was found, however, that the elevation of the heater did not produce any
effect on the direction in which the fibre moved at pressures of less than 6
or 8 inches of mercury for air, and less than 20 inches for hydrogen. For
pressures greater than these, considerable alterations in the elevation of the
heater did produce very slight modifications in the motion of the fibre.

Bending of the fibre.

50. The possibility of the results being due to a tendency of the fibre
to bend with the warmth was also considered. Observations were taken at
different points up the fibre and on different sides ; and the results were such
as to lead to the conclusion that the bending of the fibre did not produce any
material effect.

Spider line.

51. A spider line was also used : it was not found possible to suspend
this freely in the tube. It was attached top and bottom to a wire frame, but
it was quite loose between the points of attachment, so that it could swing to
either side.

Considerable difficulty was found in observing the spider line, as it was
lost sight of the instant it was the least out of focus ; but the general result
of the observation was, that at higher pressures both for air and hydrogen
the motion was negative or to the heater ; but at pressures of less than about
8 inches it was decidedly positive, the fibre being driven away from the



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