AN OBSTACLE ON A TKAIN OF ELECTRIC WAVES. 
307 
Now 
AiBi = {(E,A^ + R“^) cos <^ + A + B cos^ </)}^-(A-B cos^ cos^ (^, 
and writing 
A—B cos^ (j) = 2H cos (f) cot 2t//, 
this becomes 
A,Bi = cos^<^(B-^-/r^) 
where 
(RA^ + /i~^) cos (^ +A + B cos^ (^ —2H cos (f> cosec 2i/; = 0, 
(B.r^ + / 2 ~^) cos ^ +A + B cos^ (j) + 2H cos (f> cosec 2</; = 0, 
and 
2H: = (/i ') sin xjj cos xp, 
+ cos^ xpf fi + sin^ xp 1/2 + 2B cos fp = 0 , 
Bi“^ + sin^ xpf f-^ + cos^ xpf f2-\-2A sec (p = 0 , 
cot 2d = —B“^) (cos^r// —sin^i//cos^(/)) 
+ —(siiP xp—cos^ xp cos^ (p)} /(/A^ —/A^) shB xp cos <p. 
The value of the principal part of the integral 
e"‘''(’■'+'■) dS 
is now given by 
that is, 
or 
I = ;,-2g-..(R. + R) 
I = 
CO ^ CO 
f e-de 
J — 00 
277 
(A,B,y^ 
g-iK(R] + R) 
IK 
I = 
277 
LK COS (p 
and therefore the principal parts of the components of the magnetic force at the point 
[x, y, z) due to the surface distribution are given by 
an = — 
IK 
V COS (p 
{(/£o + + niP) {y - ^0) + n {y^z - i^y) }/R'Rd, 
^ {(^^o + WT^o + ^Co) {x-^<P) + n (^u2-4a.’)}/R^R-, 
V2«‘/^(Vi-R,-R) 
{^^( 77 oa;-|■o^)}/R"Rd■ 
2 R 2 
