spherical Wave of Light. 85 



= -^(A2+B2)sin/3. 



o 



It is obvious that this represents a displacement of the 

 same nature as the original displacement, namely along 

 the original axis of j. 



When ?2 =^ 3 we get no component. 



When ;2 = 4 the displacement at the origin assumes a 

 different direction, and we are therefore led to consider the 

 admissible values of ;/ to be 2 and 3. 



To determine the nature further — the original displace- 

 ment being sin/(^T— .t-) directed along the axis of jj/, the 



rotation is given by — -cos/(<^T— ,t'). And if we form 



the expression for the rotation in the secondary wave, and 

 then find the integral rotation at the origin, it should be 

 related to the original rotation as the integral displacement 

 at the origin is to the original displacement. The expres- 

 sions for the rotation in the secondary waves are : 

 2X1 = 0. 



2Y1 =/2^U_iros/|/;(T + 2Q + ^|/\^" 



2Z1 = -/2:-,U_iCos/-j /;(T + 2/,) + J -A^". 



We must resolve these along the fixed axes as before, and 

 integrate over the whole sphere. 



Thus 



X2 = YisinO 



Y2 = - Yicos0cos(^ + ZisirK^ 



Z2 = - Yicos0sin0 - ZiCOS(/). 



Pursuing the integration we now see that we get no com- 

 ponent corresponding to ;^ = 2, and that when ^2 = 3 the 

 resultant rotation will not have the suitable direction unless 

 A3 =63. 



