274 ELEMENTARY LESSONS ON [CHAP. v. 



Again, suppose we could bring up a unit N. -seeking 

 pole against the repulsion of the N. -seeking face of a 

 shell of strength 2, and should push it right up to the 

 shell ; when it actually reached the plane of the shell the 

 shell would occupy a whole horizon, or half the whole 

 space around the pole, the solid-angle it subtended being 

 therefore 2-rr, 1 and the potential will be + 2<rz. If we 

 had begun at the S. -seeking face, the potential at that 

 face would be 2^2. It appears then that the potential 

 alters its value by 4^1 on passing from one side of the 

 shell to the other. 



317. Reaction between a Pole and a Magnetic 

 Shell. Again, Figs. 52 and 53 will show graphically 

 that lines of force from two poles of opposite kind run 

 into one another, whilst those from similar poles turn 

 aside as if mutually repellant. If a N. -seeking pole be 

 brought up to the N.-seeking face of a shell few or none 

 of the lines of force of the magnet will cut the shell ; 

 whereas if a N.-seeking pole be brought up to the 

 S. -seeking face of a shell, large numbers of the lines will 

 be cut by the shell and the pole, as a matter of fact, will 

 be attracted up to the shell, where as many lines of force 

 as possible are cut by the shell. We may formulate this 

 action by saying that a magnetic shell and a magnet-pole 

 react on one another and urge one another in such a 

 direction as to make the number of lines of force that are 

 cut by the shell a maximum (Maxwell's Rule, Art. 193). 

 Outside the attracting face of the shell the potential is - /, 

 and the pole moves so as to make this negative quantity 

 as great as possible, or to make the potential a minimum. 

 Which is but another way of putting the matter as a 

 particular case of the general proposition that bodies 

 tend to move so that the energy they possess in virtue 

 of their position tends to run down to a minimum. 



318. Magnetic Potential due to Current. The 

 propositions concerning magnetic shells given in the 



1 See note on Ways of Reckoning Angles, Art. 133. 



