368 
PHYSICS: H. BATEMAN 
1 t 
4:7rg = q ip - ~ (v X p) - (v X q) 
c c 
V = r (r) \x - ^ (r)] + V (r) (r)] + ^ (r) [2 - ^ (r) ] - (/-r) 
= r [(2; • 5) - c\ 
= [a;-Kr)]2 + [); - ^(r)]2 + [2 - T (r)]^ = (/ - r)^. t> r. 
In these equations denotes the velocity at time r of the moving point 
P whose coordinates at this instant are ^(r), t/(r), ^(r); x, y, z are the 
coordinates of an arbitrary point Q; 5 is a unit vector in the direction of 
the line PQ; p and q are vectors representing the electric and magnetic 
moments at time r; / is the time, and c the velocity of light. 
From these equations we find that 
ExH = y-s[g*'gt-{s'g'){s' g*) -i{s'{g^x gt)}] 
where is a certain complex vector and g*o the conjugate complex 
vector. A similar expression may be obtained in the case of an elec- 
tromagnetic pole and also in the case of the combination of an electro- 
magnetic pole and an electromagnetic doublet. In the latter case the 
appropriate expression for is 
where 
h = ^' ■\- mi)' + f — (z^ X 2^0> 
c 
and 
m = h-\r ie. 
Here 4xe and ^-wh are the electric and magnetic charges associated with 
the pole and primes denote differentiations with respect to r. 
Calculating the rate of radiation / across a very large sphere whose 
centre is at the moving point P we find that / may be represented by 
the real part of the following expression 
+ 3zi'2 -gO-^^iv- V") {h ■ go) + 2 v''^ {b -go) + 2 iv' • V") {g'-g,)-\-\ v"\g ' go) 
+ I ■ (S' • sO + 16 {V ■ vy {b • go) + v'\v ■ V') (g' ■ go) 
5 (c^ — v^)^ I 7 
