M, 
6 Dr. D. F. Comstock on the 
Since the proof o£ equations (1) is equally valid for relative 
motion, the integrals involving (v 2 ) in the above correspond 
to flow o£ energy with respect to axes moving with the 
system. There is also an implicitly involved internal term in 
each o£ the Poynting vector integrals. Since the system is 
isolated, the sum o£ such " internal " terms must on the 
average vanish. There remains therefore to represent the 
actual average rate of transfer of energy through space only 
the explicit Poynting terms and the terms involving fa). 
The electromagnetic momentum corresponding to any 
electrioal system is given by the components 
1 f 
which, except for the factor V 2 , are the same as the integrals 
of the components of the Poynting vector throughout the 
system. Hence equation (3) may be written 
Wv 1 = lMx + nM 2/ + nlSl z -lv l \ (7X„+ mY^ + nZ^dr 
—mv 1 i (ZXy+mY y + wZ y )rfT— nv^ 1 (IX^mYl + iiL z )dr 
. . (3a) 
Also if the electrical system here dealt with is to represent 
a material body, we may assume that the resultant momentum 
(M) is in the direction of the velocity, and hence 
M=lM. x +mMf+nM e . 
This may be considered as due to the fact that the lack of 
symmetry necessarily involved in the intimate structure of any 
electromagnetic system has become a symmetrical average in 
particles large enough to be dealt with. This symmetrical 
point may of course have been reached in the case of single 
atoms. We may now write (3 a) in the form 
Wt>! = V*M - v, j { (/ 2 X, + m?Y 9 + n?Z e ) 
+ Zm(X y +Y x )+Zn(X s + Zx)+win(Y^+Zy)}rfT. . (5) 
7. To reduce this expression further requires some relation 
to be established between the stresses and the electric and 
magnetic force intensities. This process is closely analogous 
to the derivation of the Maxwell stress in the free aether 
