146 COEFFICIENTS OF INDUCTION. 



777. MAXWELL'S METHOD. We may, in certain conditions, use 

 a method of Maxwell* which depends on the following theorem : 



Given a circle defined by its distance x from a fixed point of the 

 axis, and by its radius r, the coefficient of induction M, in reference to 

 this circle of any given system of magnets, or of currents, satisfies 

 the ratio , 



D 2 M D 2 M i DM 



(49) + - = - 



For let P be a point of the circle on a radius which makes the 

 angle 6 with a radius of fixed direction, and let V be the potential 

 of the system at the point P. The normal component of the force 



DV 



is equal to - ; the flow of force across an element of surface 



rdBdr is 



DV 



-rdBdr--. 

 DJC 



If the radius of the circle is increased by &r, the flow of force 

 increases by 



DM 

 as this increase is itself equal to the variation Dr of the co- 



efficient of induction, we have 



DM 

 ir 



Let x now have the increment (hr, the corresponding variation 



DJC of the coefficient of induction is equal and of opposite sign 

 <h: 



to the total flow of force cut by the lateral surface of the cylinder of 

 radius r, and height 8x. The value of this latter is 



o 

 and therefore 



DM 



(51) - 



^ o 



MAXWELL. Electricity and Magnetism, Vol. II., p. 307. 



