264 Free Path Phenomena [OH. xm 



We have, however, since there is only one kind of gas, by equations (537) 

 and (535) 



V7TZ/0- 2 rr 



C = ^ = ~hm^^ (C ^^ 



so that 



9 95 



and hence the terms in and -^ destroy one another in equation (601). 



Also 



hmc 3 



(c VAm) 

 so that the equation can be written in the simplified form 



, 2 ^/h s m 5 FT 1 dv 1 dh me* dh , 

 dn c = J = \B C K- -i- STY- T- + -H- T- e~ hmc C 5 dc. 



o I / .11 \ I * O-. -J OI, J _ ' O J *, I 



7ro" ! y > (c 



317. Clearly the corresponding number which cross the plane in the 

 opposite direction, say dn e ', is given by an expression which is of the same 

 form except that the signs of all differential coefficients with respect to z are 

 changed. Hence Bn c , the excess flow of molecules with velocities intermediate 

 between c and c + dc, is given by 



8n c = dn c ' dn c 



2 V^T 5 f 2 dv ,. 1 dh~\ 



= - - -j- + (1 - Hmc 2 ) T -r~ 



TTO-Y (c vAro) L- 3l/ * * *J 



If we write x for c VAm, this becomes 



8n c = - - + (1 - l^ 2 ) ^ e - 2 ^ ...... (602). 



7TO- 2 V& ^ (;) L*- * 7i dz J 



318. The total transfer of mass across the plane z = z is 



(603), 



!t=0 



while the total transfer of translational energy is 



f O O/l v* * *\ / 



x=Q " x=0 



Heat can, as we know, be transferred either by conduction, or by con- 

 vection. If we are dealing, as in the present case, with conduction only, we 

 must introduce the condition that there is to be no convection. This simply 

 requires that there shall be no transfer of mass, and therefore that expression 



