EQUATIONS OF PROPAGATION OF ELECTRIC WAVES. 
43 
which is of order cos k (c^ — R), the right order when R is great. We treat 
every term exactly as this term has been treated. The second line of is of 
order R“^ cos k {ct — R), and is to be rejected ; the tlhrd line gives 
TTCC'^ xh/ sin k (ct — R) 
T W R ’ 
and the fourtli line gives 
ircc^ y + {z — rj- sin k {ct — E) 
T R R^ R ■ 
Hence the most important part of at a distance from the a]:)erture is 
-16 C 
11^ 
cos K (ct — R) — 7] sin K (ci — R) J- . 
In like manner the most important part of ^ 4 . is 
f ^ K^x (z — ?’f|) 
16 
R'^ 
cos K {ct — R) — ^ K {*-■■ — 
and all the terms of are of a higher order than these. 
The results just obtained can he written 
fCf^ Z _ V 
(m+, 10+) = j cos K{ct — R) ~ P sin k {ct — R) 
■ \ 11’ 1 
iw W ('»5) 
By a similar process it may he shown that the approximate forms foi- /+, (j+, // ^ at 
a great distance from the a})erture are given by the equation 
o 4, 
fc'^a^ 
n, {.(, Z ~~ 1' 
{/+, (/+, h^) = 1 sin K {ct — R) + p cos k {ct — R) 
!x{z - r^) y (z - r„) 
IF 
IV~ 
n3 / 
u / 
(96). 
We observe that the value of the magnetic force {u+, u'p) at a great 
distance is 
('R, R, Rp) c sin K (c^ - R) + p cos k (ct - R) I . (0 
16R 
— ? 
y X 
R’ R’ 
(97), 
SO that the factors, that contain f, are the same for the electric and magnetic forces at 
a great distance from the aperture. 
36. Now let I, m, n l)e the direction cosines of the normal to a closed surface S 
drawn in a specified direction (inwards or outwards); then the rate at which energy 
