460 
MR. O. HEAVISIDE OH THE FORCES, STRESSES, AND 
surrounding it, determinable in the isotropic homogeneous case by the above formulae. 
Then we may ignore E 1 and Hj in estimating the forcive on the matter and current 
in the region A ; thus, 
+ VJjBo) + 2 (E.^ + \ D.iGj),.(166) 
where oq = div B x = div B, and Jj = curl = curl K in region A, is the resultant 
force on the region A, and 
2(11] <To + \ JoB|) + 2 (Ej^o + A DjGo),.(167) 
is the resultant force on the region B ; the resultant force on A due to its own E and 
H being zero, and similarly for B. These resultant forces are equal and opposite, and 
so are the equivalent surface-integrals 
2 (HoA + VJfBo) + 2 (Eo/V + VDoGf),.(168) 
and 
2 (EbA + VJo'Bj) + 2 (E]A + VDjGo'),.(169) 
taken over the interface. The quantity summed is that part of the stress-vector, P N , 
which depends upon products of the H of one region and the B of the other, &c. 
Thus, for the magnetic stress only, 
H.BN - NAHB = (HpBjN - N.iHjBj) + (Hj.B.N - NAHjB.) 
+ (Ho.BoN - NAHtB,) + (IL.BjN - N.-pEBj), . . . (170) 
and it is the terms in the second and fourth brackets (which, be it observed, are not 
equal) which together make up the magnetic part of (168) and (169) or their nega¬ 
tives, according to the direction taken for the normal; that is, since HjB.} = H,B 1 , 
2p n = 2(H 1 .B 3 N + IH.BjN - N.HjBo) = 2(h.BN - NAHB) 
= 2(h i A + VJo'Bj) = 2(H 2 A + VJ/Bo) = 2(H(t' + VJ'B) 
= 2f = 2(Hjff 3 + VJoBj) = 2(h,<x 1 + VJ,Bo) = 2(h<t + vjb), . . . (171) 
where the first six expressions are interfacial summations, and the four last summa¬ 
tions throughout one or the other region, the last summation applying to either 
region. No special reckoning of the sign to be prefixed has been made. The 
notation is such that H = H-j fi- Eh, <x = oq -f- on, &c., &c. 
The comparison of the tw r o aspects of electromagnetic theory is exceedingly curious ; 
namely, the precise mathematical equivalence of “ explanation ” by means of instan¬ 
taneous action at a distance between the different elements of matter and current, 
each according to its kind, and by propagation through a medium in time at a finite 
velocity. But the day has gone by for any serious consideration of the former view 
other than as a mathematical curiosity. 
