316-319] Conduction of Heat 265 



r\ 



(602) shall vanish. This condition will of course lead to a relation between ^~ 



oz 



^7 



and 3- . Substituting for 8n c in expression (602), the relation in question is 



seen to be 



1 dv r x^e-^ , Idh r (a 2 - f 

 -- - - ~ 



\ 



v dz J o -^ (x) 



Idh r (a 2 - f) tfe-* , ,---, 



= TT- ~ rf-x --- dx ............ ( 605 )- 



hdz J ty(x) 



The integrals have been calculated by W. Conrau, and the result is given 

 in Meyer's Kinetic Theory (p. 464). It appears that equation (605) can be 

 written in the form 



1^ = 0-71066^ ........................... (606), 



v dz hdz 



so that, instead of equation (602), we have 



9 O flfr 



- (2-21066 -x^tfe-^dx ...... (607). 



7TO- 2 V Am ty (x} 3 hdz 

 Hence, upon substitution for Sn c in equation (604), we obtain 



T, = ^-=i / (608), 



where 



/=/ ' . T \ <fa ...(609). 



Jo Y (*) 



319. The mean total energy carried over the plane z = z by the 

 molecules crossing it, no matter where they come from, will always bear 

 the same constant ratio to the mean translational energy, this ratio being 

 E/^mC 2 , or 



^ (610). 



Hence the total transfer of energy F stands to F in this same ratio, and is 

 therefore given by 



.(611). 



9-7TO- 2 \/hm h dz 

 Also, since the ratio (610) is constant in space, we have 



jr? dh t dl A 



Hi -^ f- h i = 0, 

 dz dz 



so that F can be put in the form 



-j- (612). 



dz 



