AN OBSTACLE ON A TEAIN OF ELECTRIC WAVES. 
331 
The components of the electric force at the point x, y, z due to this distribution are 
X= - 
V 
4lTTLK j J 
ff 
'9' ^ ,9' 9^ /A . \ 1 9^ / 
0rr dy dxdz^^ ^ ' 
de rriY 
LK 
477 
— ^ 1^1 (//u-i—mXi)+ ^ {nz/iY + Z (Xi^ + /x/)} 
rri 
Y= - 
47rtK: J 
9' X . 9^ 9^ nx , X 1 3" ■ 
Lfa- dy 3^ dy dz ^ V=> d^ 
IK 
rrjV 
,... (X^+p-i’i + w/iiVi} + ^ ^1 (^/Ai-wXj) 
■fm 
Z = - 
X 
47rtK’. 
t/c 
r7\ 
LK 
cZS, 
_ rrjV 
gi/<(Tf ri )-)^g 
~ Att ff {'^i'lK + HK^ + H-i)} - {m {ki +iXi) + nfXiVi} 
retaining only the principal parts and writing 
{x-i)fr = X,, {y-v)tr = y2, {^-Cjlr = v^, 
these are equivalent to 
X = —j" j" [—z/j (Xj + Xg) (^Xj+ 'n?p,j + 7 ^X 2 (X 1 X 3 + P. 1 P 2 +^ 1 *^ 2)—'^^1 
+ (/^i -wXi) (p,2Vi -/ 41 V 2 )] 
7Ti 
,1). (Vi-r,-r) 
dS, 
r,r 
Y = ^11 [ —7^2 (Mi+A'-s) (^Y + '^P,l +^^^ 1 ) +'>'1/^2 (Y^3 + /^1/^2+^'X — 
WP-1 
+ (//xi —mXi) (vaXi—viXg)] 
,1* (Vf-n-r) 
Ar 
c^S, 
Z = ^ |j [{X2(Xi + X2) + /X2()U.i + /X2)} (/Xi + mp.i+nVi)+7lV2(XiX3 + P-l/^3 + ^1^2) — 
-\-{lyi 777 X 1 ) (Xa^i P'2^i)l 
CK (Vi-rj-r) 
cZS. 
7-17’ 
The principal parts of these integrals are contributed by the elements in the 
neighbourhood of the points for which r^ + r is stationary, and, as in the case of the 
conducting obstacle, there are the two cases when the point Q, for which 7’Ari is 
stationary, is on the straight line OP and when the lines OQ, QP make equal angles 
with the normal to the surface at Q. In the first case, the point P is on the side of 
the obstacle remote from the oscillator and at the point Q 
X 2 — Xi, 
y2 — y-if 
2 u 2 
V 2 = vi, 
