

\7r'--BoHg- 

 k 



The first integral yields \ f Bg^tg . — ^ 



l/p"— A-'Aü 



dx 

 as d Bqtq is again = . 



Bnt the second integral cannot so easily be integrated. As then 



X dx 



clBqtq is =^ — — — , the said integral becomes: 



{/x'-x.'V^f^x-^ 



P « 



-BgtgXdBgtg= ^ 7-^ Bg tg ,/ XdBgtg,,,- 



xa 



when we put (./•' — -I'o') ■■(}** — ,i'') = //% which causes .«^ to become 

 (/?y + .V):(l-h /A and .c"-—x„''io become ^(;;«_a;„'): (J-fy'). 

 With Bgt(ji/ = \p the last integral passes into-. 



\/p^ x^^ (* <öf ip ^ ^ r sin ip 



^ r taxb s r 



1/ «'^ h'H cos^xp 



V a' 



r sin \p 



IX sinx 



+ 

 



as V^p' — .Vo':/> in consequence oï p'^ = — , .ï'o', lience />' — .i',' 



a 



a' — s" 



s' s 



.t',', can be replaced by -, and .i'o^:/>' by (^«^ — .v^): a', while 



.» oS 



a* — s a 



further 



.5 o> ^' t.' 



a — s — s .^ a' — .s / s' 

 t' V' H T^ cos' i|> = — ^ [- - sin^ xp = — ^— 1 + ■- dn^ ip 



a' a a a 



and 5' : ((7^ — 5^) ^ /;^ The last transcendental, quasi-elliptical integral 

 can now easily (see appendix) be developed into a series, and then 

 be approximated. Previously we may observe that ,!'„, hence r/ (and 

 therefore also T), no longer occur in it, so that the result — like 

 that of the first part of (/j)i — will noi he dependent on 

 the temperature, as little as this was the case with /j (see § XV J). 

 It is further easy to see that the said integral approaches 



k sin tp , 1/ _ 



xpdyp = (i ip')„ ' =i Xi -'t" 111 the limiting case n ^1 



ƒ, 



Vk^ sin" ilJ 

 



