FUNDAMENTAL FORMULATIONS OF ELECTRODYNAMICS. 
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separately in the dynamical variational equation. The coefHcients of' the 'latter 
variations lead to the equations 
c at c at 
Curl A, = 
c dt 
from which it follows that the multipliers 0 and Aj are the ordinary scalar and vector 
potentials of the theory so that further 
Curl E = - - 4 Curl A^. 
c dt 
As regards the vector Ag, this is a new vector potential whose curl is required in 
our subsequent discussions. For this we have 
Curl B = Curl H + 47r Curl I = - Curl A^, 
G dt 
whilst if we use C^ as the total current of true electric flux v e have, by Ampere’s 
equation 
Thus, if we use 
we have 
Curl H = - ^ + —C,. 
c dt c 
C'g = C, + c Curl I, 
I (Curl A,) = ^+4.0',. 
The main part of Curl Ag is therefore represented by the electric force : there is 
however in addition a local term depending on the time integral of the current 
density at the point. We can thus write 
Curl Aa = E + E„. 
If we use the values thus determined for the various undetermined multipliers 
introduced at the outset, the remaining terms of the variation give for the motion of 
the material and electrical elements equations of the type 
/0Lo\ _ 8L 
dt \dxm/ 
