472 
MR. O. HEAVISIDE ON THE FORCES, STRESSES, AND 
force due to matter m in a medium of unit inductivity, or the normal component of 
induction due to m in its own medium. For this is 
ji] — fia ma 
/<-i + H 2 TTytjr 3 
%tt dr = 
m 2 a 2 fj.i — [i 2 
47T/41 + /lo. 
dr 
= (203) again. 
Another way is to calculate the variation of energy made by displacing either the 
pole m or the mass. The potential energy is expressed by 
i (P + p) m = 1 Pm + i 2p^,.(205) 
where P = mf^Trppr and p = 2 a/Anr, the potentials of matter m//y and <x, where r 
is the distance from m or from cr to the point where P and p are reckoned. 
The value of the second part in (205), depending upon cr, comes to 
i /M — Ma _ ra 2 
fij -)- /tj 4^^ • 2 a 
(206) 
and its rate of decrease with respect to a expresses the repulsion between the pole 
and the region. This gives (203) again. 
A fourth way is by means of the g^ast-electromagnetic force on fictitious interfacial 
electric current, instead of matter, the current being circular about the axis of 
symmetry AB. The formula for the attraction is 
2v curl B.R n , 
(207) 
if R 0 be the radial magnetic force from m in its own medium, tensor 
Here the curl of B is represented by the interfacial discontinuity in the tangential 
induction, or 
2zm yMq 
4?rr 3 yUj + JUo 
Also the tangential component of R 0 is Therefore the repulsion is 
[2 mz — yttjj mz 
J4Trr 3 /x 1 + /i 3 4 
2 irr dr — 
4i7Tfl-y 
/a — h 
H + H 
m 2 /<i — /<j 
4^1 ‘ /a + /O 
(208) 
as before, equation (203). This method (207) is analogous to (204). 
§ 37 . There are several other ways of representing the attraction, employing fictitious 
matter and current ; but now let us change the method, and observe how the attrac¬ 
tion between the magnetic pole and the iron mass is accounted for by a stress dis¬ 
tribution, and its space-variation. The best stress is the third, equation (188), § 31. 
Applying this, we have simply a tension of magnitude I/hIV = Tj in the first medium 
