106 H. A, Rowland— Studies on Magnetic Distribution. 



This last result is useful in preparing magnets for determin- 

 ing the intensity of the earth's magnetism, and shows that the 

 magnets should be made short, thick, and hard for the best 

 effect* 



But for all ordinary purposes the results for the second and 

 third cases seem most important, and lead to nearly the same 

 result ; and taking the mean we find for the maximum magnet 



1=}-:^ (24) 



d p 



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

 magnet to its diameter should vary inversely as the constant ;). 

 This constant increases with the hardness of the steel, and 

 hence the harder the steel the shorter we can make our mag- 

 nets. 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 disadvan- 

 tage 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 electromagnets, it seems as if magnets might be made 

 shorter, thicker and harder, than is the custom. With the rel- 

 ative 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 com- 

 pound magnet of hardened steel plates there will be an advan- 

 tage in placing 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 indi- 

 cated 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 approximation. 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 for- 

 mula, but would be found so for the exact one. 



Thus for the " normal magnet'' the distribution becomes 



where C is a constant, and x is measured from the center. The 

 distribution will then be as follows : 



* Weber recommends square bars eight times as long as they are broad, and 

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



