﻿and some Applications to Physical Measurements. 401 



is proportional to the width of the zone and to its distance 

 from the equatorial line. 



Consider such a zone at distance x from the equatorial 

 line, x being measured in the positive direction of the field, 

 width dx. Then the total quantity of free magnetism on 

 it is equal to -f Cxdx, where C is determined from the fact 

 that the total quantity of positive (or negative) magnetism, 



?'. e. 1 Gxdx, is equal to 7m 2 I 



magnetization. 



magnetism on the strip is 



I being 

 a- 



the intensity of 



This gives C = 27r - 1, and hence the free 



a 2 c 

 ■ 7r -., I . xdx. 



Let us consider the effect of this quantity of positive 

 magnetism at the distance x, and an equal quantity of 

 negative magnetism at —x at a point on the equatorial plane 

 outside the specimen. Suppose the free magnetism on the 

 strip to act, in regard to external points, as if it were 

 concentrated at its centre of gravity, and let d be the distance 

 of the point in question from the axis of the specimen. 

 Then the magnetic force in a direction parallel to the axis 

 at the point 0, d will be 



a 2 j xdx x 



and the effect due to the whole specimen will be the integral 

 of this from to c, which becomes 



4*< 



^c*+d/ 



+ sinh" 1 - )• 

 d' 



If H is the value of the magnetic force within the specimen, 

 which we have seen is also the original value of the field 

 within the coil before the specimen was inserted, we may 

 write I=KJE, and the field at the point 0, d is reduced 

 from H to 



H^ 1-4tAX 



•I 



\/? + d 2 



+ si nh 



i)}- 



Taking ^ = 0*5 cm., i. e. just within the winding of the coil, 

 and with the same numerical data as before, this becomes 



H(l-l'79xl0- 6 ). 



At a point on the surface of the specimen, for ^ = 0*25 cm. 

 we obtain for the reduced field, 



H(l-2*5xl0- G ). 



The correction in this case is also negligible, and we are 



