200 
DE. T. J. FA. BROMWICH ON THE 
Then in the immediate neighbourhood of O we can represent the incident wave by 
the components of electric force 
(A, B, 
where = 1, so that rn is the cosine and 7 i the sine of the angle of incidence. 
We have also the relation 
Bm + Cn. = 0 
because the electric force is perpendicular to the incident ray. 
The corresponding reflected wave has the components 
* (A', B', 
where 
A + A'= 0, B + B' = 0, 
and 
B'm—C'n = 0, 
so that 
C'-C = 0; 
these results follow by making the tangential components of force zero on the 
tangent plane 2 = 0 (instead of at the surface). 
It is now clear that, at the point 0, the components of the total force will be 
(7-2) (0, 0. 2G), 
and the normal differential coefficients of the total force will be 
(7-21) 
iKn{K-A.\ B-B', C-C') = 2«/cn(A, B, O). 
We shall now insert these values for 
TV and — in the general formula (7'13), 
CV 
including also the factor on account of phase-difterences at points near to 0. 
Since reflexion takes place only from the immediate neighbourhood of 0, the error 
introduced by this simplification will be small. 
