804 
MR. J. LARMOR ON A DYNAMICAL THEORY OF 
it woalti follow that the circurnstaiiees of the induced electric force are nut determined 
merely by the distribution of magnetic induction in the held, but involve the actual 
disti'ibution of electric cui’rent and of magnetism throughout all space. For there aic 
very various distributions of electric current and magnetism in the more distant parts 
of space which lead to the same distribution of magnetic induction in the neighbour¬ 
hood of the system in which the currents are induced : these would be ecpaivalent as 
regards the magnitudes of induced currents, but not as regards the distribution of 
induced electric force. 
This state of things would not be inconsistent with general principles. The electric 
influence arising from a distindjance of one system is propagated elastically to other 
systems across the intervening medium, the propagation being nearly instantaneous 
without showing any sensible trace of the disturbance during its transit through the 
medium, and this on account of the high elasticity and consequent great velocity of 
propagation. The magnetic field is a residual effect of this propagation ; that field is 
sufficient to re})resent the aggregate features of the result in cases in which the current 
is mostly conducted, but it need not represent the features of the propagation in 
detail. There are in fact cases in wdiich induction takes place across a space in which 
there is at no time any sensible electric or magnetic force at all: for example the 
starting of a current in a ring electro-magnet induces in this way a current in any 
outside circuit which is linked with the ring : the elastic propagation here leaves no 
trace in the form of motion of the mther or magnetic force. 
111. When the velocity of electric propagation may be taken as indefinitely great 
compared with the velocities of the conductors in the field, the phenomena of induced 
currents will depend only on the relative motion of the inducing and induced systems ; 
thus we may simplify the conditions by taking tlie induced system at rest subject to 
the electric influences sent out from an inducing system in motion and otherwdse 
changing. Now in this simpler case the electric intensity consists of two parts, one 
of them required to keep the current going against the viscous resistance of the 
conductor and the elastic resistance of the dielectric, and the other a free disturbance 
which will be continually cancelled with the velocity of radiation as fast as it is 
produced. The latter part therefore practically does not exist in ordinary problems 
of induction, in which the movements are slow compared with the velocity of light. 
Thus the elastic displacement of the electric medium may be taken as in internal 
equilibrium by itself in all such cases ; rhere can be no free electric force inside a 
conductor, and the electric charge, if any, will reside on its surface. TTie amount of 
this superficial charge will be the time-integral of the displacement current which is 
involved in the total current, and which is wholly in the outside dielectric. Now the 
determination of the complete current is a perfectly definite problem, on the principles 
of Ampere and Faraday ; tlius the electric force at any point and the static 
electrification on the conductors are also on the same principles definite and 
deteiminate, subject to this proviso of slow movement of the bodies concerned. 
