294: Mr. S. R. Milner on the Heats of 



which the molecules move towards the plane will therefore 



I v 



be increased in the ratio - 7 or 



l — s v — b' 

 Multiplying (5), therefore, by q cos e~—-r and integrating, 



we find for the number of molecules striking the division 

 plane of the layers per second from below, and passing 

 through it into the upper one. 



^,= -^ . -^-r{ V ' 2 r sinO cos eqh-^ 2 dqde, . (6) 



v — bjo J VI 



V 



Troc 



in which the lower limit of q is the v 1 of (4) . The integration 

 in q, which must be performed first, since Vi is a function of 

 6, gives 



r n/2_2JdU t v-i sec2e f , . 



N 1= =^-.-^- e a " ' i a s sin0cos0+2JdLi— tan0><#, 



s/rrra v — bj I V ) 



which on further integration reduces to 



Ni=o-^=- re « 2 * (7) 



2vtt v — b 



In the upper layer, the number of molecules per c.c. has 

 become N — c?N, and the specific volume v-\-dv, and all the 

 molecules which strike the boundary plane from above pass 

 through it into the layer below. The number doing this per 

 sec. is therefore, 



_ 2(N-cZN) v + dv 

 2 ~ ^Tr.a 3 'v + dv — b 



it . a 

 or 



f ^ f sin e cos Oqh-WdqdO, 



JN «- 2^ 'v + dv-b' ■ • • • W 



(N— dN)a v + dv 



IT 



where « is assumed to have the same value as before. 



The total number passing through the boundary plane in 

 either direction must be zero when the vapour is saturated, 

 hence Nj = N 2 , and equating the right-hand sides of (7) and 



m, 



***.?± v + dv-b 



e " v-b ' 



fcince N/(N— dN) =(v + dv)jv. 



Taking logarithms and expanding, and writing for a 2 its 

 value §g 2 , or M , where R is the ordinary gas constant 



