in the Kinetic Theory of Gases. 313 



the integration being over the spherical surface, described 

 about C, as in (6). 



Now, if \ c fju c v c be direction-cosines of OC, and OP = a>, 



Xco - \(V — R cos E) + v/l-X c 2 R sin E cos y, 



where E is the angle OCP, and y is the angle between the 

 plane OCP and a fixed plane, and therefore the second term 

 disappears when we form the integral 



fldSu,*^ 



Also, since <» 2 = V 2 + R 2 — 2V R cos E, we may write, ex- 

 pressing Taylor's theorem, 



o) \/V 2 + R 2 ' 



where 



d 



Thus we obtain 



(TxrfS=X flX (A) r^E27r sin E(V-R cos E>- 2VR qme, jl™^!^ 2 ). 



The integration according to E can now be effected in a series, 

 and with the assumed form of </>(/*Ma> 2 ) no negative powers 

 of V or R will appear. \\a;d$ can be treated in the same 

 way. 



By an extension of this method we might form — ■£- in a 



at 



series of positive powers of co, and we should then have 



theoretically sufficient data for determining the coefficients 



C , Ci, &c. in the expression for <£(AM&) 2 ) by equating to 



zero the coefficients of powers of co in the expression 



dt + ~dt 



In order to find ^(A) we resume the discussion of the equation 

 d\ 

 dt 

 19. If in the expression 



dt + ~dt 



OXv) 1 rdYe- hM+mY2 Y* r^Re-^ M+wE2 R^(/ i MYNn 2 ) 



I 7T 



all the integrations were effected, the result would be in- 

 dependent of h, whatever the form of </> might be. As we 



