SCATTERING OF PLANE ELECTRIC WAVES BY SPHERES. 203 



It is easy to modify the general formulas (7 -5) so as to cover the case of waves incident from a point 

 source (say at distance s from the point of incidence). 



Then 



i a = 3? + (ms - yf + (ms - )" 



= s 1 - 2s (my -t- m) + x 1 + y* + z*. 

 Thus with the usual approximation of geometrical optics 



Similarly 



= s - (my + nz)+ {x 2 + (ny - KHZ}*}. 



R = 



Now z is of the second order in comparison with x, y ; and so we can write 



/ j 



Thus here we find 



J iKiur 



where 



r n\r 



, r2 being the distances of the focal lines (of geometrical optics) from the point of incidence. 

 Thus now the principal parts of the reflected wave are given by 



assuming that r is not close either to r\, or to r a . 



The results of the foregoing analysis depend on the tacit assumption that n is not 

 zero ; and as a consequence the character of the approximations will change when n 



