president's address — SECTION A. 43 



near the contour than in the middle. In fact, it is quite the 

 wrong idea : what is meant by the shell is a pair of parallel 

 uniform sheets of magnetism — one N., the other S. — placed 

 at a certain distance apart, and having air, not iron, in 

 between them. It is to this case that the mathematics of 

 shells applies, and to this alone. The magnetic shell is the 

 exact analogue of the plate-condenser in electrostatics, the 

 plates bearing equal and opposite charges. The magnetic 

 field of a shell corresponds to such part of the electrostatic 

 field of the plate-condensers as lies outside the plates, and not 

 between them, the part which, in the electrostatic problem, is 

 not the important thing, but the correction. The strength of 

 the shell is the amount of magnetism per unit area of either 

 sheet multiplied by the distance between the sheets, and is no 

 measure of the actual magnetisation of a real shell which would 

 produce the same effect. So also the moment of a magnet is 

 the product of either of two equal aaiounts of magnetism — 

 one negative, one positive — placed a certain distance apart 

 in air, and of this distance, and has nothing to do with the 

 actual magnetisation of the magnet whose effect is defined 

 by its aid. 



When a current runs round a circuit and produces a 

 magnetic field in the neighbouring medium, we may consider 

 the effect as that of a magnetomotive force acting upon a 

 magnetic circuit and producing a magnetic displacement 

 along the circuit. If the medium about the current be 

 uniform and of permeability fx, then a given current C acts 

 with a magnetomotive force Air C, and the total induction 

 through the circuit is LC, where .L is called the co-efficient 

 of self-induction of the circuit. We may realise this by 

 turning to our analogy for a moment. We have a uniform 

 pressure 47rC acting upon our membrane : the membrane is 

 displaced so as to move through or generate a volume pro- 



LiC 



portioned to C, say equal to -z — . Hence the energy stored 



Lj C 



up in the medium is equal to J.47r C. -j— ' or | LC 



47r 



Since a magnetomotive force equal to 4 tt C produces a 



total induction through the plane of the circuit of L C, we 



may look upon ^ as the " resistance " of the magnetic 



circuit. 



In fact, if fi were constant at any particular point for all 

 past and present values of Bj the magnetic circuit would be 

 strictly analogous to the electric one. 



