Magnetomotive Force. 207 



netizing force *£). The old theory says there are all together 

 /uA«£) lines of force (A = section of bar), and 



M£=A£(l+v>, . . . . . (l) 



where A«£j are the lines of force of the magnetizing force 

 itself, A«£)A, those added by the induction. 



These last form the poles. And, since there are 4-7T lines of 



force round a unit pole, strength of pole = . ^ » 



Again, 



Moment = pole x distance of foci, 



(ultimately) = pole x length of bar, 

 = -~ x volume; 



47T 



and ^ _ moment _ X«§ 



volume 47r 

 Substituting for \«§ in (1), 



**$=*$ + 4n-3; 



whence come the equations of the ordinary theory first above 

 written. 



From our point of view yu,=X in the above, the action of 

 the magnetic matter replacing that of space instead of being 

 added to it ; and our fundamental equation becomes 



/n = 4:7rK, or 23 = 47r3. 

 I believe that there is no evidence whatever for the view that 

 represents «£) as subsisting independently throughout the mag- 

 netic body. 



If we are really to carry out Faraday's theory of magnetism, 

 we must take into account the entire resistances of the circuits 

 formed by iron and air, and then determine the magnetic 

 induction through the circuit as the quotient of the " magne- 

 tomotive force " by the total resistance. 



We may define the unit of " magnetomotive force " as that 

 which, acting through a unit of magnetic resistance, produces 

 a unit of field -intensity or magnetic induction. 



Consider a solenoid having its ends joined. Then, if the 

 resistance unit be that of 1 centim. of the length in air, x is 

 the resistance of length x of the solenoid. Similarly, if the 

 solenoid be filled with an iron ring of permeability //,, x/fi is 

 the resistance of length x of the ring. And if x be the whole 

 length of the ring, M the whole magnetomotive force, 



X 



