44 president's address — section a. 



As an example, let us take the sinple case of an anchor- 

 ring- coil of length /. All the opposition to the magneto- 

 motive force will come from the medium within ihe coil. 

 Hence, if A be its area of section, d the displacement along 

 it, E the elasticity, then, reasoning from the analogy, we 

 have — 



A X pressure = ^.A.c^.E; 

 or, translating, 



fx 47r 



4 P 

 Hence the total induction = A.B = — 7— 



^ A. 



Thus the " resistance " of the circuit is equal to . 



^ IxA. 



The energy in the case of an anchor-ring coil wound with 

 71 turns to the centimetre is plainly — reasoning from the 

 analogy — 



I A X pressure x d. 



But47rC./wA = l.A.d.^ 



. 47rC./i 

 :.d = —^- 



Hence, substituting, the energy 



= ^ AAwCl.n. — ^ — 

 Z ill 



= 2 7rA./.nV.C« 



the well-known formula. 



I will just give one more example of the use of the 

 analogy. Consider the following problem, as it has been 

 several times stated. 



If a diamagnetic substance be made to approach a magnet, 

 moving from a position A to a position B, work will have to 

 be done : suppose the diamagnetic substance to possess, as it 

 may do, some small amount of retentiveness, then a slight 

 tap, involving an infinitesimal expenditure of work, will cause 

 tho diamagnetism, and therefore the repulsive force to increase. 

 If now the substance be withdrawn to its former position and 

 again slightly tapped, the substance will have gone through 

 a complete cycle, and there has been a nett gain of energy. 

 This is an absurd result ; and the flaw in the reasoning- 

 occurs in the assumption that the first slight tap will increase 

 the diamagnetism : it will, of course, diminish it. All this is 

 very easy to picture by the analogy. A diamagnetic sub- 



