EQUATIONS OF PROPAGATION OF ELECTRIC WAVES. 
the point P in a spherical figure (fig. 2 ), in which Z represents tlie direction of pro¬ 
pagation of the primary waves, II the direction of r, NX is the great circle of wlncli 
Z is pole, NI is the great circle of which II is pole, and P is on NI })roduced so that 
z 
NP = NX. It is easy to verify that tlie direction cosines of the radius vector, drawn 
from the centre of the sphere to P, are 
n — Jia ^ 
1 -t n ’ r+^. ’ ~ ' 
Again, at a great distance from the plane, the contribution of the element of area 
cZS to (/, cj, h) is 
(— hn , + P + , — m — mn) -- ' k cos k {z — cf -f 7'); . . . (53) : 
-iirr 
and its magnitude is 
(1 + '0 4 :^ X cos K {z' ~ Ct -\- r) ] .(54) ; 
its direction miglit he shown by means of a constrnction similar to tliat used for the 
direction of the contrilnition to (n, r, ir). 
The le.sidt obtained by tSir (T. Stokes"'" woidd be expressed, in the notation here 
employed, by the statements that the magnitude of the contribution of the element 
(/S to {v, V, U’) is 
/.s 
y/(7/r + 71-) (I -f ii) - sin K (f — C( -f r) 
-\7rr 
. . (55), 
and tliat its direction is that whicli would be shown by the point antipodal to (Q, 
where PX and NI intersect (fig. 2). It has l)een pointed out by Lord UAYEEiont that 
* ‘Papers,’ 2, p. 286. 
t ‘ Wave Theory of Light,’ pp. 452, 453, 
VOL. CXCVIT.-A. 
E 
