174 I^R- James Bottomley on 



b for inn, and c for inn — fA, Since P, the value of/ at time 

 /=0 is supposed to be known, if/ be expanded in powers 

 of/ by Taylor's theorem, it will be easy by means of (58) 

 to obtain the coefficients of the successive powers of t', the 

 following is the expansion as far as the fourth power 



p = P - a(e''^ - E'^)t + a2(e^^ - £'^^)(6e^^ - ce*=^)^ 



As in previous examples particular values may be 

 assigned to the three parameters a, b, c, giving rise to 

 distinct solutions of (58). Suppose that the action of light 

 on the body A is of such a nature as to discharge the colour- 

 and convert it into a perfectly colourless medium, in such a. 

 case 



r/i = 0, a = , 6 = 0, c = — u, 



and equation (58) may be written in the form 



dp -f^P ^r.q\ 



^ = -a(l-c ), (o9> 



of which the integral is 



or if the constant C be determined by the conditions />= P' 

 when /=0, we may write it in the form 



Another variety of the problem will be as follows : suppose- 

 the solution of A to be perfectly transparent for the kind 

 of light under consideration, then fx will have the value 0,,. 

 and the letters b and c in (58) will have the same value 7rm,.. 

 hence (58) will now have to be written 



