PROPERTIES OF MATTER IN THE GASEOUS STATE. 
825 
Therefore 
and (114) becomes 
(AVI Mj—Mo _ dp 
P n= — cF 2 ( -)k\/ 
1 dp 
\/M dx 
If C is small, then F 9 
s z 
Hence in this case 
pn= — - m'Xj/cv/r 
1 dp 
a/M dx 
(115) 
(11C) 
And this is in exact accordance with Graham’s law, which is that the rate of 
transpiration is proportional to the difference in the square roots of the densities of 
the gas. For— 
dN l 
dx ’ 
and since M x —M 2 is small 
dp 
dx 
=v / m( v 'm 1 - v /m ! 1 
dx ’ 
or 
c _ _ d~N 
pn= --mVv' T { i/My— x 
(117) 
This form of equation is obtained by neglecting the difference of Mj and M 3 ; but by 
taking into account the two systems of molecules throughout the investigation, an 
equation similar to (117) would have been obtained without any such assumption. 
Thus we see that the general equation of transpiration may be made to include not 
only the cases of transpiration under pressure and thermal transpiration, but also the 
well known phenomena of transpiration caused by the difference in the molecular con¬ 
stitution of the gas. And in this case, as in that of transpiration under pressure, the 
equation reveals laws connecting the results obtained with plates of different 
coarseness and different densities of gas, which doubtless admit of experimental 
verification. 
This completes the explanation of the phenomena of transpiration through porous 
plates. 
Section XI .—Application to apertures in thin plates and impulsion. 
Condition of the gas. 
109. When the gas within a vessel is in uniform condition, excepting in so far as it 
is disturbed by a steady flow of gas or of heat from what, compared with the size of 
5 N 2 
