124 Astronomical and Nautical Collections. 



of terrestrial magnetism. The laws of these different variations, 

 obtained by calculation, agree with those which Mr. Barlow, 

 Professor at Woolwich, has deduced from a numerous series of 

 experiments which he has made on the subject. The theory ex- 

 plains also a very remarkable fact observed by Mr. Barlow, relat- 

 ing to the magnetic action of a hollow sphere ; he found that the 

 intensity of this action does not sensibly vary with the thickness of 

 the metal, at least when the thickness is not very inconsiderable, and 

 is not less than about one thirtieth of an inch, for a sphere often Eng- 

 lish inches in diameter ; whence he has inferred that the magnetism 

 is confined to the surface of the magnetized bodies, or that it does 

 not penetrate them beyond a very small depth. It appears, how- 

 ever, from the calculation, as founded on the distribution of two 

 fluids throughout the mass of the magnets, that the action of a 

 hollow sphere is very nearly independent of its thickness, as long 

 as the proportion of this thickness to the radius is not expressed 

 by a very small fraction, the value of which is different for differ- 

 ent substances ; a result which agrees perfectly with the experi- 

 ment. 



This remarkable agreement affords a very important confirmation 

 of the accuracy of the analysis, and of the theory of magnetism on 

 which it is founded. We might, however, be desirous of a still 

 more diversified comparison of the theory with the phenomena ; 

 and for this purpose I have endeavoured to resolve the general 

 equations of the first memoir, as applied to bodies not having a 

 form so simple as that of the sphere. I have found, for example, 

 that these equations may be resolved in a very simple manner for 

 any elliptic spheroid, provided that the force which produces its 

 magnetism be constant in magnitude and in direction throughout 

 its extent ; which happens with respect to the terrestrial magnetism. 

 This solution is the object of the first paragraph of the memoir 

 which I now offer to the Academy. 



After having given the formulae relating to a spheroid of which 

 the axes have any imaginable relations to each other, I have par- 

 ticularly considered the two opposite cases of spheroids extremely 

 flattened and extremely elongated. A spheroid greatly flattened 



