CHAP, v.] ELECTRICITY AND MAGNETISM. 277 



be respectively i and z", and their areas of surface s and 

 s' 9 and if the distance between their centres be r, and e 

 the angle between them, it can be shown that their 



mutual potential is = - if ss f . This expression 



represents the work that would have to be done to 

 bring up either of the circuits from an infinite distance 

 to its present position near the other, and is a negative 

 quantity if they attract one another. Now, suppose the 

 strength of current in each circuit to be unity; their mutual 



potential will in that case be ss', a quantity which 



depends purely upon the geometrical form and position 

 of the circuits, and for which we may substitute the 

 single symbol M, which we will call the " coefficient of 

 mutual potential:" we may now write the mutual 

 potential of the two circuits when the currents are i and 

 z* as = - z'z'M. 



But we have seen in the case of a single circuit that 

 we may represent the potential between a circuit and a 

 unit-pole as the product of the strength of the current 

 - z into the number N of the magnet-pole's lines of force 

 intercepted by the circuit. Hence the symbol M must 

 represent the number of each other's lines of force 

 mutually intercepted by both circuits, if each carried 

 unit current. If we call the two circuits A and B, then, 

 when each carries unit current, A intercepts M lines of 

 force belonging to B, and B intercepts M lines of force 

 belonging to A. 



Now suppose both currents to run in the same 

 (clock-wise) direction ; the front or S. -seeking face of one 

 circuit will be opposite to the back or N. -seeking face of 

 the other circuit, and they will attract one another, and 

 will actually do work as they approach one another, or 

 (as the negative sign shows) negative work will be done 

 in bringing up one to the other. Wl^en they have 

 attracted one another up as much as possible the circuits 

 will coincide in direction and position as nearly as can 



