650 Prof. J. H. Jeans on the Analysis of 



Hence A = A /a, where A is a constant. On differentiating 

 (30) with respect to a, we have 



r e _ aG -JG-i G dG = _ Bl = 2A i K 2 (iri). 



When p is large x is large, so that this integral vanishes 

 with j9 large in the same way as e~ V* or <? -2 v ( ab ). Hence on 

 integrating with respect to ft it is found that F F vanishes 

 when p is large, through the exponential 



e -2 s /(2 P h^) Qr g -2 v '(^i/ET) t g § § ^ 31 ) 



As in equation (1) we have 



F P = 47r^V 2 E P , (32) 



and it is known from experiment that when p is large 

 E p vanishes through the exponential 



e-wlK? (33) 



These results could only be reconciled if we were at liberty 

 to suppose that c p could increase, when p became large, in 

 the same way as the exponential ^V RT . But all evidence, 

 both theoretical and experimental, indicates that c P must 

 decrease when p becomes large. 



10. It can be seen that the difficulty which has been dis- 

 closed by the foregoing analysis is inherent in any theory 

 which refers the origin of radiation to orbits in which 

 Maxwell's law of distribution of energy is obeyed. For the 

 radiation from a single orbit when p is large must, by a 

 general law *, be of the form e~w^ in the limit, so 

 that on integrating over all orbits we obtain an integral o£ 

 the type (cf. expression (18) 



J< 



- p f(G)-hmGc d Q rt 



For large values of p the whole value of this integral comes 

 from contributions from that value Gr of G which makes the 

 index of the exponential a minimum ; this is given by 



JP/'CGo) = hm = f^> 



so that G is of the form </>(i?T) , and the integral becomes 

 proportional to 



-Plf(G o )-<*of'W\ or e-^^ T \ 



For this to be of the form e~ cp l^ required by experiment, 

 F(^>T) would have to be of the form c/T, which is of course 

 impossible. 



* Phil. Mag. [6] xvii. p. 250. 



