FUNDAMENTAL FOR^rTTLATIONS OF ELPXTIiODYNAMTCS. 
241 
theory is to reduce these forces to a representation by means of an applied stress 
system of ordinary character. This discussion leads in the usual way to the intro¬ 
duction of the concept of electromagnetic momentum. 
The actual calculations for the present form of the results are not materially 
different from those given m extenso elsewhere, so that it will again be sufficient to 
outline the principal stages in the discussion. The method employed is to attempt to 
express, say, the x component of the force per unit volume in the form 
3T.. 8T., 8T;. 
?y 02 
Now the total forcive of electrodynaniic origin acting on the medium of the field at 
any place is such that its x component per unit volume is 
Again writing 
-[P. Curl K],-[I, Curl Bl-i 
+ /I Ej + y r„, B] j + - [C, B]^ 
H' = 
L 
1 
_1 
[ 
+ — 
E,^ 
c 
L dt j 
c 
dt _ 
it is proved just as in the u.sual form of the theory that the forcive of wliich this is 
the representative component is represented in the main by a stress system in which 
and 
T = E D EV— — H'“ 
with symmetrical expressions for the other constituents; but with this representation 
there is an outstanding part of the complete forcive, viz., 
J. ^ 
4c dt 
[EB]-f 
1 d 
c dt 
J_ d 
inc dt 
which cannot be so reduced. The first tei'in in this outstanding part, being a complete 
differential with respect to the time, is usually taken to represent a part of the 
complete forcive arising as the kinetic reaction to a rate of change of momentum, and 
this is the origin of the concept of electromagnetic momentum. This idea is however 
partly destroyed by the remaining term in the above expression which cannot be 
developed either as a forcive of oi’dinary type or as a kinetic reaction to a rate of 
2 L 2 
