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PROFESSOR C. NIVEN ON THE INDUCTION OF ELECTRIC 
current sheet; the trail here becomes conical, the locus of points in it, which corre¬ 
spond to a given point of the influencing system, forming a curve which would 
become portions of an equiangular spiral, if the cone on which it lies were developed 
on a plane. 
The determination of the coefficients in the problems having reference to a sphere 
or spherical shell depends on the elementary formulae of reduction of the spherical 
functions. By adopting a particular mode of constructing the theory of these 
expressions, it is possible to obtain the necessary properties almost immediately from 
the definitions : a short sketch of the subject is therefore given, confined, however, to 
the results which are necessary for the subsequent analysis. 
General equations. 
§ 2. The general equations of the field in Maxwell’s theory are expressed in 
terms of 
The electro-magnetic momentum at a point, F, G, H 
The magnetic induction a , b, c 
The magnetic force a, ( 3 , y 
The total electric current u, v, w 
The current of conduction p, q, r 
The electric displacement f g, h 
The electromotive force P, Q, R 
The velocity of a point x, y, z 
We have also the following scalar quantities, 
The electric potential \)j, 
The magnetic potential fi, 
The conductivity for electric currents C, 
The resistance to conduction, cr=y, 
The dielectric inductive capacity K, 
The free electricity at any point in the substance of the conductor e 
per unit of volume, on the surface e per unit of area. 
Since the dielectric surrounding the conductors is air, we may treat the magnetic 
induction and magnetic force as identical, and we may put 
dy dz ’ 
&c. 
( 1 ) 
