486 PROFESSOR CLERK MAXWELL ON THE ELECTROMAGNETIC FIELD. 
quantities, namely, 
For Electromagnetic Momentum F G H 
„ Magnetic Intensity a /3y 
„ Electromotive Force P Q R 
„ Current due to true conduction p q r 
„ Electric Displacement f g h 
„ Total Current (including variation of displacement) . . p' c[ n* 
„ Quantity of free Electricity e 
„ Electric Potential T 
Between these twenty quantities we have found twenty equations, viz. 
Three equations of Magnetic Force (B) 
„ Electric Currents (C) 
,, Electromotive Force (D) 
„ Electric Elasticity (E) 
„ Electric Resistance (F) 
„ Total Currents (A) 
One equation of Free Electricity (G) 
„ Continuity (FI) 
These equations are therefore sufficient to determine all the quantities which occur 
in them, provided we know the conditions of the problem. In many questions, how- 
ever, only a few of the equations are required. 
Intrinsic Energy of the Electromagnetic Field. 
(71) We have seen (33) that the intrinsic energy of any system of currents is found 
by multiplying half the current in each circuit into its electromagnetic momentum. 
This is equivalent to finding the integral 
E=i2(F/+G 2 '+Hr')<ZV (37) 
over all the space occupied by currents, where p, q, r are the components of currents, 
and F, G, H the components of electromagnetic momentum. 
Substituting the values oif, q', r' from the equations of Currents (C), this becomes 
s*K2-S)+Ke-3)+ h (£ -*) b- 
Integrating by parts, and remembering that 
expression becomes 
dG 
8- z rU“* 
M 
dF 
dz 
a, /3, y vanish at an infinite distance, the 
dH\ . /dG dF\] 7T 
dx)~^~/\dx dy ) J ’ 
where the integration is to be extended over all space. Referring to the equations of 
Magnetic Force (B), p. 482, this becomes 
E =^2{u.(Aoi + p.[Ap+y.py}dV, 
(38) 
