in the Kinetic Theory of Gases. 315 



Now if we form 



f = ^^^{flo g E + |lo g /}, 



the terms containing \ or A/ in the first degree disappear, and 

 so 



where 



o, 2 =^ 2 +y 2 +z 2 , 



yjr 2 = x ,2 +y 2 + z' 2 . 



y(h) 



As a function of h, this expression has dimensions .- ; 



s/ h appearing in the denominator in consequence of the 

 factors co and ty. 



21. Now by virtue of the equation 



3H 3 .H _ 



jit T^TT 



-y- and ^— will, as functions of A, have the same dimensions. 



dt ^t 



(xW) 



And therefore in diffusion V/LV — has the same dimensions as 



y(h) . . s/h 



^7" ? or xW * s a constant, independent of h. 



But the stream of gas M through the tube, that is the rate 

 of diffusion for given space variation of density, is 



7 -\T ? /■» °° 



N f — \ ' \ dcoe-™« 2 co*co X {h)<t>{hMco 2 ), 



and therefore varies as ~JT > or as the square root of the abso- 

 lute temperature. This is a consequence of the assumption 

 that its 2 is independent of R, and therefore holds only for 

 elastic spheres. 



22. We will now treat conduction of heat in the same way. 

 Since the disturbance is of the first order, we shall as before 

 assume for the solution \yJJc]^>(k(o q ) , k being written for hm. 



?TT 



Then -=- will, as a function of k, have the same dimensions as 



before, viz. (%M) 2 



s/k 



