144 Mr. J. C. Maxwell on the Dynamical Theory of Gases. 

 ascertained when n is given, and B 1 and B 2 may be found by 



2 



multiplying A, and A 2 by ( K( ^^ M -) "V^. 



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 ^?N 1 and dN 2 will be 



n— 5 



It will be shown that we have reason from experiments on 



the viscosity of gases to believe that n = 5. In this case V will 



disappear from the expressions of the form (3), and they will be 



capable of immediate integration with respect to dN x and e?N 2 . 



If we assume n = 5 andput a 4 = 2 cot^^anda? = \/l — • tan 2 <£ cosi^, 



elf 



2 -*= Vc°s2</> J^ ^_ sin2 ^ ?in2 ^ 

 =v / cos20F sin(p , ...... 



(14) 



where E s i n(p 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 x and A 2 . 





I. 



Distan ° 



9. 



sin 2 9 



sin 2 20 



(p. 



of apse. 



sin- 2^ 



sin 2 2(p 



O 1 







infinite 



infinit e 



O 1 















5 



2381 



2391 



31 



•00270 



•01079 



10 



1658 



1684 



1 53 



•01464 



03689 



15 



1316 



1366 



4 47 



•02781 



•11048 



20 



1092 



1172 



8 45 



•05601 



•21885 



25 



916 



1036 



14 15 



•10325 



•38799 



30 



760 



931 



21 42 



•18228 



•62942 



35 



603 



845 



31 59 



•31772 



•71433 



40 



420 



772 



47 20 



•55749 



102427 



4] 



374 



758 



51 32 



•62515 



•96763 



42 



324 



745 



56 26 



•70197 



•85838 



43 



264 



732 



62 22 



•78S72 



■67868 



44 



187 



719 



70 18 



•88745 



•40338 



44 30 



132 



713 



76 1 



•94190 



•21999 



45 







707 



90 



1-00000 



•00000 



A 1 = J47r«d'« sin 2 6>= 2-6595, 

 A s =jW* sin 2 26= 1-3682. 



• • • 



(15) 

 . (16) 



