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matter of some surprise. There appeared, however, to be a possible cause
for this in the thinness of the meerschaum. It was possible that there was
some flaw in the plate, or more probably that the thinness of the plate allowed a
considerable equalisation of temperature by the conduction of heat. It was,
therefore, resolved to try a thicker plate of meerschaum, and a plate '25 inch
(6'3 millims.) was introduced in place of that previously tried.

TABLE III. Thermal transpiration of air by meerschaum plate No. 2 (*25 inch
or 6'3 millims. thick). Temperature of steam, 212 F. or 100 C. ; tem-
perature of water, 47 F. or 8 C.



Mean pressure by vacuum
gauge


Difference of pressure by
siphon gauge, March 15


Ratio of mean pressure to
difference of pressure


inches


millims.


inch


millims.




30-2


764-5


25


6-096


121


12-9


327-6


20


5-080


64


8-53


216-7


17


4-318


50


3-70


94-0


12


3-048


31


2-0


50-8


08


2-032


25


0-88


12-35


045


1-143


20


0-5


12-7


035


0-889


13-6



272 ON CERTAIN DIMENSIONAL PROPERTIES OF MATTER [33

Whether the fact that the thicker plate of meerschaum gave nearly
three times the difference of either of the previous plates was due to the
thicker plate maintaining a greater difference of temperature, or to some
difference of texture in the thin plate, such as a flaw, has not been clearly
determined, but it now appears probable that it was largely due to the first
of these causes.

With this plate lower pressures were for the first time tried, and Table III.
shows these differences falling with the pressure.

The ratio of the difference of pressure to the mean pressure, however, as is
shown in the last column, increases as the pressure falls, and apparently is
approximating to a constant value at lower pressures. This is according to
Law III., Art. 9.

From Law IV., Art. 9, it appears that this ratio should, as the pressure
fell, have approximated to the ratio which the difference of the square roots
of the absolute temperature on the two sides of the plate bears to the square
root of the temperature on the side at which the pressure was measured.
Assuming 1 -i- 13 to be this ratio, it would appear that there must have been
considerable differences of temperature between the surfaces of the meer-
schaum and the side of the plate ; but it also appeared probable that with
still lower pressures the ratio might have been considerably lower.

It would have been desirable to have carried the experiments to lower
pressures, but at that time this was impossible as there was then no special
means of reading the differential gauge ; so that this had to be deferred until
such a means was provided.

Hydrogen.

21. In the meantime other gases were tried. Owing to its lightness it
was thought probable that hydrogen would at the higher pressure give a
somewhat higher result than air. How much this might be the theory gave
no certain indication, for it depended on qualities of the gas which had not
been determined. But at the lower pressure, according to Law IV., the
difference of pressure should approximate towards the same value relatively to
the absolute pressure.

This was clearly a point which might be tested even though no very close
approximation should be reached. Hydrogen was accordingly tried.

Table IV. shows that at the pressure of the atmosphere the difference
with hydrogen was four times as great as it had been with air, and reached
the very considerable figure of '92 of an inch of mercury. This was much
more than had been anticipated, although there was nothing in the theory to
show that it should not exist. This great difference at the higher pressures
only serves to bring out more forcibly the convergence, according to Law IV.,



33]



IN THE GASEOUS STATE.



273



TABLE IV. Thermal transpiration of hydrogen by meerschaum plate No. 2
('25 inch or 6'3 millims. thick). Temperature of steam, 212 F. or
100 C. ; temperature of water, 47 F. or 8 C.



Mean pressure by vacuum


Difference of pressure by


Katio of mean pressure to


gauge


siphon gauge


difference of pressure


inches


millims.


inch


millims.




30-2


767


88


23-37


32-4


13-0


330


60


15-24


21


7-5


190-5


44


11-18


17


4-25


107-9


28


7-11


15


2-0


50-8


15


3-81


13-3


1-0


25-4


08


2-03


12-5


0-5


12-7


036


0-91


13-7



as the pressure falls. At pressures of 1 inch it will be seen that the
differences for air and hydrogen are as 12'5 to 20, while if the results at
'5 inch could be trusted, the ratio is 13'7 to 13'6.



Meert


chaum Plate.


/


Hydrogen


Difference of pressure in inches of mercury.

P O * CM
O O O O


No


2.
X


X






/






/


/






/








/








/


^___




Air




Y/jz-


-""




"Carbonic




~^-^


f






Acid



10

Mean pressure in inches of mercury.

Fig. 4.

The convergence of these results is best seen in the accompanying
diagram. The curves are drawn through points of which the pressures are
abscissae, and the differences of pressure (on a different scale) are the
ordinates.

o. E. 18



274



ON CERTAIN DIMENSIONAL PROPERTIES OF MATTER



[33



The maximum difference of pressure (carbonic acid).

22. The curves, fig. 4, show that the differences both for hydrogen and
air appear to be tending, as the pressure rises, to a maximum value. This
was exactly what was expected from Law III., Art. 9, and had the apparatus
been capable of withstanding considerable pressures it would have been
desirable to have raised the pressure until the maximum was passed. But
it appeared that the same end might be more readily accomplished in other
ways.

Owing to the great density and low coefficient of diffusion of carbonic
acid, it seemed to be probable that with this gas the difference of pressure
would reach a maximum at considerably lower pressures than either hydrogen
or air. Carbonic acid was therefore tried.

TABLE V. Thermal transpiration of carbonic acid by meerschaum plate
No. 2 ('25 inch or 6'3 millims. thick). Temperature of steam, 212 F. or
100 C. ; temperature of water, 47 F. or 8 C.



Mean pressure by vacuum
gauge


Difference of pressure by
siphon gauge, March 10


Ratio of mean pressure to
difference of pressure


inches


millims.


inch


millims.




30-1


764-5


13


3-302


230


19-5


495-3


16


4-064


122


14-25


361-8


16


4-064


89


10-5


266-7


15


3-810


70


8-0


203-2


13


3-310


61


4-5


114-3


11


2-794


40


2-0


50-8


08


2-032


25


1-0


25-4


05


1-270


20


0-5


12-7


04


1-016


12



Table V. shows that with carbonic acid the maximum difference was at a
pressure between 20 and 15 inches, the difference rising as the pressure fell
from 30 inches to this point. After this point was passed the difference fell
with the pressure.

The curve on fig. 4 which represents this table shows the point of
maximum difference, and the figure also shows that as the pressures became
small the curve for carbonic acid converges towards the curves for air and
hydrogen.

These results for carbonic acid are perhaps sufficient to verify Law III.
respecting the existence of a maximum. But they were obtained with
considerable trouble, as the india-rubber tubing absorbed the carbonic acid
very rapidly, and so caused considerable disturbance. For this reason
carbonic acid was not again used.



33]



IN THE GASEOUS STATE.



275



Stucco plate No. 1.

23. As it appeared from Law V., Art. 9, that any increase in the coarse-
ness of the plate should reduce the pressure at which the difference should
be a maximum for each gas, a plate of stucco was tried with this object.

It was clear that the differences would be much smaller with the stucco
than with the meerschaum. Therefore this plate was not tried until the
differential gauge had been furnished with the cathetometer to read to
f an i ncn (4^0^^ f a niillim.).



Final experiments.

A series of experiments, commencing with stucco plate No. 1, but continued
with meerschaum plate No. 3 and stucco No. 2, were commenced on May 6,

TABLE VI. Thermal transpiration of air by stucco plate No. 1 ('25 inch or
6-3 millims. thick). Temperature of steam, 212 F. or 100 C. ; tem-
perature of water, 65 F. or 18'4 C.



Mean pressure by
vacuum gauge


Difference of pressure by
siphon gauge, July 11


Eatio of mean
pressure to
difference
of pressure


Log of
mean
pressure


Log of
difference
of pressure


inches


millims.


inch


millims.








29-80


756-9


0220


559


1360


2-474 - 1


2-342 - 4


28-50


723-9


0225


571


?J


2-455


2-352


25-85


656-6


0235


597





2-412


2-371


23-40


594-4


0250


635


903


2-369


2-397


22-20


563-9


0266


675


835


2-346


2-424


17-40


443-9


0294


746




2-240


2-468


15-40


391-2


0336


813





2-187


2-526


13-60


345-4


0342


868




2-133


2-534


12-25


311-1


0348


884




2-066


2-541


11-35

10-00


288-3
254-0


0366


929


326


2-053
2-000


2-541
2-563


9-00


228-6


0380


965




1-954


2-579


7-50
6-75


190-5
171-4


0376


955


200


1-875
1-630


2-579
2-575


6-00
5-15


152-4
130-8


0362


955
917


142


1-778
1-711


2-575
2-559


4-35


110-5


0354


899


120


1-638


2-549


3-50


88-9


0306


828


107


1-544


2-513


2-90


73-7


0314


797


92


1-462


2-496


2-35


59-7


0290


736


81


1-370


2-462


2-25


57-15


0284


721


79


1-350


2-453


1-25


31-75


0230


584


54


1-097


2-361


0-60


15-24


0149


378


42


1-778


2-258


0-25


6-35


0080


203


31


1-398


1-903


0-15


2-66 -0066


167


23


1-176


1-819



182



276



ON CERTAIN DIMENSIONAL PROPERTIES OF MATTER



[33



and repeated in July. To give all the observations made in this series of
experiments would occupy too much space, therefore a selection has been
made, those results being chosen which appeared to be least subject to
disturbance. However, the results all agree so well that there was but little
choice, and it was clearly unnecessary to resort to the usual method of taking

TABLE VII. Thermal transpiration of hydrogen by stucco plate No. 1
(25 inch or 6'3 millims. thick). Temperature of steam, 212 F. or
100 C. ; temperature of water, 63 F. or 17 C.



Mean pressure by
vacuum gauge


Difference of pressure
by siphon gauge


Ratio
of mean
pressure to
difference
of pressure


Log of
mean
pressure


Log of
difference
of pressure


May 6


July 11




inches


millims.


inch


inch


millims.








33-00


858-0


...


1340


3-404


252


2-518-1


3-127-4


31-00


787-4




1366


3-470


227


2-491


3-135


29-00


736-6


...


1396


3-546


207


2-462


3-145


28-50


723-9


1408





3-576


203


2-454


3-149


27'-00


685-8




1400
1436


3-556
3-647


188


it
2-431


3-147
3-157


25-30


642-6





1446


3-672


174


2-403


3-160


23-75


603-2




1460


3-708


162


2-375


3-164


22-00


558-8




1490


3-784


147


2-342


3-173


20-00


508-0




1530


3-886


130


2-301


3-185


19-00


482-6





1540


3-912


123


2-279


3-187


18-00


457-2






3-912


116


2-255


3-187


16-70


424-1




1542


3-917


109


2-222


3-188


16-00


406-4


1532


...


3-891


104


2-204


3-185


15-80
14-90


401-3

378-4




1532
1538


3-906


103
94


2-199
2-178


3-185
3-187


13-35


339-0




1536


3-901


87


2-125


3-186


12-50


317-5


*


1534


3-896


81


2-096


3-186


11-55


393-4




1512


3-840


76


2-062


3-179


9-80


248-9




1506


3-825


65


1-991


3-178


9-50


239-7


1512




3-840


62-5


1-977


3-170


9-00


228-6


*


1480


3-759


60-8


1-954


3-175


8-00


203-2





1470


3-734


55


1-903


3-167


6-00


152-4




1320


3-353


45


1-778


3-120


3-25


82-5




1046


2-637


31


1-511


3-019


3-2


81-3




1020


2-590


>t


1-505


3-008


2-0


50-8


. .


0760


1-930


25


1-301


2-880


1-8
1-15


45-72
29-21


0760


0500


1-270


23-5
23


1-255
1-176


2-880
2-698


0-7


17-78




0330


838


21


0-845


2-518


0-6


15-24


0280


...


711




0-778


2-447


0-4


10-16




0190


482


n


0-602


2-278


0-3


7-62


0158




401


19


0-477


2-198



mean values. Such differences as do exist are sufficiently accounted for by
the small differences in the temperature of the water, which was several
degrees higher in July than in May.



33]



IN THE GASEOUS STATE.



277



With the stucco plate the greatest differences of pressure, both in the
case of air and that of hydrogen, are small, something less than one-fourth
the differences previously found in the case of the meerschaum plate No. 2 ;
but then with the stucco the points of maximum difference are well below
the pressure of the atmosphere.

The difference of pressure between the observations is so small, and the
agreement of the observations so great, that by merely joining the points
plotted to represent the observations, very fair curves are formed.
Stucco No. 1







.


r -Hydrogeu


0-1



^"^~~







_





Air


) 10 20 30

Fig. 5.



These curves bring out in a marked manner the agreement of the results
with Law III., Art. 9.

With air the difference rises from '02 of an inch ('508 inillim.), at a
pressure of 30 inches, to '0380 of an inch or ('965 millim.), at a pressure of
7'5 inches, which is the maximum.

With hydrogen the difference also rises as the pressure falls from 30, but
the rise is not so great and the maximum is reached at 16 inches.

After passing the maximum the curves both fall, and in falling obviously
converge.

This is all exactly in accordance with what was expected.

Corresponding pressures {stucco 1, meerschaum 2).

24. Law V. shows that there should be correspondence between certain
portions of the curve for stucco and those for meerschaum, although the
corresponding points would not be at the same pressures.

Assuming the temperatures to be the same, the corresponding points
would be those for which the ratio of the mean pressure to the difference of
pressure were the same. Which points may at once be found by comparing
the figures in the columns showing this ratio in Tables III. and IV., with the
same columns in Tables VI. and VII. respectively.

Before making such a comparison, however, it is necessary to introduce
certain small corrections for the difference in the temperature of the water
in the two experiments ; this, as will be subsequently explained, will be



278



ON CERTAIN DIMENSIONAL PROPERTIES OF MATTER



[33



equivalent to diminishing the difference in the Tables III. and IV. in the
ratio 7 to 8.

Then we find that the pressures at which the ratios are the same in
Tables III. and VI. are approximately as 6 to 1, taking only the higher
pressures, while the Tables IV. and VII. give the ratio 6'7 to 1.

TABLE VIII. Thermal transpiration of air by meerschaum plate No. 3
(44 inch or 11'2 millims. thick). Temperature of steam, 212 F. or
100 0. ; temperature of water, 63 F. or 17 C.



Mean pressure by
vacuum gauge


Difference of pressure
by siphon gauge


Ratio
of mean
pressure to
difference
of pressure


Log of
mean
pressure


Log of
difference
of pressure


May 11


May 14




inches


millims.


inch


inch


millims.








31-00


787-4


2200




5-588


141


2-49 - 1


2-342-3


29-50


749-3




2140


5-436


138


2-47


2-330


28-50


723-9


2160


...


5-486


132


2-45


2-334


27-50


698-5




2126


5-400


129


2-44


2-327


24-50


622-3




2100


5-334


116


2-37


2-322


23-00


584-2


2130




5-410


108


2-36


2-328


21-50


546-1




2054


5-217


104


2-33


2-312


20-00


508-0


2120


...


5-385


94


2-30


2-326


19-50


495-3





1970


5-003


99


2-29


2-294


18-00


457-2


2100


...


5-334


85


2-25


2-322


17-00


431-8




1890


4-800


90


2-23


2-276


12-50


317-5


1730


...


4-394


72


2-09


2-238


11-50


292-1




1630


4-140


70


2-06


2-212


8-25


209-5


1446





3-672


57


1-92


2-160


7-80


198-1


.


1336


3-393


59


1-89


2-105


5-20


133-3


1184


.


3-007


44


1-72


2-073


4-70


118-4




1050


2-667





1-672


2-021


3-40


86-4


0904




2-290


37


1-531


1-954


3-10


78-7


...


0806


2-047


38


1-491


1-906


2-10


53-3


0710




1-803


29


1-322


1-851


2-00


50-8




0630


1-604


32


1-301


1-799


1-40


35-6


0510




1-294


27


1-146


1-707


1-32


33-5


...


0486


1-234


>5


1-120


1-687


1-10


28-0


0394


*


1-000


28


1-041


1-595


0-83


21-06


>..


0380


0-965


22


0-919


1-580


0-65


16-51


0304





0-762


21


0-812


1-482


0-52


13-21




0290


0-736


18


0-716


1-462


0-40


10-16


0250


...


0-635


16


0-544


1-392


0-39


9-91




0220


0-559


17


0-531


1-342


0-28


7-11


0192




0-488


14


0-361


1-283


)>





. ..


0180


0-457


14


0-361


1-255


0-20


5-08


0168





0-427


12


0-301


1-225


0-19


4-82




0146


0-371


12


0-278


1-164


0-15


3-81


0154


...


0-391


10


0-176


1-187



The results of this comparison, although not strictly consistent, indicate
that there is a correspondence, the points on the curves for meerschaum



83]



IN THE GASEOUS STATE.



279



corresponding with points on the curves for stucco, for which the pressures
are about ^ for air, and ^ for hydrogen.

It was clear, however, that the number of observations with the
meerschaum plate was not sufficient to allow of a very close comparison
with the curve for stucco, for the accuracy with which the differences had
been read without the cathetometer was not sufficient to allow of any use
being made of the lower pressures.

TABLE IX. Thermal transpiration of hydrogen by meerschaum plate No. 3
('44 inch or 11 '2 millims. thick). Temperature of steam, 212 F. or
100 C. ; temperature of water, 63 F. or 17 C., May 15 and 18;
temperature of water, 65 F. or 18 C., July 10.



Mean pressure by
vacuum gauge


Difference of pressure by
siphon gauge


Batio
of mean
pressure
to differ-
ence of
pressure


Log of
mean
pressure


Log of
difference
of pressure


May 15


May 18


July 10




inches


millims.


inch


inch


inch


millims.








35-00


889-0






7940


20-17


44


2-544-1


2-900-3


34-00


863-6




7930




20-14


43


2-531


2-899


32-00


812-8


7930






20-14


40


2-505


2-899


30-00


762-0




7670


*


19-48


39


2-477


2-885


29-50


749-3


7760







1971


38


2-470


2-889


>j


5)






7776


19-75


37


>5


2-890


27-50


698-5


7600




...


19-30


36


2-439


2-880


22-00


558-8


6914





...


17-56


32


2-342


2-840


18-50


469-9




6250


...


15-87


29-5


2-267


2-795


18-00


457-2


5710






14-50


31


2-255


2-757


)>









5960


15-14


30


2-255


2-775


12-00


304-8




*


4800


12-19


25


2-070


2-681


11-40


289-6




4626





11-75


24-6


2-056


2-664


10-50


266-7


4156







10-56


25


2-021


2-618


7-70


195-6







3594


9-13


21


1-886


2-555


7-60


193-0




3169




8-03


24


1-880


2-500


6-95


176-5


3046


...




7-74


23


1-842


2-484


4-75


120-6




2206





5-60


23


1-676


2-343


)j


))






2584


6-57


18





2-412


4-50


114-3


2120


. .


* *


5-38


21


1-653


2-326


3-00


76-2


...


1568




3-98


19


1-477


2-200


n


55






1784


4-53


17





2-251


2-60


66-0


1420






3-60


18


1-414


2-152


1-95


49-6






1204


3-06


16


1-290


2-080


1-70


43-2


1063






2-70


16


1-230


2-026


1-25


31-8






0784


1-991


16


1-096


1-894


1-10


27-95


...


0630





1-600


17


1-041


1-799


1-00


25-40


0660






1-676


15


1-000


1-819


0-70


17-78






0380


0-965


18


0-845


1-580


0-65


16-51


...


0325




0-825


20


0-813


1-511


0-60


15-26


0380






0-965


15


0-778


1-500


0-35


8-88




0250




0-635


14


0-544


1-297


0-32


8-13


0200






0-580


16


0-505


1-301


0-175


...


0150


...




0-381


12


0-243


1-176



280 ON CERTAIN DIMENSIONAL PROPERTIES OF MATTER [33

Meerschaum plate No. 3.

25. A fresh meerschaum plate, '44 inch thick, was therefore tried,
another diffusiometer, exactly similar to the original one, being constructed
for the purpose.

Although this plate was so much thicker than meerschaum plate No. 2,
the results were no greater. They appear rather less, but this was owing to
the somewhat higher temperature of the water, which would reduce the
results in Table IV. in the ratio 8 to 9, and when this correction is applied
the agreement is very close.

Effect of the thickness of the plate.

26. It had been expected, however, that the extra thickness of the plate
No. 3 would have caused it to give somewhat higher results, and its not doing
so seemed to imply that the plates were so thick that the conduction of heat
through the plate produced no appreciable effect on the temperature of the
surfaces of the meerschaum. It appeared, however, from subsequent ex-
periments that in all probability there was a small difference in the two
instruments. The original instrument, that in which the experiments on
plate No. 2 were made, had been used a great deal, and the surfaces of the
tin plates which were opposite to the meerschaum had lost all their polish
and become black, while in the second instrument the plates were new and
bright. It might, therefore, be expected that the old plates would radiate
more heat thai) the bright plates, and so better maintain the difference of
temperature, and 1 besides this the india-rubber rings in the new instrument
were somewhat thicker than those in the old one, and so the space between
the plates and the surface of the meerschaum was greater than in the old
instrument. It appears, therefore, that these causes may have neutralised
the increase in the difference of temperature that would otherwise have
resulted from the extra thickness of the plate. And it will be seen that this
conclusion was confirmed when on introducing a new stucco plate into the
old instrument new tin plates and thicker rings were also introduced.

Infusion of air.

The curves, fig. 6, show the degree of regularity attained in these ex-
periments. Such discrepancies as there are, are apparently owing to the
absorption and exhalation of the gas by the india-rubber and possibly by the
plate itself, for these discrepancies only occur at the lower pressures.

In the case of hydrogen the greatest care was taken to get the gas pure ;
but it is not to be supposed that as the gas was pumped out the residual
gas would maintain a high degree of purity, for the gases given off by the



33]



IN THE GASEOUS STATE.



281



india-rubber and the air which diffused through it would gradually replace
the hydrogen.

=^ iO-8



Meerachaum No 3.




10



20

Fig. 6.



30



0-7
0-6
0-5
04
0-3
0-2
0-1




Corresponding pressures with stucco No. 1 and meerschaum. No. 3.

27. Comparing the ratio columns in Tables VIII. and IX. with the
corresponding columns in Tables VI. and VII. respectively, the corresponding
pressures are found to be as shown in Tables X. and XL

In Tables X. and XL the first columns are the ratios taken direct from
Tables VIII. and IX., the second columns are the pressures also taken direct
from Tables VIII. and IX.

In order to find the pressures with the stucco plate which would yield
exactly the same ratios (difference of pressure to mean pressure) as those in



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