SHUDDEMAGEN. — DEMAGNETIZING FACTORS FOR IRON RODS. 191 



impossible to realize such a distribution. If we have a possible case, 

 then 



H=H' - H t = II' - '2mibc-K -I. 



Now the factor 2-abc • K is constant for a given ellipsoid, and is called 

 its " demagnetizing factor " K. When the iron is an ellipsoid of revo- 

 lution (b = c), we can integrate K and get a simple formula for N as 

 a function of a/b, the ratio of the length of the ellipsoid to its greatest 

 diameter. 9 It is, when written in terms of m, 



]V = , V™ . log (2 mv^^l + 2 m 2 - 1) - 



(m- - l)> m 2 - l 



When 1 is negligible in comparison with in' 2 the formula assumes the 

 simple form 



jV= -^(log2m- l). 



This N does not depend, therefore, on the softness of the iron nor on 

 the magnetizing field, provided the iron ellipsoid was initially demag- 

 netized and our magnetizing field has been continuously increased from 

 zero to its final value. 



If the iron is perfectly "soft," or incapable of retaining magnetism 

 when the magnetizing force II' is withdrawn, then any field H' will 

 produce a unique magnetization. The uniform H' along the major 

 axis of the ellipsoid of revolution will therefore produce such a magnet- 

 ization as we found would be kept in equilibrium by the same //'. 

 As the iron we deal with in practice is not "soft," but shows hyster- 

 esis, we find it necessary to define susceptibility as the ratio of I/H 

 when the iron is slowly carried from zero magnetization to the value 7, 

 the magnetizing field to increase slowly and continuously up to the 

 proper value H'. Under these conditions it is reasonable to suppose 

 that any magnetizing field will give a unique magnetic distribution, 

 and our results hold true. 



Suppose we desire to measure the susceptibility of a specimen of 

 iron in accordance with our ideal definition, so that it may be free 

 from ambiguity ; let us consider the suitability for this purpose of the 

 various experimental methods now in use. The fluxmeter is an instru- 

 ment recently invented, which attempts to give permanent deflections 

 which are proportional to the changes of magnetic induction through 

 a secondary circuit, and these deflections are independent of the time- 



9 Maxwell, II, §§ 437-438. 



