INTRODUCTORY OBSERVATIONS. 17 



if there were any substances in nature whose magnetic powers, 

 like those of iron and nickel, admit of considerable developement, 

 and in which moreover the coercive force was, as we have here 

 supposed it, the same for all their elements, the results of the 

 preceding theory ought scarcely to differ from what would be 

 observed in bodies formed of such substances, provided no one 

 of their dimensions was very small, compared with the others. 

 The hypothesis of a constant coercive force was adopted in this 

 article, in order to simplify the calculations : probably, however, 

 this is not exactly the case of nature, for a bar of the hardest 

 steel has been shown (I think by Mr Barlow) to have a very 

 considerable degree of magnetism induced in it by the earth's 

 action, which appears to indicate, that although the coercive 

 force of some of its particles is very great, there are others 

 in which it is so small as not to be able to resist the feeble 

 action of the earth. Nevertheless, when iron bodies are turned 

 slowly round their axes, it would seem that our theory ought 

 not to differ greatly from observation ; and in particular, it is 

 very probable the angle 7 might be rendered sensible to experi- 

 ment, by sufficiently reducing b the component of the force/. 



The remaining articles treat of the theory of magnetism. 

 This theory is here founded on an hypothesis relative to the 

 constitution of magnetic bodies, first proposed by COULOMB, and 

 afterwards generally received by philosophers, in which they 

 are considered as formed of an infinite number of conducting 

 elements, separated by intervals absolutely impervious to the 

 magnetic fluid, and by means of the general results contained 

 in the former part of the Essay, we readily obtain the necessary 

 equations for determining the magnetic state induced in a body 

 of any form, by the action of exterior magnetic forces. These 

 equations accord with those M. PoiSSON has found by a very 

 different method. (Me*m. de 1'Acad. des Sciences, 1821 et 1822.) 



If the body in question be a hollow spherical shell of con- 

 stant thickness, the analysis used by LAPLACE (Mdc. C<51. Liv. 3) 

 is applicable, and the problem capable of a complete solution, 

 whatever may be the situation of the centres of the magnetic 

 forces acting upon it. After having given the general solution, 

 we have supposed the radius of the shell to become infinite, its 



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