MAGNETIC PERMEABILITY OF IRON, STEEL AND NICKEL 39 



& = total length of helix. 



s' = resistance at end of helix of the rest of bar and medium. 

 M = magnetizing-f orce of helix. 

 We then obtain 



Ml -A / rx r (-*)-) (l\ 



1M M 1 A 



m - ~ A fe r 4-1 s n e r (-*)^ f9\ 



s' ~f 2R A^- I ( 



IJE 



-VTT 



in which 



and 



for near the centre of an infinitely long bar, where x > and < &, and 

 6=00 , we have 



Q.= 0,and V=%. . .-'. (3) 

 For a ring-magnet, s' = 0; 



.-. & = 0,and Q=X ...... (4) 



And if a is the area of the bar or ring, 



al =B = -ir ori = iSr ..... (5) 



in which A is the same as in the equations previously given. These 

 equations show that we may find the value of ^, and hence the permea- 

 bility, by experimenting either on an infinitely long bar or on a ring- 

 magnet. Equations (4) evidently apply to the case where the diameter 

 of the ring is large as compared with its section. The fact given by 

 these equations can be demonstrated in another and, to some persons, 

 more satisfactory manner. If n is the number of coils per metre of 

 helix and n' the number on a ring-magnet, i the strength of current, 

 and p the distance from the axis of the ring to a given point in the 



Formulae giving the same distribution as this have been obtained by Biot and 

 also by Green. See Biot's Traite de Physique, vol. iii, p. 77, 10 and 'Essay on the Ap- 

 plication of Mathematical Analysis to the Theories of Electricity and Magnetism,' 

 by Green, 17th section. 



IO [In the original paper this was " vol. iv, p. 669." The correction was made later 

 by Professor Rowland.] 



