456 
MR. O. HEAVISIDE ON THE FORCES, STRESSES, AND 
how their influence affects the energy transformations ; but if we consider only such 
changes as depend on the strain, i.e., the small changes of value which p and c 
undergo as the strain changes, we may express them by thirty-six new coefficients 
each (there being six distortion elements, and six elements in p, and six in c), and so 
reduce the expressions for 3U c /dt and 3T Jdt in (148) to the form suitable for 
exhibiting the corresponding change in Q N and in the stress function P N . As is 
usual in such cases of secondary corrections, tire magnitude of the resulting formula 
is out of all proportion to the importance of the correction terms in relation to the 
primary formula to which they are added. 
Professor H. Hertz'”' has considered this question, and also refers to von Helmoltz’s 
previous investigation relating to a fluid. The c and p can then only depend on the 
density, or on the compression, so that a single coefficient takes the place of the 
thirty-six. But I cannot quite follow Hertz’s stress investigation. First, I would 
remark that in developing the expression for the distortional (plus rotational) activity, 
he assumes that all the coefficients of the spin vanish identically ; this is done in 
order to make the stress be of the irrotational type. But it may easily be seen that 
the assumption is inadmissible by examining its consequence, for which we need only 
take the case of c and p intrinsically constant. By (139) we see that it makes S = 0, 
and therefore (since the electric and magnetic stress are separable), YHB = 0, and 
VED — 0 ; that is, it produces directional identity of the force E and the flux D, 
and of the force H and the flux B. This means isotropy, and, therefore, breaks 
down the investigation so far as the eolotropic application, with six p and six c 
coefficients, goes. Abolish the assumption made, and the stress will become that used 
by me above. 
Another point deserving of close attention in Hertz’s investigation, relates to the 
principle to be followed in deducing the stress from the electromagnetic equations. 
Translating into my notation it would appear to amount to this, the d priori assump¬ 
tion that the quantity 
. (1S0) 
where v indicates the volume of a moving unit element undergoing distortion, may 
be taken to represent the distortional (plus rotational) activity of the magnetic 
stress. Similarly as regards the electric stress. 
Expanding (150) we obtain 
0T 
& 
T dv 
v dt 
= H 
0B 
dt 
+ T div q - 
at 
(151) 
Now the second circuital law (90) may be written 
0B 
— curl (E — e 0 ) = K + -^ + (B div q — BV.q) 
(152) 
* ‘ Wiedemann’s Annalen,’ v. 41, p. 869. 
