118 Messrs. Evans and Smith on the Magnetic [Mar. 16, 



which the problem of the distribution of induced magnetism can be 

 exactly solved. It is known that when a uniform mass of iron is magnet- 

 ized by induction in a uniform field of force, the effect of the whole mag- 

 netism induced throughout the mass is precisely the same as that of a 

 certain distribution of free magnetism on the surface (including, in the case 

 of a hollow shell, a distribution on the inner surface), the amount and law 

 of this distribution depending on a coefficient K, which is zero for non- 

 magnetic bodies, and infinite for a body infinitely susceptible of induction. 

 Very few observations of the value of this coefficient have been made. 

 The only observations of which the authors are aware, made for this spe- 

 cial purpose, are those by Weber (Getting. Trans, vol. vi. p. 20), Thalen 

 (Nov. Act. Soc. Reg. Upsal. 1861), and by the authors. Weber finds for 

 hard steel K=4'934, for soft steel *r=5'61, for soft iron A.- =36. Thalen 

 finds for soft iron K varying from 27'24 to 44-23, the mean being 36'75. 

 The authors find, for a rod of iron probably not very different from the 

 iron used in the construction of iron ships, K=;12 when the iron is not 

 struck between reversals, but when hammered sharply it rose to up- 

 wards of 80. The effect of rods or plates magnetized longitudinally is 

 nearly proportional to K ; but when a mass is magnetized at right angles to 

 its surface the case is very different, and the free magnetism is almost in- 

 dependent of *:. Thus in the case of a plate magnetized at right angles to 

 its surface, in the case of a sphere, and in the case of a cylinder magnetized 

 at right angles to its axis, the free magnetism is proportional to 



4-7TK 4 TK 2lTK 



, - , , and ~ - respectively, 



1 -j- 4-7TK 1+ ^TTC 1 + 2lTK 



which are so nearly independent of the value of K, that the effect of a 

 sphere of the hardest steel magnetized by induction is within 4 per cent. 

 of the effect of a similar sphere of the softest iron, and the effect of the 

 latter within 1 per cent, of what it would be if the iron were infinitely 

 susceptible of induction. Hence the magnetism of thin masses of iron 

 depends very much on the quality, and also on whether the iron is ham- 

 mered or not. The magnetism of thick masses of iron is almost wholly 

 independent of these circumstances. 



One of the most interesting applications of the formulae is the compa- 

 rative effects of solid and hollow spheres, and bodies of analogous shapes. 



The proportion of the effect of a solid sphere to that of a spherical 



o 



shell of thickness t (in terms of the radius of the sphere) is as t-\- : t. 



STTK 

 In the case of soft iron this is about 



so that when the thickness of the iron considerably exceeds -^ of the 

 radius of the sphere, the effect of the spherical shell is sensibly the same 

 as that of a solid sphere of the same external diameter. Mr. Barlow found 



