202 
DR. T. J. FA. BROMWICH ON THE 
Thus we get 
(7-41) 
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) ^ e-'. 
In order to interpret (7'5) for any axes of co-ordinates, we need only notice that 
{ — A, — B, -f-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 {9, <p) is given by (|-0, (p). 
Then the incident wave at 0 has the components of electric force 
and 
— cos 06'““ in the plane of incidence, 
+ sin 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 — acoB^O. Accordingly the components of force at P, in the 
reflected wave, are 
-I- — cos cos iKT perpendicular to r in the plane ZCP, 
2 r 
d 
— ^gi'-Kacosie-iKr perpendicular to the plane ZCP. 
These results agree with (6‘7) and (6‘9) of § 6 above. 
