40 HENRY A. KOWLAND 



interior of the ring-solenoid, the magnetic field at that point will, as is 

 well known, be 



2n'i - , 

 f> 



and at a point within an infinitely long solenoid 



If the solenoid contain any magnetic material, the field will be for 

 the ring 



and for the infinite solenoid 



4x/ttft, 



Therefore the number of lines of force in the whole section of a ring- 

 magnet of circular section will be, if a is the mean radius of the ring, 



S 



Q'= n' in dx = 



J B a x 



or, since n' = 2 * an and M = in, we have, by developing, 



Qf= ^jfoorj?) (i + \ f + i jr + & c .y . . (6) 



For the infinite electromagnet we have in the same way for a circular 

 section, 



Q' = 4*Mn(*B*) ......... (7) 



When the section of the ring is thin, equation (6) becomes the same 

 as equation (7), and either of them will give 



which is the same as equation (5). 



In all the rings used the last parenthesis of (6) is so nearly unity 

 that the difference has in most cases been neglected, the slightest change 

 in the quality of the iron producing many times more effect on the 

 permeability than this. Whenever the difference amounted to more 

 than -^TT it was not rejected. 



The apparatus used to measure Q' was based upon the fact discovered 

 by Faraday, that the current induced in a closed circuit is proportional 

 to the number of lines of force cut by the wire, and that the deflection 

 of the galvanometer-needle is also, for small deflections, proportional 

 to that number. In the experiments of 1870-71 an ordinary astatic 

 galvanometer was used; but in those made this year a galvanometer was 



