C. A. Perkins — Magnetic Permeability of Nickel. 225 



In the case of very strong currents which would heat the 

 ring rapidly the measurements of temporary magnetism were 

 omitted and the tangent galvanometer reading was taken be- 

 tween the measurements of the induced current. In measur- 

 ing the temporary magnetism, the current, instead of being 

 broken, was turned into the shunt, so that the battery strength 

 should remain constant. 



Eeadings of the thermometer were made before and after 

 each observation and the deflection produced by the earth in- 

 ductor was taken each time, though in most of the experiments 

 this was so uniform that the mean of all the values was taken 

 as the true value. 



Since the rings used in this experiment were of rectangular 

 section, the solution given by Kirchhoff does not accurately 

 hold, but the theory is equally simple. 



Let 58 = magnetic induction through unit area. 



jj. = magnetic permeability. 



H = horizontal component of earth's magnetism at the earth 

 inductor. 



H' =horizontal component of earth's magnetism at tangent 

 galvanometer. 



i = intensity of the primary current. 



A = total area included by the earth inductor. 



A' = area of the section of the ring. 



n = whole number of windings about the ring in the pri- 

 mary circuit. 



n' = whole number of windings in the secondary circuit. 



Q = current due to reversing earth inductor. 



Q' = current due to reversing magnetism of the ring. 



S - = deflection of galvanometer produced by Q'. 



S 7 = deflection of galvanometer produced by Q. 



R = mean radius of the ring. 



Then the magnetic induction at any point in the ring is 



2niu '., ........ . ... 



■ and the total induction through any section is : 



• 7 ■/*£ 1 -, 



2niuo I -g ■ ax 



d a XV — X 



where p is the distance of any point from the axis of the ring 

 and a and b are the sides of the rectangular section. 

 The value of the integral is 



R + - 



2 a I i a? ■ ., . a 4 \ 



log —«. = e I l + i wr +i (W + eto v 



• SB =-ir( 1+ %R? +etc -) 



