THEORY OF ELECTROMAGNETISM. 
689 
where dp a , dp b , dp c are three arbitrary independent increments of p, and dpj, dpi, dp' 
the consequent increments of p. 
F and <£ will have meanings closely connected but not identical with their meanings 
in the former paper. This will be explained later. 
6. The displacement, current, magnetic force, &c., at the point p will not be denoted 
by D, C, H, &c., but by D, C', H' , &c., with which the former symbols are connected in a 
way now to be described. In Maxwell’s ‘ Elect, and Mag.,’ 2nd ed., § 12, he* 
remarks : “ Physical vector quantities may be divided into two classes, in one of 
which the quantity is defined with reference to a line, while in the other the quantity 
is defined with reference to an area. ... In electrical science, electromotive and 
magnetic intensity belong to the first class, being defined with reference to lines. 
When we wish to indicate this fact we may refer to them as intensities. On the 
other hand, electric and magnetic induction, and electric currents, belong to the 
second class, being defined with reference to areas. When we wish to indicate this 
fact we shall refer to them as fluxes.” Now in connecting dashed with undashed 
letters it is absolutely necessary to bear in mind whether the vectors indicated are 
intensities or fluxes. The connection between D and D' will differ from that between 
H and H'. 
7. Nearly all the physical vectors at a point will belong then to one of the 
following classes :— 
Class I. Intensities. 
(Examples : V, A, E, H, 0, dS/ds, T V/.) 
cr being a vector of this class, the three allied vectors, cr, a , cr", are connected by 
the equations 
Sdpcr = Sdpcr', cr =y , ~ l cr, cr" — 1 <j' q =z \fj~ l cr .... (5). 
Class II. Fluxes. 
(Examples : B, C, D, dp/ds, v Vl.) 
t being a vector of this class, the three allied vectors, r, r', t" , are connected by the 
equations 
S d%r = S dlir, t = 7ii -1 yT, t‘ — = m~ 1 xfjT .... (6). 
* This part of the present paper should be read in connection with Maxwell’s paper “ On the 
Mathematical Classification of Physical Quantities,” ‘ Collected Scientific Papers,’ vol. 2, p. 257, or 
‘ Proc. London Math. Soc.,’ vol. 3, No. 34. In connection with the naturalness of the present methods, it 
may be of interest to note that the present paper was completed before I had seen this most suggestive 
paper of Maxwell’s. 
MDCCCXCII.—A. 4 T 
