478 
MR. O. HEAVISIDE OH THE FORCES, STRESSES, AND 
Exchange E and D, and H and B, in (221) or (222) to obtain the conjugate vector 
Q n ; from which we obtain the flux of energy due to the stress, 
- = B.Eq - q (ED - U) + B.Hq - q (KB - T) 
= VEVRq + VHVBq + q (U + T),.. . (224) 
or 
- q% = VeH + VEh + q (U + T), .(225) 
where e and h are the motional electric and magnetic forces, of the same form as before 
(88) and (91); so that the complete form of the equation of activity, showing the 
fluxes of energy and their convergence, is 
e 0 J 0 + h 0 G 0 + cony [V(E - e 0 ) (H - h„) + q (U + T)] - conv [VeH + VEh + q( U + T)] = Fq + (Q + U + T), (226) 
where F has the above meaning. 
There is thus a remarkable preservation of form as compared with the corresponding 
formulae when there is proportionality between force and flux. For we produce 
harmony by means of a Poynting flux of identical expression and a flux due to the 
stress, which is also of identical expression, although U and T now have a more general 
meaning, of course.* 
Example of the above, and Remarks on Intrinsic Magnetisation when there is 
Hysteresis. 
§ 40. In the stress-vector itself (for either the electric or the magnetic stress) the 
relative magnitude of the tension and the lateral pressure varies unless the curve 
* As the investigation in this Appendix has some pretensions to generality, we should try to settle 
the amount it is fairly entitled to. No objection is likely to be raised to the use of the circuital equations 
(212), (213), with the restriction of strict proportionality between E and H and the fluxes D and B, or 
C and K entirely removed ; nor to the estimation of J 0 and G 0 as the “ true ” currents ; nor to the use of 
the same form of flux of electromagnetic energy when the medium is stationary. For these things are 
obviously suggested by the preceding investigations, and their justification is in their being found to 
continue to work, which is the case. But the use in the text of language appropriate to linear functions, 
which arose from the notation, &e., being the same as before, is unjustifiable. We may, however, remove 
this misuse of language, and make the equation (226), showing the flux of energy, rest entirely upon 
the two circuital equations. In fact, if we substitute in (226) the relations (217a), (2175), it becomes 
merely a particular way of writing (214). 
It is, therefore, to (217a), (2175) that we should look for limitations. As regards (217a), there does 
not seem to be any limitation necessary. That is, there is no kind of relation imposed between E and C, 
and H and K. This seems to arise merely from Q meaning energy wasted for good, and having’ no 
further entry into the system. But as regards (2175), the case is different. For it seems necessary, in 
order to exclude terms corresponding to E(0c/0£)E and H(0/<./0t)H in the linear theory, when there is 
