MR. 0. HEAVISIDE ON THE FORCES, STRESSES, AND 
47 6 
Appendix. 
Receiver! June 27, 1891. 
Extension of the Kinetic Method of arriving at the Stresses to cases of Non-linear 
Connection between the Electric and Magnetic Forces and the Fluxes. Preserva¬ 
tion of Type of the Flux of Energy Formula. 
§ 39- It may be worth while to give the results to which we are led regarding the 
stress and flux of energy when the restriction of simple proportionality between 
“ forces ” and “ fluxes,” electric and magnetic respectively, is removed. The course to 
be followed, to obtain an interpretable form of the equation of activity, is sufficiently 
clear in the light of the experience gained in the case of proportionality. 
First assume that the two circuital laws (89) and (90), or the two in (93), hold 
good generally, without any initially stated relation between the electric force E and 
its associated fluxes C and D, or between the magnetic force H and its associated 
fluxes K and B. When written in the form most convenient for the present appli¬ 
cation, these laws are 
curl (H - h n ) = J 0 = C + + (D div q - DV.q),.(212) 
Bt 
- curl (E - e 0 ) = G 0 = K + ^ + (B div q - BV.q).(213) 
Bt 
Now derive the equation of activity in the manner previously followed, and arrange 
it in the particular form 
e 0 J 0 + h () G 0 + conv V (E — e 0 ) (H — h 0 ) 
E 0D + H rS \ + ( KDViq _ ED diy q ) + (n.BV.q - HB div q), . (214) 
Bt Bt) 
which will best facilitate interpretation. 
Although independent of the relation between E and D, &c., of course the dimensions 
must be suitably chosen so that this equation may really represent activity per unit 
volume in every term. 
Now, guided by the previous investigation, we can assume that (e 0 J 0 -}- h,,Gr 0 ) 
represents the rate of supply of energy from intrinsic sources, and also that 
V (E — e 0 ) (H-h„), which is a flux of energy independent of q, is the correct form in 
general. Also, if there be no other intrinsic sources of energy than e 0 , h 0 , and no 
other fluxes of energy besides that just mentioned except the convective flux and that 
due to the stress, the equation of activity should be representable by 
- (EC + HK) + 
