790 Prof. J. H. Jeans on the 



where e= Hence, knowing the current i at time t\ 



nix & ' 



the value of i 2 , the current at time t 2i i. e. after an interval 



0, is 



where j is a quantity of which the u expectation " is zero. 

 Similarly, since the motion is reversible, the value of i x is 



-'J ,-*$ 



=i'e~"+f, 



where f has expectation zero, and has no correllation with j. 

 Putting in these values, equation (36) becomes 



A 2 + B 2 =f JJ i' 2 e~ 2e9 cos 2 P 6 d(26) dt\ . . (39) 



the terms in j, f and jj' being omitted because, as their 

 average value is zero, they vanish on integration. The 



exponential e~ ~ e9 vanishes very rapidly as the interval 29 

 between t ± and t 2 increases — this is the mathematical expres- 

 sion of the fact that there is very little correlation between 

 the values of i at intervals of time far apart. Hence we may 

 integrate with respect to from — go to + co, taking 



always positive in the exponential e~ ~ e6> , and so obtain 



t'=t 



t'=o 



e z +p 2 m 



by equation (32). Replacing e by its value, this gives the 

 emission of the element do in the form (cf. equation {28)) 



(JSv -rh^ p * mdp ) tdv - ■ - (40) 



1+ NV 



This, as before, must be equal to the absorption given by 

 expression (34). The proper value for c is now that calcu- 

 lated for continuous motion, and given in equation (10). 

 Thus the absorption must be 



" i-i — 



