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PROFESSOR CLERK MAXWELL ON THE ELECTROMAGNETIC FIELD. 
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 
shown. 
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 , & dy & 
M= J( F 5?+ G S+ H * i )*> 
where F, G, H are the components of electromagnetic momentnm 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) 
d°F , d 2 F , d 2 F . 
with corresponding equations for G and H, p', <[, and F being the components of the 
current in A. 
Now if we consider only a single element ds of A, we shall have 
2 '=5*i 
and the solution of the equation gives 
where § is the distance of any point from ds. Hence 
HJ?( 
dx dx dy dy dz dz\ , 7 , 
dj+dsdP+dsdP) dsds 
= |j ^cos 6dsdd. 
where 0 is the angle between the directions of the two elements ds, ds', and § is the 
distance between them, and the integration is performed round both circuits. 
In this method we confine our attention during integration to the two linear circuits 
alone. 
(110) Second Method. M is the number of lines of magnetic force which pass 
through the circuit B when A carries a unit current, or 
M = 'Zfacil+pftm -\-^yn)dS l , 
where pa, py are the components of magnetic induction due to unit current in A, 
