FLUXES OF ENERGY IN THE ELECTROMAGNETIC FIELD. 
467 
The above three stresses are all of the simple type (equal tension and perpendicular 
pressure), and are irrotational, unless p, be the eolotropic operator. No change is, in 
the latter case, needed in (186), (188), whilst in the force formulae (187), (189), the 
only change needed is to give the generalised meaning to Vp,. Thus, in (I 89), instead 
of H'Vp., use 2VT m , 
(H/iH), 
(V B - V h )HB, 
i (HVjB - BVjH) + j (HV,B - BY.H) + k (HY.B - BV 3 H), 
showing the i, j, k components. 
Similarly in the other cases occurring later. 
The following stresses are not of the simple type, though all consist of a tension 
parallel to R or H combined with an isotropic pressure. 
§ 32. Alter the stress so as to locate the force on an intrinsic magnet bodily upon 
its magnetised elements. Add R.p,h 0 N to the stress (186), and therefore pih () .RN 
to its conjugate ; then the divergence of the latter must be added to the N-component 
of the force (187). Thus we get, if I = ph 0 , 
f P N = R.BN - Nff R/«R, .(190) 
(4) s 
[F = IY.R + YJ/.R - iR-Y/<.(191) 
But here the sum of the first two terms in F may be put in a different form. Thus, 
Also 
IY.R — I]YjR -j- IjVoR T" IgVgR 
= i.IVRj + j.IVRj + k.IYR 3 . 
IVRj = IVjR + I (VRj - VjR) = IV X R + iVJI. 
These bring (191) to 
F = (i.IVjR + j.IVgR + k.IVgR) + YJB - 4 R-V/-, 
(192) 
where the first component (the bracketted part) is Maxwell’s force on intrinsic 
magnetisation, and the second his electromagnetic force. The third, as before, is 
required where p. varies. 
§ 33. To the stress (190) add — N.^ RIj without altering the conjugate stress 
making 
3 o 2 
