448 Prof. A. Gray on the Dynamical 



generally observed is opposite to that which would be pro- 

 duced by the inductive change in y 2 . We are led to conclude 

 that2/ 2 , on which, according to Ampere's theory, the intensity 

 of magnetization depends, must remain practically constant. 

 Writing, then, the second of (10) in the form 



L^ + M^-L/y, 



where 7 is the initial current before the magnet was brought 

 into the field of the circuit, we see that if the dynamical 

 theory is applicable, My 1 /L 2 must be a quantity small in com- 

 parison with y. This gives dy 2 a small quantity of the second 

 order, and makes the value of dT, the change in the electro- 

 kinetic energy, depend only on the term ~L l y { dy\, which is zero 

 if the system is not in relative motion. Thus the fact that 

 the mechanical value of a current in a conductor is not affected 

 by bringing permanent magnets into its neighbourhood is 

 not contradicted by the dynamical theory, if the supposition 

 here made as to the value of M^j/L 2 be actually true. We 

 have to inquire what physical reasons can be adduced in 

 support of it. 



Suppose that, instead of a simple magnetic shell, we have 

 a solenoid made up of equal distinct circuits, in each of 

 which a current y flows. If the number of circuits per unit of 

 length be n, the coefficient of self-induction per unit of length is 

 47rn 2 A, where A is the area of the circuit, and the total induc- 

 tion through the solenoid (neglecting the effect of its ends) 

 is 47m 2 /yA, if I be its length. If the circuit carrying the 

 current y 1 consist of n' turns of wire closely surrounding the 

 solenoid, the induction through it and the solenoid is 4:irnn'yK, 

 Thus the maximum value of M is Airnn'A. Thus we get 



L 2 " nl ; 



that is, the ratio, which the theory indicates must be vanish- 

 ingly small, is equal to the ratio of the number of turns in 

 the circuit to the number of circuits in the solenoid. Thus 

 we are led to the supposition, probable on other grounds, that 

 the number of molecular circuits in the solenoid is exceed- 

 ingly great. 



It is also necessary, in order that the Amperian molecules 

 may give an inductive magnetization in iron agreeing with 

 experiment, that the self-induction of each molecular circuit 

 must be great, that is A/L 2 must be small. If the current 

 flow in a ring channel this condition, as Maxwell has pointed 

 out*, may be fulfilled by supposing the radius R of the mean 



* Maxwell, ' Electricity and Magnetism,' vol. ii. § 844, 



