STUDIES ON MAGNETIC DISTRIBUTION 125 



intensity of the earth's magnetism, and shows that the magnets should 

 be made short, thick, and hard for the best effect. 11 



But for all ordinary purposes the results for the second and third 

 cases seem most important, and lead to nearly the same result; taking 

 the mean we find for the maximum magnet 



fCtA\ 



(24) 



We see from all our results that the ratio of the length of a magnet 

 to its diameter in all cases is inversely as the constant p. This con- 

 stant increases with the hardness of the steel; and hence the harder the 

 steel the shorter we can make our magnets. It would seem from this 

 that the temper of a steel magnet should not be drawn at all, but the 

 hardest steel used, or at least that in which p was greatest. The only 

 disadvantage in using very hard steel seems to be the difficulty in 

 imparting the magnetism at first; and this may have led to the practice 

 of drawing the temper; but now, when we have such powerful electro- 

 magnets, it seems as if magnets might be made shorter, thicker, and 

 harder than is the custom. With the relative dimensions of magnets 

 now used, however, hardening might be of little value. 



We can also see from all these facts, that if we make a compound 

 magnet of hardened steel plates there will be an advantage in filing 

 more of them together, thus making a thicker magnet than when they 

 are softer. We also observe that as we pile them up the distribution 

 changes in just the way indicated by M. Jamin, the curve becoming 

 less and less steep. 



Substituting in the formula the value of p which we have found for 

 Stub's steel not hardened, but still so hard as to rapidly dull a file, we 

 find the best ratio of length to diameter to be 33-8 and for the same 

 steel hardened, about 17, though this last is only a rough approxima- 

 tion. This gives what M. Jamin has called the normal magnet. The 

 ratio should be less for a U-magnet than for a straight one. 



For all magnets of the same kind of steel in which the ratio of 

 length to diameter is constant the relative distribution is the same; 

 and this is not only true for our approximate formula, but would be 

 found so for the exact one. 



Thus for the " normal magnet " the distribution becomes 



11 Weber recommends square bars eight times as long as they are broad, and tem- 

 pered very hard. (Taylor's Scientific Memoirs, vol. ii, p. 86.) 



