Properties of Matter in the Gaseous State. 105 



out rendering a difficult subject tenfold as elaborate as was 

 necessary. For instance, using Prof. Reynolds's notation, 

 in calculating the mass carried across i^nit area perpendicular 

 to x, his assumption, as far as the first approximation goes, 

 comes to the same as supposing that the components of the 

 velocity of a molecule going in the direction whose direction- 

 cosines are I : m: n< are 



it 



so that 



and 



and 



where 



and 



= lq + JJ, v = jnq + V, iv = nq+W; 

 lq = %, mq=< n , ?iq = £, 



q 2 = PW + ?, 



d% ~dv d £= q 2 dq dl d<p, 



m=\/l — ^sin<£ 



n=\/l — I 2 cos<£. 

 From these we get that 



o / „M= (" f * r°^-4-(lq + U)q 2 dqdld<l> 

 Jo J-1J0 « 3jr2 



= P V, 



and 



\ dx dy dzf 



s f dpu 

 ~ s/tt' doc 



As the molecules going in the u + direction come from — die 

 &c, this leads to the same result as Prof. Reynolds obtains, 

 namely 



r v/tt dx 



This is really the same process as his, only that his takes up 

 several pages and is very complicated, owing to his divi- 

 ding his space into those eight regions and then even per- 

 forming his integrations at different places several pages apart 

 instead of all at once. 



Now I come to a point that I hope Prof. Reynolds will be 

 kind enough to explain; for I am sure he must have considered 

 it, and that there must be some reason for what he does, 

 though he gives none and, as far as I can see, does not notice 



