814 
MR. .T. LARMOR ON A DYNAMICAL THEORY OF 
which determines the ratio of to r.^ in the steady motion; and then the value of w 
gives the period of the rotation. 
For example when the electrons are equal and opposite = L^, and 
7*1 — r.^: thus the square of the velocity of either, is equal to VV( 2 L?’ — f). 
For the case of a spherical nucleus of radius a, L = Sir/Sa ; thus the velocity of either 
must be considerably less than jV, which is small enough to allow this method to 
approximately represent the facts for that case. 
It may be observed that in the general problem of the dynamics of a system of n 
electrons, the equations of conservation of momentum assume the forms 
(IT 
Clii J 
dT . dT 
+ ,• + • • • + 7 - — const. 
c/.r.-, liXu 
3 
with similar equations in y and z. For the case of two electrons moving in the same 
line, the equations of energy and momentum determine the motion completely ; their 
forms illustrate the complexity of the electric inertia which is involved. 
119. In the general theory of electric phenomena it has not yet been necessary to 
pay prominent attention to the molecular actions which occur in the interiors of con¬ 
ductors carrying currents : it suffices to trace the energy in the surrounding medium, 
and deduce the forces acting on the conductors, considered as continuous bodies, from 
the manner in which this energy is transformed. The calculations just given suggest 
a more complete view, and ought to be consistent with it; instead of treating a 
conductor as a region effectively devoid of elasticity, we may conceive the ions of 
which it is composed as free to move independently, and thus able to ease off electric 
stress; the current will thus be produced by the convection of ionic charges. Now 
if all the atoms took part equally in this convection, their velocity would be exceed¬ 
ingly small ; a current of ^ amperes per square centimetre would imply a velocity of 
about 10 "^ i centimetres per second. The kinetic energy of an ion due to intrinsic 
electric inertia is, according to the formula above, \ STrjSa. (cv)^, where a is of order 
< 10 “®, e of order 10 “^^ ; this would imply as above a centrifugal electric force of 
intensity 87 r/ 3 a.e.uYI ^5 which may be of order 10 “^® I’b acting on this particular ion 
when it is going round a curve of radius R. Now even if the conductor were of 
copper, the slope of potential along it would be, with this current intensity, as much 
as 16 4b The effects of the intrinsic electric inertia are therefore so far quite beyond 
the limit of observation. We have however been taking: the electric drift v to be 
the only velocity of the ions or electrons. If they possess a velocity of their own in 
fortuitous directions of order V, the average centrifugal electric force on an electron 
due to the current will possibly be as high as 87 r/ 3 a. e. uV/R, because change of sign 
of V does not change the sign of the force. This would still hardly be detectable 
even if V were comparable with the velocity of radiation. 
But an electric force of a cognate kind has in fact already been looked for and 
detected by E. H. Hall. When the current is moving in a field of magnetic 
