302 
The influence of gravity upon the gas is left out of account in 
the calculation, as is also the pressure difference which KNuDsEN’s 
researches show must exist. If necessary both corrections may be 
applied to the observed pressure at which equilibrium is attained *). 
The influence of slipping along the walls of the capillary is also 
left out of account, while the volume of the capillary has been regarded 
as negligible compared with that of the reservoir and of the volu- 
menometer. It is also assumed that the speed may be regarded as to 
remain the same over a short period of time, and that the speed is 
small (far below the critical); further that the temperature, 7’, and the 
pressure, p, may be regarded as uniform over any cross-section, 
so that if 2 is the length and y and z two axes at right angles to 
it and to each other, p is independent of y and z; and, finally, that 
the speeds v and w in the directions of y and z may be taken to 
be zero. A flow is therefore assumed such that in a tube at constant 
temperature throughout and for a substance whose density is inde- 
pendent of the pressure Porsrurre's law should hold, and such as 
may be regarded as subject to this law over any element of length, 
dx, of the capillary when the values of the pressure gradient, the 
density e and the viscosity 4 at that particular place are inserted. 
Working out the equations of motion subject to the given assump- 
tions *) at once leads to the result 
dm a ‚0 dp 
aS a i ee, 
a Ben dz 1) 
where m is the mass of the gas contained in the reservoir, and hence 
dm 5 rage 
— the mass which flows per unit time across any section of the 
at 
capillary. 
We assume 7 to be independent of the pressure so that 4 = / (7), 
and for f(7’) we take SurmHeRLAND's formula 
AG 
| En 973 7 
da C 273 
parce 
= 7 
1) As a general rule, however, both corrections may be neglected. For the 
lowest pressure occurring in the course of the experiments for which this cal- 
culation was made the KNUDsEN correction just reached that limit at which the 
calculations by KAMERLINGH ONNES for the capillaries of his hydrogen and helium 
thermometers show it would begin to be appreciable. 
2) Cf. O. E. Meyer, Pogg. Ann. 127. p. 253, 353. 
