52 Conway—FEleetro-magnetic Mass. 
the same system, the other arising from external sources. Then the principle 
we proposed to use is that ¢he internal forces when treated according to the ordinary 
laws of statics will amount to a force and couple equal and opposite to that due to 
external sources. Conceiving an electron to be a rigid electrical system, we 
reproduce the properties of Newtonian mass; whilst from more general systems 
we arrive at the conventional expressions for induction coefficients, energy, and 
energy flux, momentum, linear and angular, and the stresses of Maxwell. 
I].—Tue Crreuitat RELATIONS. 
The electric force (X, Y, Z) and the magnetic force (a, 8, y) are connected 
by the circuital relations in free ether 
V%olot(X, Y, Z) = Curl(a, B, y) 
— d/ot(a, B, y) = Curl (X, Y, Z). 
These equations involve the facts that OX/dr + 0V/oy + 0Z/0z, and 
da/dx + OBloy + dy/ez, are independent of the time. In the scheme of 
Maxwell, we take these expressions to be zero. 
If the electricity has a volume-distribution p, the above equations have to 
be modified. ‘The vector sum of the products of each charge in a volume 
element by its velocity is a certain vector (7%, %, 7;)d7, where dz is the volume 
element. The fact of the persistence of electric charge gives rise to the 
equation of continuity 
Oplot + 0%,/0x% + 02,/dy + 013/02 = 0. 
The modified equations are 
Vo/ot (X, IY 4) + 4a (a, ay 73) = Curl (a, B, Y)s 
— d/ot (a, B, y) = Curl(X, Y, Z). 
As before, 
da/ox + 0B/oy + dyloz = 0; 
but 
0X /da + 0V/oy + 0Z/0z = 4apV’. 
If the distribution of electricity is a surface-distribution, which in the most 
general case we may take to be in motion, we have the following boundary 
conditions.* Take the Z-axis normal to the surface, so that the plane of zy is 
the tangent plane, and let the values of the vectors on the positive side of the 
*Trans. Roy. Dublin Soc., vol. viii., part vii. 
