202 DK. T. J. I'A. BROMWICH ON THE 



Thus we get 

 (7'41) ue 



Hence, using (7 '4), we see that the principal part of the reflected wave is 

 given by 



(7-5) (X, Y,Z) = (-A, -B, +C)<r- . , '' ''\! 



In order to interpret (7 '5) for any axes of co-ordinates, we need only notice that 

 ( A, B, +C) represents a force numerically equal to the force in the incident 

 wave ; and that the new force is perpendicular to the reflected ray, arranged in such 

 a way that the tangential components are opposite to those in the incident wave. 



We can apply the formula (7 '5) to the problem of 6 at once ; clearly p = a. 



The point of incidence corresponding to the scattered wave (#, 0) is given by (%6, <j>). 





and 



Then the incident wave at O has the components of electric force 

 cos (j>e" a oos ** in the plane of incidence, 

 + sin 0e" acosje perpendicular to the plane of incidence. 



Further, the r of formula (7'5) is measured from O ; to compare with 6, we take 

 r to be the distance CP, measured from the centre of the sphere. Thus we are to 

 replace r in (7 '5) by r a cos ^6. Accordingly the components of force at P, in the 

 reflected wave, are 



+ 7 -cos <t>e*" aeoa **" perpendicular to r in the plane ZCP, 



and 



- ^-sin e 3 " cacoaJ8 -" tr perpendicular to the plane ZCP. 



t 



These results agree with (6 7) and (6 '9) of 6 above. 



