THE DYNAMICAL THEORY OF GASES. 41 



It is evident that 6 is a function of a and w, and when n is known 6 

 may be expressed as a function of a only. 



so that if we put 



r = I 4:irada sin 2 0, A 3 = I vada sin 2 20 ................ (13), 



Jo Jo 



.4! and A, will be definite numerical quantities which may be ascertained when 

 n is given, and B l and S, may be found by multiplying 4, and A 3 by 



Before integrating further we have to multiply by V, so that the form in 

 which V will enter into the expressions which have to be integrated with respect 

 to dN t and dN t will be 



It will be shewn that we have reason from experiments on the viscosity 

 of gases to believe that n = 5. In this case V will disappear from the expres- 

 sions of the form (3), and they will be capable of immediate integration with 

 respect to dN l and dN t . 



If we assume n = 5 and put a* = 2 cot" 2<^> and x = Jl tan 1 < cos |>, 



IT 

 /"I fijj 



^-0Wcos2(f> /, . , .-s-rr 



2 r J o v 1 -^ sin <p sin ii }. 



(14), 



where ,f 8ln ^ is the complete elliptic function of the first kind and is given in 

 Legendre's Tables. I have computed the following Table of the distance of the 

 asymptotes, the distance of the apse, the value of 6, and of the quantities whose 

 summation leads to A 1 and A v 



VOL. II. 6 



