480 
PEOFESSOE CLEEK MAXWELL ON THE ELECTEOMAGNETIC FIELD. 
will be limited sheets, terminating in the electric circuit as their common edge or 
boundary. The number of these will be equal to the amount of work done on a unit 
pole in going round the current, and this by the ordinary measurement = 4xy, where y 
is the value of the current. 
These surfaces, therefore, are connected with the electric current as soap-bubbles are 
connected with a ring in M. Plateau’s experiments. Every current y has 4 icy surfaces 
attached to it. These surfaces have the current for their common edge, and meet it at 
equal angles. The form of the surfaces in other parts depends on the presence of other 
currents and magnets, as well as on the shape of the circuit to which they belong. 
PAET III.— GENEEAL EQUATIONS OF, THE ELECTEOMAGNETIC FIELD. 
(53.) Let us assume three rectangular directions in space as the axes of x, y, and z , 
and let all quantities having direction be expressed by their components in these three 
directions. 
Electrical Currents (p, q, r). 
(54) An electrical current consists in the transmission of electricity from one part of 
a body to another. Let the quantity of electricity transmitted in unit of time across 
unit of area perpendicular to the axis of x be called p, then p is the component of the 
current at that place in the direction of x. 
We shall use the letters p , q, r to denote the components of the current per unit of 
area in the directions of x, y, z. 
Electrical Displacements (f, g, h). 
(55) Electrical displacement consists in the opposite electrification of the sides of a 
molecule or particle of a body which may or may not be accompanied w r ith transmission 
through the body. Let the quantity of electricity which would appear on the faces 
dy.dz of an element dx , dy , dz cut from the body be f.dy.dz, then /is the component 
of electric displacement parallel to x. We shall use / g, h to denote the electric 
displacements parallel to x , y, z respectively. 
The variations of the electrical displacement must be added to the currents p, q , r to 
get the total motion of electricity, which we may call/, q\ r 1 , so that 
(A) 
r , =r+ 
dh 
dt\ 
Electromotive Force (P, Q, R). 
(56) Let P, Q, R represent the components of the electromotive force at any point. 
Then P represents the difference of potential per unit of length in a conductor 
