Mr. H. A. Rowland on Magnetic Distribution. 365 



result ; taking the mean we find for the maximum magnet 



b_Vb 

 d~~ p 



(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;?. 

 This constant 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 tem- 

 per; 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 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 com- 

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

 tage 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 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 formula, 

 but would be found so for the exact one. 



Thus for the " normal magnet " the distribution becomes 



\ = C(e 6-e" 3 6), 



where C is a constant, and x is measured from the centre, 

 distribution will then be as follows : — 



The 



X 



b~ 



0. 



•1. 



•2. 



•3. 



4. 



•5. 



H • 



•609 



127 



2 05 



302 



426 



