23 



treated integral cos if» at llio upper limit), but becomes = 





h 



because cosh if? tlien is =r igO^ -. k. At tlie upper limit everjthiiif? 

 disappears, because then if' = <>. (Besides, the terins with odd powers 

 of If? still contain the factor sink \\\ which now likewise becomes 

 =r 0, because coshxY becomes =1 at (he up|)er limit. (Cf. further 

 the text of § 18)). We may, therefore, write: 



log' / 3(1 +P) 2 \ log' 



'ƒ=-- 



e. 



•f etc. - 



¥^. 





+ iT^^Jr2ö + ^*^- 



Let us now introduce the quantity y, determined by equation (6) 

 of the last paper but one, viz. 



d' M 



iu which, therefore, (p depends on the temperature (determined by 



Vsf-'^^')- ^^or 1 + ^y-YVj, we may write -^, because k" il-\-(f>) : 



S' f s^ 

 : (1 — ^-^z) may be substituted for Uf(i^=. (i-)-r/): ] (1+7 



with 



a'—s'' 



we get : 



'ƒ 



yi+F 



/,•^ For ttf 0,-^1:' we lind /.'^(I+zL^f : (I— /.'V/), so that 



•^1+7^' -IT + .-^7^ ITT + etc.) - 



HP 6 ^ 



1+P 24 



(1-F^)'^(9— l5Pv) 



(l-F(-/?)(8— 12^VA%'* 



in wliicli 



(tgO^ 

 log = /o^ I — -- + 



f//^^n 



1 = log 



+ etc. 



^' y ' |/l-Prp 



Let us now examine, what are the limiting values to which the 

 found integral approaches at high temperatures, and at low tempe- 

 ratures {(p near (p^=z^. : /;"). 



At high temperatures {(p = 0) log draws near to log 1^0, so 

 that all the terms with high powers of log are cancelled by the 



