42 president's address — section a. 



hand, if we replace the magnet by a circular current we know 

 that the opposite effect takes place. The current still attracts 

 the iron, but as the iron approaches the circuit the energy of 

 the field increases, for the nearer the iron is to the circuit 

 the greater is the amount of induction produced by the con- 

 stant magneto-motive force of the current ; consequently, the 



greater is the volume integral of q— • B H, i.e., the energy of 



OTT 



the field. 



Now, this is very well represented by the analogy. Instead 

 of the magnetic shell or the current round its contour, 

 imagine a thin plane membrane placed in an elastic medium. 

 Apply a uniform pressure all over one side of this membrane, 

 it is displaced, and lines of displacement spring into existence, 

 starting at one side of the membrane and curving round to 

 the otiier. This gives us the analogue of the field due to a 

 circular current, and the quantities are so related that pres- 

 sure per unit area corresponds to 4 tt x current. The amount 

 of the displacement will depend on circumstances — on the 

 nature of the bodies in the field, their positions and elasticities. 

 Even if the medium be uniform the displacement of the 

 various parts of the membrane will not all be uniform, but 

 will be greater near the edges than in the middle. To get the 

 analogue of a magnetic shell we must suppose the membrane 

 moved just as a uniform pressure would move it in a uniform 

 medium and then fixed. 



Now, in the former case, where the pressure is constant, if 

 part of the medium near the membrane be weakened (iron be 

 brought near it), the energy of the field will be increased, but, 

 in the latter case, where the displacement is constant, the 

 energy will be diminished. Just so the energy of a spring 

 stretched by a given force is increased if any part of the 

 spring is weakened, but if it be stretched a given amount the 

 energy is by the same cause diminished. 



A curious mistake is often made with regard to the nature 

 of magnetic shells. It is supposed that they can be built up 

 of numbers of small similar magnets placed side by side, so 

 as to have all their N. poles adjoining one another, and so 

 making up one face of the shell, all the S. poles making up 

 the other tace. But the result of such a combination, 

 according to the most natural interpretation, would be to 

 cause lines of induction to start uniformly from the shell-face, 

 so many lines per unit of area. This would not at all 

 resemble the effect of a current, which causes more induction 



