90 PROCEEDINGS OF THE AMERICAN ACADEMY. 



whence 



F 2 - F x = T R * m ~ Rm log * + 2T (R, - R 2 ). (29) 



th — rii no 



If i?i is equal to R 2 , this reduces to the familiar form 

 F 2 -F l = RTlog -, or - = e «r 



the Boltzmann equation which we have called (4). 



The condition for gas-pressure equilibrium in case of thermal 

 effusion, being p = (RT) 1 - X a constant, becomes now, in the iso- 

 thermal bridge passing from M\ to M 2 , p = R* X a constant. If 

 there were no electrical complication, the condition for equilibrium 

 in this bridge would be 



d f p\ _ 1 dp p dR _ 



dl \&) " R~ i ~dl ~ 2ffi~dT '' ' 



or 



and so 



dF= - TR—-1 TdR. (27') 



n 2 



Substituting for R and dR from (24) and (25) we get 



dF=-l T ^=*-» dn -T(fr- m) ^^ - (28') 



2 Tli — 7*2 Wi — tl2 n 



whence 



p T R 2ni -R in2 n 1+ 3 



ni — w 2 w 2 2 



This differs from (29), which was obtained without the hypothesis of 



3 

 thermal effusion, only in having ^, instead of 2, as the coefficient of 



