550 PROPERTIES OF THE ELECTROMAGNETIC FIELD. 



the co-ordinates, that is to say, which enclose a surface across which 

 the strength of the current is u dy dz^ and if we determine the same 

 work by the magnetic forces, we find by a calculation analogous to 

 that applied to (567), the three new equations 



ax 



- . 



oy f& 



570. POTENTIAL ENERGY OF CURRENTS. Let us consider 

 various currents C^ C 2 , C 3 , . . . in which the strengths are Ij, 

 I 2) I 3 . . . ; let Lj, L 2 , L 3 be their coefficients of self-induction and 

 M 1-2 , M 1-3 , M 2<8 , . . . their coefficients of mutual induction. 



The flows of force which traverse each circuit are 



and the potential energy of the whole of the currents (524) is 



(5) W = -(Q 1 I 1 + Q 2 I 2 + ) = 



From equation (i), we have therefore 



Taking u, z>, and w in the same signification as above (569), 

 the components of the current across the section S of one of 

 the conductors are 



!$- 8. 



ds 



