FLUXES OF ENERGY IN THE ELECTROMAGNETIC FIELD. 
463 
stress ; the actual forces and stresses being only determinable from a knowledge of 
the mechanical conditions of the conductor-, as its density, elastic constants, and the 
way it is constrained. Now, if there is any dynamical meaning at all in the electro¬ 
magnetic equations, we must treat the ether in precisely the same way. But we do 
not know, and have not formularised, the equations of motion of the ether, but only 
the way it propagates disturbance through itself, with due allowance made for the 
effect thereon of given motions, and with formularisation of the reaction between the 
electromagnetic effects and the motion. Thus the theory of the stresses and forces in 
the ether and its motions is an unsolved problem, only a portion of it being known so 
far, i.e., assuming that the Maxwellian equations do express the known part. 
When we assume the ether to be motionless, there is a partial similarity to the 
theory of the propagation of vibrations of infinitely small range in elastic bodies, when 
the effect thereon of the actual translation of the matter is neglected. 
But in ordinary electromagnetic phenomena, it does not seem that the ignoration 
of q can make any sensible difference, because the speed of propagation of disturbances 
through the ether is so enormous, that if the ether were stirred about round a magnet, 
for example, there would be an almost instantaneous adjustment of the magnetic 
induction to what it would be were the ether at rest. 
Static Consideration of the Stresses. — Indeterminateness. 
§ 27. In the following the stresses are considered from the static point of view, 
principally to examine the results produced by changing the form of the stress func¬ 
tion. Either the electric or the magnetic stress alone may be taken in hand. Start 
then, from a knowledge that the force on a magnetic pole of strength m is Em, where 
R is the polar force of any distribution of intrinsic magnetisation in a medium, the 
whole of which has unit inductivity, so that 
div R = to = conv h 0 .(180) 
measures the density of the fictitious “ magnetic ” matter; h 0 being the intrinsic 
force, or, since here P = !, the intensity of magnetisation. The induction is 
B = h + ft. This rudimentary theory locates the force on a magnet at its poles, 
superficial or internal, by 
F = R div R ...(181) 
The N component of F is 
FN = RN. div R = div [R.RN - NAR 3 ], 
(182) 
because curl R, = 0. Therefore 
P N = R.RN - N.4R- 
(183) 
is the appropriate stress, of irrotational type. Now, however uncertain we may be 
