218 
MR. G. H. LIVENS ON THE 
In the main the details of the variational calculation possess no novel features and 
need not here be elaborated. There are, however, one or two terms which require 
careful handling, especially when finding the variations due to the alteration of position 
of the matter. 
The variations of terms of the type 
div Vdvy [Pf’m]) 
due to variations in the position co-ordinates of the elements of matter to which the 
vectors P and are attached should not be performed until the differential operators 
affecting the P function are eliminated by an integration by parts. If we bear this 
in mind we shall find that the final result for the variation consists of terms at the 
time and space limits, which require separate adjustment, together with 
- - ( 8r, 
Curl Ai, 
c dt / 
dP 
dt 
1 
-( 
c 
Curl P 
dt 
i(Jr.V)(Curl A„ [P,g) + 1 (l, 
, I 
-t - ((^r, 
c 
Curl A,, ^ 
dt 
+ - ( 
G 
Curl 
dAa 
dt 
+ -{^rJ7) (Curl As, [IrJ) 
+ w,+ ( _V^._ 1 ^ + i Curl AJ, JP 
+ (- ^ - - [»'«■ Curl Aj], (?I 
\c dt C 
where in the terms (Sr^V) (Curl Ai, [PrJ) and (dr^^V) (Curl Aa, [IrJ) the vector 
/ 3 3 0 \ 
operator V whose components are — > — > ;:r) presumed to affect only the 
\ dx dy dzj 
functions A, and A 2 . 
The variations which determine the virtual displacements of the electrical 
and material elements and the variations (5E, dB, ^P, ..., can now be considered as all 
independent and perfectly arbitrary, and hence the coefficient of each must vanish 
