Statistical mechanics 



71 



(163) 



T = K, 



. { dt e t{2 -\-2t — /-) 



= K 



where 

 (163*) 



; ät fit) 



o 



— t 



f{t) = e {2t-\- _ fi). 



This integral cau always be computed through mechanical quadrature, but a 

 more analytical procedure is to be preferred. 

 . Put t — qx, so that 



dx e 



qx 



x' 



{2x + 2qx^ — g-.r^^ 



and consider the transcendent 



(164) 



then we have 



» — qx 



dx e 



2~ ' 



1 + X 



— qx 



f (?) = 



J 1 +x-^ 



and generally 



<!>('%) = (~i) 



x''dx e 



qx 



1 -f x 



,„2 



so that 

 (165) 



T = {- 2f (g) + 22-™ + f"(g)}. 

 We easily obtain a differential equation for the function We have indeed 



or, if 



(166) 



y = 'K?) 

 _ 1 



We want an analytical representation of i^, which allows us to compute for 

 very great values of q (molecules) and for very small values of the same variable 

 (stars). 



