466 
MR. 0. HEAVISIDE ON THE FORCES, STRESSES, AND 
But as we do nob know definitely the forcive arising from the magnetic stress in the 
interior of a magnet, there are several formulae that suggest themselves as possible. 
Special Kinds of Stress Formulas statically suggested. 
5 29. Thus, first we have the stress (183); let this be quite general, then 
J P N = R.RN - N.I-R 3 ,.(184) 
M ' [ F = R div R + VJR.(185) 
Here It is the magnetic force of the field, not of the flux B. If g = 1 , div It is 
the density of magnetic matter, the convergence of the intrinsic magnetisation, but 
not otherwise. In general, it is the density of the matter of the magnetic potential, 
calculated on the assumption g = 1 . The force on a magnet is located in this system 
at its poles, whether the magnetisation be intrinsic or induced. The second term in 
(185) represents the force on matter bearing electric current (J = curl It), but has to 
be supplemented by the first term, unless div R = 0 at the place. 
§ 30. Next, let the stress be g times as great for the same magnetic force, but be 
still of the same simple type, g being the inductivity, which is unity outside the body, 
but having any positive value, which may be variable, within it. Then we shall have 
f P x = R.N/.R - N.VR/.R, .(186) 
( 2 ) < 
[ F = Rw + VJ/<R - *R 2 V/(,.(187) 
where m = conv g\ = div /xR is the density of magnetic matter, gh 0 being the 
intensity of intrinsic magnetisation. 
The electromagnetic force is made g times as great for the same magnetic force ; 
the force on an intrinsic magnet is at its poles ; and there is, in addition, a force 
wherever g varies, including the intrinsic magnet, and not forgetting that a sudden 
change in g, as at the boundary of a magnet, lias to count. This force, the third term 
in (187), explains the force on inductively magnetised matter. It is in the direction 
of most rapid decrease of g. 
§ 31. Thirdly, let the stress be of the same simple type, but taking H instead of 
R, H being the force of the flux B = gB. = g ( R + h 0 ), where h 0 is as before. 
We now have 
fP N = H.NB - N.1HB, .(188) 
(O) J 
\f = VJB + Vj (1 B - |H-V/(,.(189) 
where j 0 = curl h 0 is the distribution of fictitious electric current which produces the 
same induction as the intrinsic magnetisation gh 0 , and J is, as before, the real current. 
It is now qwasi-electromagnetic force that acts on an intrinsic magnet, with, 
however, the force due to y/x, since a magnet has usually large g compared with air. 
