FUNDAMENTAL FORMULATIONS OF ELECTRODYNAMICS. 
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of the fundamental equations based on the principle of Least Action, in the course of 
which certain inconclusive aspects of this derivation present themselves for 
consideration. 
2. A complete statement of Maxwell’s theory as originally given and in the form 
which will include most of the recent extensions depends on certain field vectors 
which first require consistent and independent definition. These vectors :—• 
{a) E, the electric force, defined at any point of the field as the vectorial ratio to a 
small electric charge of the force acting on it when placed at rest in that position. 
When the point under consideration is inside the matter in the field there exists the 
possibility of an additional contribution to this force due to local conditions of the 
matter in the neighbourhood of the point, but for the present we shall disregard any 
complication of this kind. 
(6) C, the complete electric current; in the most general case this consists of 
several distinct parts. Firstly, there is the differential drift of free ions constituting the 
true conduction current and the material dielectric displacement current; then there 
is a part due to the convection of charged and electrically polarised media, and finally 
the mthereal constituent essential and peculiar to Maxwell’s theory. 
It has been definitely established that all but the last constituent of the current 
are in themselves true movements of electricity, or at least effectively equivalent to 
such, so that so long as we retain the definite concept of an electrical entity the 
origin of these different constituents merely remains a matter of kinematics, and they 
have, in fact, been fully dealt with on this basis.* 
(c) H, the magnetic force, defined in a similar manner to the electric force, with 
the aid of the concept of a magnetic pole, but now without the possibility of a local 
contribution due to surrounding magnetic polarity if the point is inside the matter. 
It is perhaps as well to emphasise the fact that both the electric and magnetic 
forces are defined in a theoretical manner which almost excludes the possibility of 
direct experimental verification. Electromagnetic measurements, particularly as 
regards the fields inside the matter, are concerned almost entirely with matter in bulk, 
and it is then only the mechanical or molar parts of these forces that are then under 
observation, the local parts, if they exist at all, being balanced on the spot by other 
forces of an origin not at present under review. We have however evidence that 
these local parts of the forces do exist. 
(d) B, the magnetic induction, which is defined in the elementary theory in 
terms of the magnetic force H and the magnetic polarisation intensity I by the 
relation 
B = H + IttI, 
and which is always assumed to be subject to the relation 
div B = 0. 
* Of. my ‘ Theory of Electricity,’ p. 363. 
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