54 Conway—EHlectro-magnetic Mass. 
We can infer from this that the energy per unit of volume is represented by 
(8a)7{ V2(X? 4 V4 7) 4+ + B+ y7)}, 
which is Maxwell’s expression, and that the energy-flux is (47)", the vector 
product of the magnetic into the electric force, which is the Poynting flux. 
By similar reasoning the resolved part of the reversed internal forces 
must represent the rate of change of momentum of the system. We have 
in this case to evaluate 
— [Jar _Xp + ye — Bis]. 
After some reduction we obtain for the subject of integration 
(8a) V2\— daa (X? — Y? — Z*) — d/ay (2QKYV) — ajez (2XZ)}, 
+ (8a)"| — elon (a* — BY — y*) — d/ey (2a 8) — e/dz (2ay)}, 
+ (4a)! V0/at(y¥ — BZ). 
The interpretation of these expressions gives us the electric and magnetic 
stresses of Maxwell, and the fact that the linear momentum per unit volume is 
(47)'V~, the vector product of the electric into the magnetic force. 
By taking moments about any line we arrive in a similar manner at an 
expression for the angular momentum; and it is the moment of the expression 
for the momentum written above. 
A difficulty arises in the analytical working out of the above results when 
a surface-distribution occurs. As an example of the method of proceeding, we shall 
consider only one case, that of the equation of activity. 
The rate of change of energy of the system is the surface integral of the 
scalar product (in Hamilton’s sense) of the electric force and the current. 
The electric force is now the arithmetical mean between the values on each 
side of the surface, so that, using the same axes as in the boundary conditions 
of § 2, an element of the integral is 
SCOR NAP NA, 
which becomes, on replacing (¢,7:/3) by its value in terms of the forces, 
—w (87)" V2 (20” aL yy”? ate Z” ox! DXeZ aes y"” kas Jf?) 
P(A YS = [8 NIC ap 20) = (ay (G = @ CM ap IAs 
add to this 
(S7)'(6'+ B")(X"- X") - (Bx)(a! + a")(¥'= ¥") 
—w (8a) (a? ML B” ~ fea (BP), 
