160 Dr. E. H. Hall on the "Rotational Coefficient " 



By the term " strength of the magnetic field," as just used, 

 is meant the intensity of the field between the poles which 

 obtains when the metal plate is not in the field. This inten- 

 sity is measured, as described in the article already alluded to, 

 by withdrawing suddenly from the field a small coil of wire 

 and observing the effect upon a galvanometer in circuit with 

 the coil. This gives what is called the magnetic induction in 

 this part of the field. In general, the magnetic induction in 

 any magnetized space would be changed by introducing into 

 that space a body capable of being magnetized by induction. 

 The well-known expression for the magnetic induction within 

 any such body placed in a magnetic field is (Maxwell's 

 ' Treatise,' vol. ii. art, 428) 



23 = § + 47r3; (1) 



where <£) is the magnetic force within the body (Thomson's 

 ' Polar Definition,' reprint, p. 397), and 3> is the intensity of 

 magnetization (Maxwell, art, 384). 



Now, in case of uniform magnetization, JQ is equal to the 

 intensity of the field as it would exist if the body magnetized 

 by induction were removed (i. e. just what we measure by 

 means of the coil and galvanometer), together with the force 

 exerted by what we may call the magnetism induced on the 

 surface of the magnetized body. This latter force will, of 

 course, depend upon the shape and dimensions of the body. 

 If it is a very thin disk, the reaction of the induced magnetism 

 will, as Maxwell remarks, be equal to — 47r3 ; and in this 

 case, writing §* for the intensity of the magnetic field as 

 above defined, we have 



£=$-4^3 (2) 



Substituting in (1), we have 



33=5, (3) 



which means that, in a very thin disk magnetized by induc- 

 tion, the magnetic induction is just what it would be in the 

 space occupied by the disk if the disk were removed from the 

 field. Now the strip of nickel which we employ has a width 

 600 or 800 times its thickness ; and it has been assumed that 

 we may, for our present purpose, regard it as such an infinitely 

 thin disk as Maxwell supposes. The error resulting from this 

 assumption may easily be seen to be small. At the centre of 

 the strip of nickel the real value of 33 would be perhaps -^ of 

 one per cent, greater than the value as above determined. At 

 a point 1 millim. from the edge of the strip the error might 

 amount to J or ^ of one per cent.; while at -^ millim. from 

 * Called M in previous article. 



