'p = rie-*" 



168 Dr. James Bottomley on 



a fE^^'^^dt^at, (47) 



and for Ui we have the value m~'^^ ; by substitution in 

 (46) we obtain 



. ar - a-j iPaf / ~^dt - raj 



+ 0(^(1 —dt-r^ -^x^n -^dt-r^ + kcXX 



The values of rj, rj, n, &c., are to be determined as 

 follows : let the integration with respect to t be effected^ 

 and then in the last expression make /=0 ; then if we 

 substitute for/ its initial value we shall have 



P 



and the coefficients of the remaining powers of x take the 

 value ; hence ra, i\y &c., will be the values of the integrals 



/ 1) dt, I -^dt, (fee. 



when t has the value 0. Finally we obtain as a solution 

 of (15) 



p = ^^ Y ~~Y ' ~ T / ^ ~ T / ' " J* 



o w o 



I shall now consider some particular cases, depending 

 upon special values given to the letters a, b, c. 



In the first case, consider a to have the value ; putting 

 this value in the last equation we obtain, 



P 



The relation, ^ = 0, implies the relation, ju = 0; in this 

 case the body A absorbs no light ; as B is supposed to be 

 formed by the light absorbed by A, in this case it is plain 

 that no B will be produced, and that the distribution 

 of A through the cylinder will be the same at all time, as 

 it was initially ; in this particular problem it was considered 



