FUNDAMENTAL FOEMULATIONS OF ELECTRODYNAMICS. 209 



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 sethereal 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 + 47rl, 



and which is always assumed to be subject to the relation 



div B = 0. 



* Of. my ' Theory of Electricity,' p. 363. 

 2 G 2 



