A DYNAMICAL THEORY OF THE ELECTROMAGNETIC FIELD. 589 



PART VII. 

 CALCULATION OF THE COEFFICIENTS OF ELECTROMAGNETIC INDUCTION. 



General Methods. 



(109) The electromagnetic relations between two conducting circuits, A and 

 B, depend upon a function M of their form and relative position, as has been 

 already shewn. 



M may be calculated in several different ways, which must of course all 

 lead to the same result. 



First Method. M is the electromagnetic momentum of the circuit B when 

 A carries a unit current, or 



where F, G, H are the components of electromagnetic momentum due to a unit 

 current in A, and ds' is an element of length of B, and the integration is 

 performed round the circuit of B. 



To find F, G, H, we observe that by (B) and (C) 



+ i + ~ = ~ * P ' 



with corresponding equations for G and H, p, q', and r' being the components 

 of the current in A. 



Now if we consider only a single element ds of A, we shall have 



, dx , , dy , , dz , 



P = Ts d8 ' 1=fs ds > r= ds ds ' 



and the solution of the equation gives 



u.dx , _, a dy , TT u. dz , 



F = '-- r ds, G=--r-ds, H = "-j-ds, 



p ds p ds pas 



