+ ^=o, 



312 Mr. S. H. Burbury on some Problems 



The motion of the gas is a motion of simple translation with 

 velocity v = — qy in direction x, where q is constant, combined 

 with a disturbance of the second order symmetrical about the 

 plane x=y. In this case we should assume 



F = N (^ e~^ 2 (1 + V0(a> 8 )). 

 where <£(&> 2 ) is an undetermined function, and 



Ot \7r/ r ay 



17. The complete solution of any problem of the kind would 

 have to be found from the equation 



dF BF 

 dt bt 



expressing the steadiness of the motion for each class of mole- 

 cules. It does not appear that in case of diffusion we can 

 obtain a solution by assuming the two gases to have a motion 

 of simple translation, one in one direction and the other in 

 the opposite. 



Relation of Diffusion 8fc. to Temperature. 

 Without obtaining a complete solution of any of these pro- 

 blems, we can by means of the equation 



dR , BH 



dt + ^t 



determine the relation in which the solution, whatever it may 

 be, stands to the absolute temperature of the system. 



18. When the disturbance is of the first order the solution 

 proposed is, using X to denote the disturbance as in (13), 



X=X%(A)0(AMft> 2 ), 



in which %(A) is a function of h to be determined, and 

 <£(AM<w 2 ) is a function of AMa) 2 , containing only odd positive 



powers of co \/AM, as for instance 



4> (AMa> 2 ) = Co© i/ AM + C, (AM)to) 3 + &c, 



where the C's are numerical. 



Similarly in dealing with two gases, we shall assume 



x=\ l x(h)cl> , (hm^), 

 and <// has similar form. With these values of X and x, 

 j J XdS = %(A) JJ X0 (AMa> 2 )dS, 



