200 



DE. T. J. I'A. BROMWICH ON THE 



Then in the immediate neighbourhood of O we can represent the incident wave by 

 the components of electric force 



(A, B, Gltf**** 



where m 2 +n 2 = 1, so that m is the cosine and n the sine of the angle of incidence. 

 We have also the relation 



Bm + Cra = 



because the electric force is perpendicular to the incident ray. 

 The corresponding reflected wave has the components 



where 

 and 

 so that 



(A', B', G') 



E'm-C'n = 0, 

 C'-C = 0; 



these results follow by making the tangential components of force zero on the 

 tangent -plane z = (instead of at the surface). 



It is now clear that, at the point O, the components of the total force will be 



(7-2) (0, 0, 20), 



and the normal differential coefficients of the total force will be 



(7-21) w(A-A', B-B', C-C') = 2n(A, B, 0). 



We shall now insert these values for w and -^ in the general formula (7' 13), 



CV 



including also the factor e(y+') ) O n account of phase-differences at points near to O. 

 Since reflexion takes place only from the immediate neighbourhood of 0, the error 

 introduced by this simplification will be small. 



