12 



This gets near to loijavithnücaUy injinite. Now the limits p and 1 

 are evidently = and 1, so that lies between (90°) and 0°, hence 

 comprises the whole region. 



When n^l {a ^ s), (a,), does not become = ao in 13''. For 

 as (p can never become greater than 1 : ^'' = (1 — n'):ji^y (ajj remains 



evidently smaller than to X , i-e. <^ (o X ^. Then (?i=3l — d) 



/o(/ (1: ïi") becomes 2 (1 — ?i) in (13''), «o that (aj, will approach 



(o X loq — ■ 



■ 1/1— Pr/^. 



If on the other hand ii^O {d lai-ge with respect to s), then (a,), 

 approaches to x ^p in (13«), whereas this quantity will approach 

 infinite X {loif-iuimiief in (13''), i.e. will greatly increase, when the 

 tenjperature becomes lower. 



^ XIX. Calculation of a. 



When we finally add the part of a that is independent of the 

 temperature, viz. a^ = a^ + (aJi according to (12), to the part that 

 is dependent on the temperature according to (13^'). ^hen we get at 

 hlqh temperature, taking io:= ^y^ {0,^)^ X « into account (compare 

 TXVI): 



a =^ 



7i{\—n') 



(l-e^Oi-V + 



1 



ii>,).<^ 



(l_f;0in'4- 



n 1 

 1 + " J 



or also 



{fp - 0) a = a, 



1 + 



in which therefore 



a =: 





= a^(l +ytr) , (U«) 



2n{l—7i') '-"^ ' • (l_en)(l+n)V,7r' 



We remind the reader of the fact that the coeiTicient e (see § XVII) 

 has the value 1 for n = l, the value 8:.t'=;0,811 for ?i = 0, and 

 the value 0,845 for 7i = 0,6. Further « = MN, in which M is the 

 maximum value of the function of force f(r) at contact of the 

 molecules, and N the total number of molecules in the volume v. 

 At low temperatures (r/-- = 7-, = 1 : F) we get according to (13*): 



log V„. 2 



(7) - ff^) a = a, 



1 + —^ log ^ 



(146) 



