FUNDAMENTAL FORMULATIUNS OF ELECTRODYNAMICS. 
231 . 
and then we get Poynting’s theory in which 
and 
where 
S = A[E, .H-47r[P,J] = ^[E, H'] 
H'=H-4;r[P,J 
is equivalent to the vector H' introduced in paragraph 8. 
This theory has the advantage, in addition to that already discussed at length, that 
it involves no further dynamical assumption other than those expressed in the special 
forms chosen for W and F. The Amperean equation used to effect the separation 
being more in the nature of a kinematical detinition of the electric current or magnetic 
force than of a dynamical relation between the field vectors. 
Another form can be obtained by using the equations 
with 
we then get 
with 
^ 1 I 
E =-—-o-vacl (/) 
c dt ^ ‘ 
div C = 0 
O V */ J •. 
-cj (Curl| Pr,J, (?A) 
S = 0(C-cCurl [PkJ). 
The special form of this result when the media are at rest has been shown* to be 
inconsistent with our usual conception of such things as radiation phenomena. 
Yet another form of the theory can be obtained by taking 
T = - dt 
(EC+lfk,B]. 4V^'(ECurl[IVJ) 
dt 
dyV 
and then 
S = 0. 
In such a theory there would be no such thing as radiation. 
We can go. on multiplying the different forms of this theory indefinitely and each 
form obtained would in itself be perfectly consistent with the Maxw'ellian 
electrodynamic theory. The expressions for S and T in them are of course dependent 
* ‘Phil. Mag.,’ vol. 34 (1917),q?. 385. 
VOL. OCXX.— A. 2 K 
