58 Conway— Electro-magnetie Mass. 
Hence the resultant force is given by 
13340, (p, — p.)Vo(p. — px) [Ltp. — pol 
or as we may write it ¢(c), where ¢ is a linear self-conjugate vector function. 
This suggests at once the following theorems. There exists a quadric 
Sooo = const., 
such that if the acceleration takes place along the radius vector, the opposing 
force will have its direction normal to the quadric at the extremity of the - 
radius vector and inversely proportional to the length of the perpendicular 
from the centre on the tangent plane. In general, there will be only three 
directions, for which the direction of the opposing force will coincide with the 
direction of the acceleration. 
If we define the ‘‘mass” in any direction to be the resolved part of the 
opposing force along the unit acceleration in that direction, we see that the 
mass in any direction is inversely proportional to the square of the corresponding 
radius vector of the quadric Scdo = const. in that direction. This quadric might 
be called the mass-quadric. Of actual importance, perhaps, would be the mean 
value of the mass, 7.e., the mean value of the vector function 
2 20,0, V(p, — ps) Vo(p, — ps) [L(pr — ps); 
in which every direction of o with reference to the system is equally probable. 
Expanding, we get 
2 =26,, [0 (p, — ps) — (pr — ps) So (p, — px)IL T(r = ps) F- 
For the mass in any direction Uo we get 
— 2 =3¢e,e.[— (pr — ps)’ —[SUo(p, — ps) PILL (pr — ps) 
The mean value of [SUo(p, — p,)) is evidently 
= 45 ((Oe = [ahr 
Hence the mean mass is 
2 22¢,e, [7 (p, — ps) 75 
or, aS we may put it, 4V~, the work done in assembling the system from a 
state of infinite diffusion. 
