346 
PROFESSOR J. H. POYNTING ON THE TRANSFER 
„ K 
But since f ’= P, with corresponding values for g and li, and a=ij.u, b = g/3, c = gy, 
substituting, the energy becomes 
^.flf( P!+Q 2 +R 2 )^ &+ £ \\\^+^+f)^dydz . ... (\) 
Let us consider the space within any fixed closed surface. The energy within this 
surface will be found by taking the triple integrals throughout the space. 
If any changes are taking place the rate of increase of energy of the electric and 
magnetic kinds per second is 
K 
47 T 
dxdydzAr 
p 
4 : 71 " 
( 2 ) 
Now Maxwell’s equations for the components of the true current are 
> df , dg 
U =P+di V ='i + it 
, dh 
w=r-\~— 
~dt 
where p, q, r are components of the conduction current. 
K di 
dt ^ 
df . K dP 
But we may substitute for — its value -——, and so for the other two, and we 
obtain 
K_ tfP 
47 r dt 
— U —p 
K d Q 
K dK 
• (3) 
47r dt 
—w—v 
Taking the first term in (2) and substituting from (3) we obtain 
K 
47T 
P hp + 11 dxdydz- 11 j ; P(w -p) + Q(u — g) + R ( iv- r) } dxdydz 
= [[[(Jdii+Qv J rR,w)dxdydz—[[[(Pp-\-Qq-\-l&r)dxdydz .... (4) 
Now the equations for the components of electromotive force are (Maxwell, vol. ii., 
p. 222) 
