1203 



and multiplication bj RT, as Keesom's B represents = bg — {a • RT)'], 



when N X 7» ^^r ó' --=: ^ X 4 in = {br,)^ is put (Keesom writes n, where 



R , . 



we have put iV), and for— v (=: our N X ^) « is written (Av is 



V R ^ 



namely = -—=:- r : /^T). 

 «i k 



{ a (a \^ 



For 9 = 00 this becomes a = {b,,)^ " ( "^ + ^ ;^ + i ( ;^ J + 



in agreement with what we found in § 10, as the sphere of attraction 

 becomes infinitely thin for q = cc, so. that /•„ = rj = 5, hence r = 1, 

 When with Keesom we assume q =z 4i, the functions of the tempe- 

 rature become therefore : M 



+ • 



(12a) 



hence f{a) still less pronounced than ours with the coefficients \, \, etc., 

 so that the difference between the two functions of the temperature 

 f{b) and f {a) would become still greater than ours, and the slow 

 decrease of attraction over a greater region, according to the 

 law 9 = 4, would therefore lead to still more unfavourable results 

 with respect to the experimentably found equality of the two 

 functions of the temperature (at least for 7\. and Tb) than our 

 assumptions. 



The only factor of distribution that would yield ö^rwa/ expressions 

 for the two functions of the temperature, is 



(1 + <9 P,)-2 



instead of e^^^'\ For then the integral of work JS" becomes: 



=ƒ 



ra 

 d(NPr) f N 1 



dr ^ ' y (9 I + aPr 

 =RT[ -— - 1 



\—6M J 1 — «//??' 



1) With 5 = 4 the factor would become ^{h(j)^'x, hence y = 4, which corre- 

 sponds with a mean value rj =:= 1,6 s (see § 9). 



83 

 I'loceeiiings Royal Acail. Amslenlam. Vol. XX. 



