302 
PEOF. H. M. MACDONALD ON THE EFFECT PKODUCED BY 
a zero electric current distribution on the parts of the surface in the geometrical 
shadow, and a zero magnetic current distribution on all parts of the surface. The 
components of the magnetic force at the point {x, y, z) due to this distribution are 
by the above 
a 
0 y 
Qy ^ 
where 
9 y 
dx r 
dS, 
9 a 
dy r_ 
dS, 
a = 2 {my\ — 7Ll3\), /3 = 2 {not.\ — ly\), y = 2 — 
= (^x-iy+{y-7]y+{z-cy, 
and the integration is taken over the portion of the surface on which waves from the 
oscillator are incident. Now 
whence 
a 
V'/’i 9ri 7\ 
V?’i di\ ri 
/ 
yi 
= 0 , 
- _ 2k n$ 9 
V ri 9ri rj 
2 k 717) 9 
V 7\ 9/-1 7\ 
2k 1^+7717) 9 
V 7\ 9?’i 7\ 
and therefore 
a = 
27tY 
y—7) 1^+7717) ^Z—^7l7) 
r, 
r 
,IIC (Vi-rj-r) 
9r9ri 
r7\ 
dS, 
K 
z-C 71^ x-^ l^+my 
r 7' Ti 
02 giK(V«-r|-r) 
97’9ri 7’ri 
X {f n{xy-y^) 9^ 
27rVJJ rr, 9r9ri 7-r, 
jlhe principal parts of these integrals are contributed by the elements near to the 
point for which the exponent of e-‘''(n+o ig stationary, that is, by the portion of the 
surface in the immediate neighbourhood of the point for which 7\ + r is stationary. 
The conducting surface being convex towards the point O, at which the oscillator is, 
if the point P {x, y, z) is external to the tangent cone drawn from the point 0 to the 
conducting surface or internal to the tangent cone and on the same side of the 
conducting surface as the point O, the point for which 7y + r is stationary is the point 
of contact Q of a prolate spheroid which has the points 0 and P as foci and touches 
