492 Lord Bayleigh on the Self-induction and 



Oberbeck *, including what is required for our present pur- 

 pose, viz. the value of 2tt §° crdr. In terms of the func- 

 tion <f> previously used (p. 489), (8) becomes 



whence is readily deduced 



te{\rOr=w*.i&* *J?*^l!\ , . . . (12) 

 Jo <t>{i2)fi.7ra 2 /py 



where 



The mathematical analogy between this problem and that 

 of the variation of a longitudinal electrical current in a 

 cylindrical conductor has been pointed out by Mr. Heaviside f, 

 who has also given the full solution of the latter. Maxwell's 

 investigation, somewhat further developed in my paper %, 

 relates principally to that aspect of the question with which 

 experiment is best able to deal, viz. the relation between the 

 total current at any moment and the corresponding electro- 

 motive force. 



That the argument in <j>, <$>' is the same in (12) as in (8) 

 will be evident, when it is remembered that B in (8) denotes 

 the resistance of unit length of the cylinder ; so that 



I __ira 2 



Hence, if we may assume that the material is isotropic, the 

 same numerical results are applicable to a given wire in both 

 problems. But from this point the analogy fails us. What 

 we require here to express is the ratio of the total magnetic 

 induction to the external magnetizing force, and not the 

 inverse relation, corresponding in the other problem to the 

 expression of the electromotive force in terms of the total 

 current. The experimental results are the reaction of the 

 core upon the magnetizing circuit, expressed as alterations of 

 apparent self-induction and resistance. Now if m be the 



* Wied. Ann. vol. xxi. (1884), p. 672. There seems to "be some error 

 in the way in which the magnetic constant appears in Oberbeck's solution 

 (47). According to it (as I understand) a copper core would be without 

 effect. 



t Phil. Mag. August, 1886, p. 118. 



% Phil. Mag. May 1886, p. 386, 



