Magnetized Non-crystalline Substances. 247 



13. After the explanations which have been given above, it 

 is scarcely necessary to point out that the position of unstable 

 equilibrium, determined in this experiment, is a point where 

 the magnetizing force due to the south pole is destroyed by 

 that of the more distant but more powerful north pole ; and 

 that the position of stable equilibrium is one where the excess 

 of the magnetizing force due to the north pole, above that 

 which is due to the less powerful south pole, has a maximum 

 value with reference to points in the continuation, through the 

 less powerful pole, of the line joining the two poles. If the 

 poles were mathematical points, and the bars so long that their 

 remote ends could produce no sensible action on the ball, the 

 position of unstable equilibrium would of course be such that 

 its distances from the tivo poles would be directly as the square 

 roots of the strengths of the magnets ; and, by the solution of a 

 most simple " maximum problem," it may be shown that the 

 stable position would be such that its distances from the poles 

 would be directly as the cube roots of the strengths. 



14. Experiment 2. — Place two equal bar-magnets symmetri- 

 cally with reference to the line of motion, with similar poles 

 at equal distances on two sides, in a perpendicular to this line, 

 and, to make the best arrangement, let the lengths of the 

 magnets be in the continuations of the lines joining their poles. 

 Operating by means of the stops, in a manner similar to that 

 described for the preceding experiment, it is readily ascer- 

 tained that there are two positions of stable equilibrium for 

 the ball at equal distances on two sides of the line joining the 

 poles, and that the middle point of this line is a position of 

 unstable equilibrium. 



15. Here, again, the explanation is obvious. The positions 

 of stable equilibrium being such that, with reference to points 

 in the line of motion of the ball, the magnetizing force due 

 to the two similar poles may be a maximum, are readily found 



to be at distances . on the two sides of the line joining the 



A v ^ 

 poles (the length of this line being denoted by a), if these be 

 mathematical points, and if the lengths of the bars be so great 

 that the distant poles produce no sensible effects. 



16. Experiment 3. — Hold a common horseshoe-magnet with 

 the line joining its poles perpendicular to the line of motion 

 of the ball, and, by a suitable management of the stops and 

 of the torsion-head, the existence of a force urging the ball 

 perpendicularly across the " lines of force" towards the mid- 

 dle point of the line joining the poles, may be easily made 

 manifest. 



17. Experiments on diamagnetic substances, and onferro- 



