spherical Wave of Light. 65 



Now turn the axes and the plane of yz until the new 



axis of y is in the direction of the original displacement, 



then, referred to the new axes, the components of the 



disturbance are 



U + U' = ^(/i +/2Y +/3Z +/,Y2 +/5 YZ +/6Z-^ + &c.) 



(V + V')cosa(W + W')sina 



= «(^i + .^aY + <^sZ + 04Y' + 05YZ + ^eZ^ + &c.) 



(W 4- W')cosa - (V + V>ina 



= ^(4/1 + ;^2Y + ;P3Z -I- ;i4 Y^ + ;/.5YZ + i^gZ^ + &c.) 



where 



Y =J^'coso + isinct 



Z = ccosa — ji'sinct. 



Hence, as we include all the powers ofj^ + ^r^ and Y- + Z'' in 



the functional part, we may conclude that 



/l=/4=/5=/6=&C.=0. 



<^2 = </>3 = 04 =" &C. = 0. -i/zs + 06 = 0. 



^2 = ^3 = ^6 = &C. =0. \//4 + ^5 = 0. 



And therefore that the displacement will take the simpler 



form 



U = ^cosa { /a J +^? } \ 



V = «COSa{(/)i-;//4>'2 + 0632j I (j) 



W = ^COSa { ;//! + 4/4/ - </>6J^'^} ) 

 But this gives merely the form of disturbance suitable 

 for resolution, and does not distinguish the forms for 

 representing suitably the disturbance along the different 

 axes. We may consider it obvious that ^i = when the 

 displacement is along the axis of y, the others will be con- 

 sidered later, when we shall show that/3 = 1/^4 = 0. 



§2. 

 I shall make use of the solution of the equations of the 

 vibration of light given by me in a paper bearing that title 

 (Proceedijigs of Camb. Phil. Society, vol. 5, page 279), and 

 the suitableness of this solution will receive strong support 

 in the course of the paper, from considerations arising from 

 other circumstances than those detailed in that paper. 



