6 TREATISE ON ALTERNATING CURRENTS. 



respective circuits at ds and ds', the integration extending round 

 both circuits. 



The above expression for M shows that it depends simply 

 upon the geometrical configuration of the two circuits, and that the 

 relation is reciprocal. 



It follows that if the two circuits carry currents i and i' 

 respectively, the number of lines of force interlinking both 

 circuits is M(i + i'). 



8. If two quantities, q i} q. 2) of electricity are situated at a distance 

 r apart, the mutual force exerted between them is given by 



where Jc is a constant depending upon the units chosen, and K is 

 a constant depending upon the intervening medium, and is called 

 the Specific Inductive Capacity of the medium: it is 

 taken to be unity when the medium is air. The force is attractive 

 if q\ and q$ have opposite signs, and repulsive if they have like 

 signs. 



Electrostatic Unit of Quantity. If the unit of 

 quantity of electricity is chosen so that two such units placed 

 at a distance of one centimetre apart in air exert a mutual force 

 equal to one dyne, k = 1 and equation (6) becomes 



9. When r is varied, an amount of work is done equal to 



where r$ and r\ are the initial and final values of r. If r a is 

 infinite, the work done is 



This is the work done by, or against, the electric force, accord- 

 ing as qi and # 2 have like or unlike signs, in bringing them to a 

 distance r\ from an infinite distance apart. 



The unit of work the erg is the work done by a dyne when it 

 moves its point of application over the distance of one centimetre. 



