452 
MR. O. HEAVISIDE OH THE FORCES, STRESSES, ART) 
entirely on the fluxes, however they be produced, in this respect resembling the 
electric and magnetic energies. 
To exhibit the stress, we have (131), or 
-f" Q-fl -2 + Q'39 , 3 = YeH 4- 5/ Eh 4- q (U + T).(133) 
In this use the expressions for e and h, giving 
2Chy = VHVBq + VEVDq + q(U b T) 
= B.Hq — q.HB + D.Eq — q.ED + q (U + T) 
= (B.Hq - qT) + (D.Eq - qU) ;.(134) 
where observe the singularity that q (U -f- T) has changed its sign. The first set 
belongs to the magnetic, the second to the electric stress, since we see that the 
complete stress is thus divisible. 
The divergence of being the activity of the stress-variation per unit volume, 
its N component is the activity of the stress per unit surface, that is, 
(NB.Hq — Nq.T) -f (ND.Eq — Nq.U) = q (H.BN 4- E.DN — NU — NT) = P N q. . (135) 
The stress itself is therefore 
the value of 0H c jdt arising from the variation of 1, m, n, and the other half from the c’s, provided c is 
irrotational. 
Or we may choose the three principal axes of c in the body, when 1, m, n will coincide with, and 
therefore move with them. 
Lastly, we may proceed thus :— 
E ^ E = E 
dt 
gy - D ' E = EVaD - DVaE = 2a\ 7 DE. 
(1327r) 
That is, replace 3/9 1 by Va when the operands are E and D. This is the correct result, but it is not 
easy to justify the process directly and plainly; although the clue is given by observing that what we do 
is to take a difference, from which the time-variation of E disappears. 
If it is D that is kept constant, the result is 2aVED, the negative of the above. 
It is also worth noticing that if we split up E into Ej + E 3 we shall have 
E i | E 3 = a [V(E lC )E 3 - VEdcE,)], 
0 C f 
E 3 ^E 1 = a[V(E 3 c)E 1 -Y^cE,)]. j 
(1320 
These are only equal when c — c', or Ec = cE ; so that, in the expansion of the torque, 
VDE = VDjEj + VD 3 E 3 + VD.E! + VDjEo, 
the cross-torques are not VD^Ej and VDjEo, which are unequal, but are each equal to half the sum of 
these vector-products. 
