462 
MR. O. HEAYTSTDE ON THE FORCES, STRESSES, AND 
Remarks on the Translational Force in Free Ether. 
§ 26. The little vector Veil, which has an important influence in the activity 
equation, where e and h are the motional forces 
e = YqB, h = YDq, 
has an interesting form, viz., by expansion, 
Yell = q.qVDB = | • qYEH,. (176) 
if v be the speed of propagation of disturbances. We also have, in connection there¬ 
with, the equivalence 
eD = hB,.(177) 
always. 
The translational force in a non-conducting dielectric, free from electrification and 
intrinsic force, is 
F = VJB + YDG + VjB + YDg, 
or, approximately, 
rZ I c l W 
= VDB + YDS = -n YSB = - 5 - 3 ; YEH = —.(178) 
at v z dt v~ 
The vector VDB, or the flux of energy divided by the square of the speed of 
propagation, is, therefore, the momentum, (translational, not magnetic, which is quite 
a different thing), provided the force F is the complete force from all causes actiqg, 
and we neglect the small terms A 7 jB and VBg. 
But have we any right to safely write 
F = m^,.(179) 
where rn is the density of the ether ? To do so is to assume that F is the only force 
acting, and, therefore, equivalent to the time-variation of the momentum of a moving 
particle.* 
Now, if we say that there is a certain forcive upon a conductor supporting electric 
current; or, equivalently, that there is a certain distribution of stress, the magnetic 
stress, acting upon the same, we do not at all mean that the accelerations of momentum 
of the different parts are represented by the translational force, the “electromagnetic 
force.” It is, on the other hand, a dynamical problem in which the electromagnetic 
force plays the part of an impressed force, and similarly as regards the magnetic 
* Professor J. J. Thomson Las endeavoured to make practical use of the idea, ‘Phil. Mag.,’ March, 
1891. See also my article, ‘ The Electrician,’ January 15, 1886. 
