SCATTEEING OF PLANE ELECTRIC WAVES BY SPHERES. 
‘203 
It is easy to modify the general formulae (7 • 5) so as to cover the case of waves incident from a point 
source (say at distance s from the point of incidence). 
Z 
Then 
= x^ + {ms - yf + {ns - zf 
= s^-2s {my + nz) + x^ + y‘^ + z^. 
Thus with the usual approximation of geometrical optics 
Si = s - (my + nz)+ i {x^ + {ny - mzY}. 
Similarly 
2s 
R = r-{-my-nz-\- ^ [x^ + {ny + mzy\. 
Now z is of the second order in comparison with x, y; and so we can write 
Thus here we find 
Si + R = s + r- n {ax^ + 2f3xy + yy"-) + ( ^ + ^V)- 
i«(si + E) = e-i<(s+r) 
where 
f- 
LKUiT 
+Y -- 
n) 
= - - 
*\r ril\r 
Ti, Ti 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 
(-A. -B. +C)e-y{('l-r)(l-0S 
assuming that r is not close either to r^, or to ? 2 - 
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 
