86 
of which the first should be appreciable, were it not affected 
by cos^(a^ - R), and in a practical case E, can not be con- 
stant to a degree of accuracy comparable with fractions of a 
wave length. 
In the second of the integrals, corresponding to integration 
over a sectional area, from every term such as 
X + Q + \ 
whenever p + q is an odd number, we should ultimately 
have infinite terms appearing in Y_i, Y__2, &c., terms which 
it will be remembered are affected by X, X^, &c., when com- 
pared with Yo. 
Y. 
As the result of solving the direct problem has been that 
we always arrive at a plane polarised wave, we may con- 
sider that the inverse problem is so far solved. 
We may state the problem in this way. To determine 
the form of functions |^^_l • so that the integral 
effect of the vibration whose components are rj, (T (from 
sources distributed continuously over a plane about the 
origin to a boundary given by r = E., where R is some 
function of 6 , the least value of which is indefinitely large 
compared with x) may be capable of replacing the vibration 
whose components are 
4 = 0 . 772 = hGOsp(at - x). 4 = CGO^p{at - x) 
in front of the plane, and may be null at all points behind 
the plane. And that the integral values of the components 
of the rotation and of the elements of the strain at any 
point may be equivalent to those in the plane polarised 
wave. 
Returning to the equation 
and considering the terms depending upon the upper limit 
r = R where the ratio cr/R may be neglected, we are simply 
to put x = o,y = Rcos 0 , 0 = Rsin 0 , and the integral is to vanish, 
