AN OBSTACLE ON A TRAIN OF ELECTRIC WAVES. 
313 
where 
A, = K (cos^^ cos^i// + sin^v//), Bj = 0, 
Di = [2 cos (f){ — C sin^xfj + 3L sin^i// cos (f) cos xjj -{— 3M sin xjj cos^^ cos^v/; + D cos^ ^ cos^xp) 
+ f (I/Ri^— 1 /R^)sin xjj sin (p cos^ (p] x [cos^(p cos^xp + sin^i/;)”®''-, 
and the principal part of the integral 
"g--(0+r)^/g 
is equal to the principal part of the integral 
g-iK(R] + R) j j g-V2‘'<A]f--Vf,tK (C,Js+3L,J5S)+3Mifv)^+Di7)3) 
that is to the integral 
^- 2 g-iK (R, + R) 
which is equal to 
^-2g-i/c(Ri+R) ^ 
J — CD J — CT 
that is to 
whence 
.(R. + R)M ^ 
^2k ' 
-V 2 
Vs /^,\-V3' 
.,6k"' V 6k" 
I = 7r’-K-"=2"»3-V3r (i) Ar’/^Dr^ 
where Aj and Dj have the values given above. Therefore at the point Pj the 
principal 2 :)arts of the components of the magnetic force in the reflected waves are 
given by 
a, = - ^ 6-v^r (i) r (1) Arcos <p [^2 + 2n (nmi-n/x,)]/R3, 
13/g 
= - ^ 6-Vcr (i) r (i) Ar’^^Br''^ g..(w-R.-R)+ T cos </> [-X 2 + 2n 
^ 6-v^r ( 1 ) r (i) Ar'^-^Dr'^^ ^‘^(v^-h.-r). = ^ (?^,-niX,)]/RiR. 
Similarly, at the point Pg, for which R = the principal parts of the components 
of the magnetic force are given by 
«() = -~~y^ *'* f (i) P (^) Bi v=Ci V 3 g‘*(’^* 4 cos 0 [/a2+2n 7 ipi)]/RiR, 
/3, = - ^ 6-v^ r (1) r (1) g-(v^-R.-R)+ f ^ [-X 2 +2?i 
% 
= - ^ 6-Vc r ( 1 ) r (1) Br’V'Cr'^^ g-(vt-H.-R)+ f ^ ^ 2 n (^/r,-mX,)]/RiR, 
2 s 
VOL. CCXTI.—A. 
