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Electricity and Magnetism. 435 



currents we must have 22 (My) small in comparison with 

 X (L'y'). This would make any change that can occur in a 

 y r , in consequence of opening the battery circuits, a small 

 quantity of the order of My in magnitude. In this case the 

 dynamical value of a current in a conductor would not be 

 appreciably affected by the presence of permanent magnets 

 in its neighbourhood. 



The number of molecular circuits in an ordinary magnet 

 must, if the Amperean theory be true, be exceedingly great. 

 Let a uniformly magnetized filament be illustrated by a 

 solenoid made up of a very large number of equal distinct 

 circuits in each of which a current y' flows. If the number 

 of circuits per unit length be n, and the area of each be A, 

 the value of the aggregate self-inductance, 1/ say, is 

 47m 2 ZA, where I is the length of the solenoid, and the total 

 induction through it (neglecting the ends) is 47ni 2 ZAy', for 

 current <y f in each turn. Now let a circuit carrying the 

 current y be wrapped close round the solenoid in n turns. 

 The mutual induction will be at most 47nm'yA. Thus we 

 have M/Ij' = n / /nl. This ratio will for a magnet be exceed- 

 ingly small, and thus, unless y/y'be very great, the condition 

 stated above will be fulfilled. 



The discrepancy set up by the dynamical theory is on these 

 suppositions only apparent, and the Amperean theory does 

 not seem incompatible with the unity of explanation of 

 magnetic phenomena, which is a requisite of every explanation 

 of permanent magnetism. This kind of onesidedness of 

 result if it really exists has a bearing on the question of 

 relativity, and it seems desirable to examine the different 

 cases in detail. 



As was pointed out by Maxwell (' Elect, and Mag.' vol. ii. 

 § 844) it is necessary in order that the Amperean currents 

 may give an inductive magnetization agreeing with experi- 

 ment, that the self-inductance of each molecular current be 

 great, that is A/I/ must be small. This is also in accordance 

 with the conclusion come to above. If the current flow in 

 a ring-channel this condition, as Maxwell states, may be 

 fulfilled by means of a radius II of the mean line of the 

 channel great in comparison with the radius r of the channel* 

 since L' depends on log (R/r). 



I reserve some further discussion of this subject, from the 

 point of view of an electron- theory of magnetism, for another 

 opportunity. 



