Astronomical and Nautical Collections. 123 



ments of a body to the extremely small spaces, in comparison with 

 its whole volume, through which the boreal and austral fluids can 

 be separately moved ; I have made no particular supposition with 

 regard to their form, nor to their respective disposition ; and I have 

 considered them as insulated from each other by means of intervals 

 impermeable to magnetism. According to this mode of consider- 

 ing the intimate nature of magnets, the sum of the magnetic ele- 

 ments which they contain, is a fraction of their volume, that may 

 vary in different substances susceptible of being magnetic, and 

 may also depend on their temperature ; and in this manner we 

 may explain how two bodies of the same form, but of different sub- 

 stances, or at different degrees of temperature, may exhibit, under 

 the influence of the same forces, magnetical actions of very differ- 

 ent intensities. 



Beginning with this theory, which is here but briefly recapitulated, 

 1 have deduced from it, in the first memoir, the equations which ex- 

 press, for all possible cases, the laws of the distribution of magnetism 

 within bodies that are rendered magnetical by induction, and those 

 of the attractions or repulsions which they exert on points given in 

 position. It is now only an analytical problem to resolve these 

 equations, in order to deduce from them results which may be 

 compared with experiment; but such a resolution is only attain- 

 able in a very limited number of cases, paying regard to the dif- 

 ferent form.s of magnets. That which I have taken for an example 

 in the first memoir, and which admits a complete resolution, is the 

 case of a solid or a hollow sphere, magnetized by forces of which 

 the centres of action are distributed in any given manner, either 

 without or within it. If we reduce these forces to a single on*, 

 that is, to the magnetic action of the earth, the formulee which 

 contain the solution become very simple. We deduce from it with- 

 out difficulty the direction of the needle of a compass, produced by 

 the neighbourhood of a sphere, magnetized thus by the influence of 

 the earth. This deviation varies with the distance of the middle of 

 the needle from the centre of the sphere, from the plane of the 

 magnetic meridian passing through that centre, and from the plane 

 passing through the same point, perpendicularly to the direction 



