[ 6*8 ] 
XVIII. On the Mathematical Theory of Electromagnetism. 
By Alex. MoAulay, M.A., Ormond College, Melbourne. 
Communicated by the Rev. N. M. Ferrers, D.D., F.R.S. 
Received January 8—Read April 28, 1892. 
Revised October, 1892. 
I. Introduction. 
A Electromagnetic Coordinates. 
1. It has been thought advisable to reserve an account of the general aims and scope 
of the following paper till a few preliminary matters have been disposed of. 
2. Consider the following statement, of the truth of which probably no one will 
doubt. If a body on being moved from a position A to a position B were found 
thereby to have lost a charge of electricity, physicists would not be content to explain 
the circumstance on the mere ground that it had left its charge behind. They would 
hold that processes had gone on, precisely similar to such as would have been required 
to divest it of its charge, had it remained in its first position A. 
This has an important bearing on the way in which the “ electric displacement ” is 
related to matter. The polarisation thus called is some sort of ^polarisation of matter, 
and this polarisation is carried about by the matter when it moves. There certainly is 
no lack of evidence that electric actions go on in space where there is, to the best of 
our knowledge, no matter. In this space, however, is a medium of some sort, which 
is intimately related to matter, and certainly affected in some way by the motion of 
matter. For the present we must, for the sake of simplicity, be content to assume 
that the strains of this medium are, if it only bounds matter, continuous with those 
of matter, and if it permeates matter, are at places common to both matter and the 
medium identical with those of matter. (This may or may not be true. I only say 
that in the first development of the theory of this paper it must for simplicity be 
assumed.) This will not prevent us from regarding the slipping of the one medium 
over the other as the limit of a rapid shear. With this assumption the medium in 
question will appear in our equations merely as matter with zero density, but other 
physical quantities not zero. 
Both for the medium referred to, and for matter, the statement would seem to 
remain true that the polarisation called electric displacement is a property that is 
carried about by the medium experiencing it. 
9.1.93 
