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



Fig. 8. 



O .1 .2 .3 .4. .5 



Distribution on "normal magnet." 



This distribution is not the same as that given by M. Jamin j 

 bat as his method is so defective, and his " normal magnet " so 

 indefinite, the agreement is sufficiently near. 



The surface- density at any point of a magnet is 



X X 



8= 8^R r_ 7* Vp (25) 



6 d — € d . 



OC u 



which, for the same kind of steel, is dependent only on -^ and -y 



Hence in two similar magnets the surface-density is the same 

 at similar points, the linear density is proportional to the linear 

 dimensions, the surface integral of magnetic induction over half 

 the magnet or across the section is proportional to the surface 

 dimensions of the magnets, and the magnetic moments to the 

 volumes of the magnets. The forces at similar points with 

 regard to the two magnets will then be the same. All these 

 remarks apply to soft iron under induction, provided the inducing 

 force is the same — and hence include Sir William Thomson's 

 well-known law with regard to similar electromagnets ; and they 

 are accurately true notwithstanding the approximate nature of the 

 formula from which they have here been deduced. 



Our theory gives us the means of determining what effect the 

 boring of a hole through the centre of a magnet would have. In 

 this case R' is not much affected, but R is increased. Where the 

 magnet is used merely to affect a compass-needle, we should 

 then see that the hole through the centre has little effect 

 where the magnet is short and thick ; but where it is long, 

 the attraction on the compass-needle is much diminished. Where 

 the magnet is of the U-form, and is to be used for sustain- 

 ing weights, the practice is detrimental, and the sustaining-power 

 is diminished in the same proportion as the sectional area of 

 (he magnet. The only case that I know of where the hole 



