381 
consideration could take place in our experiments, in which it be 
assumed for the present that the so highly “electritied” state of the 
gas has no influence on the diffusion-laws. 
4. Diffusion. 
In the mathematical treatment of this problem it should be borne 
in mind that in GeissLer-tubes we have to do with a rarefied gas- 
atmosphere, and that the cathode and the anode space, between 
which differences of pressure occur, are kept separated by a capillary 
tube. Besides distinction should be made between the cases in which 
the free length of path of the gas particles 7s comparable with the 
dimensions of the capillary and those in which it is not. 
For air at room temperature and a pressure of p baryes') the 
free length of path is y= 8,67/p cm. When we have e.g. a gas 
pressure of 0,1 mm. Hg = 133 baryes, then 
I. Lanemurr?) has derived that the equations holding for velocities 
of transfusion for gases in tubes whose diameter is not more than 
21/, times larger than the free length of path of the gas particles, 
are practically the same as those for which the free length of path 
of the molecules is large with respect to the tube-diameter. 
It is now the question whether in the experiments described in 
the author’s thesis for the doctorate the circumstances were such 
that always the free length of path of the molecules was greater 
than two fifths of the capillary diameter. 
The pressure effects have been found by us down to a gas 
pressure of 0.087 mm. Then at room temperature: 
__ 100 
A= 0.65 a7 = 0,74 mm. 
which is about */, of the capillary diameter of the discharging 
apparatus used. 
In reality, however, the gas diffusing back through the capillary, 
is not at room-temperature, even apart from the high “electrical” 
temperature®) of the particles subjected to the discharge. With the 
applied current densities the quartz capillary appeared to get heated 
even with air-cooling. When suddenly the current is cut ont, so 
that the luminescence of the illuminating gas column is eliminated, 
it appears that with the very great current strengths previously used 
1) Dyne/cm?. 
*) Gen. El. Rev. 1916 p. 1062. 
3) Cf. J. Stark, Ann. d. Phys. (4) 14, 506 (1904). 
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