828 
PROFESSOR 0. REYNOLDS ON CERTAIN DIMENSIONAL 
These two cases are as follow— 
1. The flow of gas through a small orifice in a thin plate when the mean pressure of 
the gas is the same on both sides of the plate, the flow being caused by a difference in 
temperature on the two sides of the plate, or a difference in the molecular condition of 
the gas. 
2. The excess of pressure which the gas exerts on a small body when the body has 
a higher temperature than the gas. 
Thermal transpiration through an aperture in a thin plate. 
111. In this case, since there is no tangential stress, we have (Art. 87) 
u=o. 
Whence by equation (121) 
dp 
dx 
= 0 
(122a) 
Since p—p~ we have, integrating equations (120) and (122), respectively 
d v/ 7r o/'-'i 
yTz Jx~ ’ 
1 
7 V r.^=-A^H. 
J ~dx b sp J 
Y • 
(122b) 
G and II are constants, such that v— is the rate at which heat is carried across a 
2 r y r z 
unit of area, and — is the rate at which matter is carried across. 
From equation (122b) we have 
H=-3« 2 G 
(123) 
Equation (123) can only be approximately true as or is not constant; therefore the 
condition U=0 is not possible, i.e., it is only approximately fulfilled, whence it follows 
that p is only approximately constant. The closeness of these approximations will 
depend on the variation of or and within the limits of our approximation we may con¬ 
sider the condition to hold. 
From equation (123) we see that the direction of flow of gas is opposite to that of 
the flow of heat, while since or cc the rate of flow of gas is proportional to the flow 
of heat, to the mass of a molecule and inversely proportional to r, the absolute 
temperature. 
