808 
MR. .T. LARMOR OX A DYNAI^IICAL THEORY OF 
This mode of representation would leave ns with these electrons as the sole ultimate 
and unchanging singularities in the uniform all-pervading medium, and would, huild 
up tlie fluid circulations or vortices—now subject to temporary alterations of strength 
owing to induction—by means of them. 
115. It may be objected that a rapidly revolving system of electrons is effectively 
a vilorator, and would he subject to intense radiation of its energy. That however 
does not seem to be the case. We may on the contrary propound the general 
principle that whenever the motion of any dynamical system is determined b}’ 
imposed conditions at its boundaries or elsewhere, which are of a steady character, 
a steady motion of tlie system will usually correspond, after the preliminary 
oscillations, if any, have disappeared by radiation or viscosity. A system of electrons 
moving steadily across the medium, or rotating steadily round a centre, would thus 
carry a steady configuration of strain along with it; and no radiation will be pro¬ 
pagated away except when this steady state of motion is disturbed. 
It is in fact easy to investigate the characteristics of this strain-configuration 
when the electric system is moving with constant velocity, say in the direction of the 
axis of X with velocity c. By § 97, the dynamical equations of the surrounding 
medium are 
(|-a»-V^)(/,r/,70 = 0, 
referred to co-ordinates fixed in space. The equations determining the disturbance 
relative to the electric system are derived by changing the co-ordinate x to a new 
relative co-ordinate x, equal to x — ct; this leaves spacial differentiations unaltered, 
but changes djdt into djdt — cdjdx', thus giving 
(V 
(P 
(d 
(«" - + ct" ^ I' if, = 2c 
dy 
dd 
dd 
r/2 
(/> .V, 
In a steady motion the right-hand side of this equation would vanish ; and the 
conditions of steady motion are thus determined by the solution of the ordinary 
jiotential ecpiation for a uniaxial medium. The constants involved in the values of 
f, g, Ih so determined are connected by the fact that at a boundary of the elastic 
medium the rotation [f, g, h) must be directed along the normal. It follows at once 
for example that for a spherical nucleus the rotation is everywhere radial. As the 
electrons rotating round each other in equal orbits, their secular effects just cancel each other, so that 
the molecule as a whole is non-magnetic. This e.xact cancelling will not however usually occiir when 
there are more than two electrons in the molecule, or when a number of molecules are bound together 
in a group as in the case of an iron magnet. Similar considerations also apply as regards the average 
electric moment of a molecule, wliich is in fact the electric moment of the Gaussian secular equivalent 
above desciibed. 
* J. J. Thomson, ‘Recent Researches . . .,’ 1893, pp. 16-22, where the existence of a superior limit 
(ivfra) to possible velocities was first pointed out: also Heaviside, ‘Phil. Mag.,’ 1889, cf. ‘Electrical 
Papers,’ vol. 2, pp. 501 seqq. The problem of the dynamics of moving charges appears to have been 
first attacked on Maxwell’s theory by J. J. Thomson, ‘ Pliil. IRag.,’ 1881. 
