GASES ARISING FROM INEQUALITIES OE TEMPERATURE. 
255 
also 
dvj 1 dp 
dv 2 fjb dz * 
The last of equations (71) may therefore be written 
G i f / 9 i , \ dp n d 0 
-;+ — (a- + 4G«) T — 7 ~a -J = 0 
it pa- 8/U 'dz 4 pd dz 
(76) 
(77) 
Equation (77) gives the relation between the quantity of gas which passes through 
any section of the tube, the rate of variation of pressure, and the rate of variation of 
temperature in passing along the axis of the tube. 
If the pressure is uniform there will be a flow of gas from the colder to the hotter 
end of the tube, and if there is no flow of gas the pressure will increase from the colder 
to the hotter end of the tube. 
These effects of the variation of temperature in a tube have been pointed out 
by Professor Osborne Reynolds as a result of the Kinetic Theory of Gases, and 
have received from him the name of Thermal Transpiration : a name in strict analogy 
with the use of the word Transpiration by Graham. 
But the phenomenon actually observed by Professor Reynolds in his experiments 
was the passage of gas through a porous plate, not through a capillary tube ; and the 
passage of gases through porous plates, as was shown by Graham, is of an entirely 
different kind from the passage of gases through capillary tubes, and is more nearly 
analogous to the flow of a gas through a small hole in a thin plate. 
When the diameter of the hole and the thickness of the plate are both small com¬ 
pared with the length of the free path of a molecule, then, as Sir William Thomson 
has shown, any molecule which comes up to the hole on either side will be in very 
little danger of encountering another molecule before it has got fairly through to the 
other side. 
Hence the flow of gas in either direction through the hole will take place very nearly 
in the same manner as if there had been a vacuum on the other side of the hole, and 
this whether the gas on the other side of the hole is of the same or of a different kind. 
If the gas on the two sides of the plate is of the same kind but at different tempera¬ 
tures, a phenomenon will take place which we may call thermal effusion. 
The velocity of the molecules is proportional to the square root of the absolute 
temperature, and the quantity which passes out through the hole is proportional to 
this velocity and to the density. Hence, on whichever side the product of the 
density into the square root of the temperature is greatest, more molecules will pass 
from that side than from the other through the hole, and this will go on till this 
product is equal on both sides of the hole. Hence the condition of equilibrium is that 
the density must be inversely as the square root of the temperature, and since the 
pressure is as the product of the density into the temperature, the pressure will be 
directly proportional to the square root of the absolute temperature. 
