Conway—A New Foundation for Electrodynamies. 59 
is necessary, for the disturbances are not propagated instantaneously. The 
difference in time ¢—7Z must be the same as that occupied by the radiation 
in travelling out a distance 7. In other words, 7 must satisfy the equation 
¢t— T=r/V, where ¢ is the distance from the position of the particle (€, , ¢) at the 
time 7’ to the point (z, y, z). (&, 7, ¢) are, of course, supposed to be known 
functions of the time. Hence, in the expression for the scalar potential, 
€,, G v @ are all supposed to be formed at the time 7’ given above, The same 
remark applies to the expression which we take for the vector potential. 
(Ff, G, H)= AVe(x%, v, v3)/(V — v cos 8), 
where 2, %, v; are the rectangular components of the velocity v at the time 7. 
We take, then, finally for the electric force (X, Y, 7) the expression 
— (0/02, d/oy, 0/02)  — do/ot (F, G, 1). 
In the differentiations it is, of course, to be remembered that €, 7, ¢ are functions 
of 7, which is a function of 2, y, 2, ¢, given by 
t—T=((e—€) +(y—a) + (2- OV. 
So that (for example) 
0€/du =0€/OT OT Ou =—0&/0T . (x — €) /r( V— 0 cos 8). 
If we take the constant A= V’, we get the electromagnetic system of units. 
Then the vector (X, Y, Z) satisfies the equations 0X/0x + dV /dy + 0Z/dz = 0, 
(V? V2 — &/ot?) (X, ¥, Z) =0, and {{7X + mY +nZ) dS=47V%e, where the 
integration is extended over any closed surface containing the particle. Also, 
if we introduce a new vector (a, 8, y), which is the curl of (7, G, 1), we find 
now 
IT? WOU (2 % A= Cwdl (G (85 99) 
— dat (a, B y)= Curl (X, ¥, 2), 
which is the Hertz-Heaviside form of the Maxwellian equations, (a, 6, y) being 
the magnetic force. If we pass from a consideration of discrete point charges to 
a system in which the volume density is p, the above equations still hold outside 
the electricity, but inside it will be found that the first relation becomes 
