for the Lifting-poicer of Magnets, 71 



Haecker's own magnets and partly with more recent magnets 

 made by Yon TTetteren, by Elias, and by Logeman, found a 

 somewhat different empirical rule. According to him the 

 permanent lifting-power should be written 



IT L 



n/A X / 5 



P=6Kv/A^/ 



where b is a constant depending on the quality of the steel 

 and its degree of magnetization, K the perimeter of the polar 

 surface, A the area of polar surface, L the length between 

 the actual poles, and I the mean between interior and exterior 

 lengths of the bar. For similar solids K \/A is simply pro- 

 portional to the surface A; so that this formula if applied to 

 similar magnets merely means that the lifting-power varies 

 as the polar surface, multiplied by a correcting factor which 

 takes into account the proximity of the two poles. Van der 

 Willigen found the coefficient b, which is virtually the same 

 as Haecker's a, to vary, for good horseshoe-magnets, from 

 19*5 to 22-d. 



If we consider the meaning of Bernoulli's and Haecker's 

 formulae, as applied to magnets of similar form, we shall see 

 that the cube root of the square of the mass of the magnet is 

 a quantity simply proportional to its polar surface, for the 

 linear dimensions are proportional to the cube root of the 

 mass, and the surface to the square of the linear dimensions. 

 Hence, so far as similar forms of magnet are concerned, these 

 rules mean nothing more or less than that the lifting-power 

 is proportional to the polar surface. This we know from 

 Joule's and many subsequent researches to be approximately 

 true for magnets carried to equal intensity of magnetization. 



Viewing the matter by the light of more recent researches 

 on the induction of magnetism in closed circuits of iron or 

 steel, we come to the same conclusion; for assuming that the 

 magnetic induction B has been carried to an equal degree in 

 the metal, the tension at any point in the circuit (in dynes 

 per square centimetre) is* 



B 2 



T = — 

 8tt> 



and the element of the pull over area dA is 

 d? = TdA = ~B 2 dA; 



whenCe P = ^ BVA ' 



* Maxwell's ' Electricity and Magnetism/ Art. G43. 



