976 



of importance that all reasoning with reference to magnetism should 

 be conducted without assuming the existence of those hypothetical 

 fluids. 



The writer of the present paper endeavours to show that a com- 

 plete mathematical theory of magnetism may be established upon 

 the sole foundation of facts generally known, and Coulomb's special 

 experimental researches. 



The first part of the paper contains a general theory of magnets ; 

 the theory of magnetic induction, or of magnetization being reserved 

 for communications which the author proposes to offer subsequently 

 to the Royal Society. The five chapters which have already been 

 communicated bear the following titles : — 



Chap. L (§§ 3 — 20). Preliminary Definitions and Explanations. 



Chap. 11. (§§ 21 — 31). On the Laws of Magnetic Force, and on 



the Distribution of Magnetism in Mag- 

 netized Matter. 



Chap. III. (§§ 32— -M). On the Imaginary Magnetic Matter by 



means of which the Polarity of a Mag- 

 netized Body may be represented. 



Chap. IV. (§§ 45 — 64). Determination of the Mutual Actions be- 

 tween any Given Portions of Magnet- 

 ized Matter. 



Chap. V. (§§ 65 — 84). On Solenoidal and Lamellar Distributions 



of Magnetism. 



In the second chapter the method of specifying, by " intensity and 

 direction of magnetization" at every part of it, the magnetism of a 

 magnet, is given ; being founded on the elementary phenomena, and 

 Coulomb's laws of magnetic force, which are explained in Chap. I. 

 and the beginning of Chap. II. 



In the third chapter, by a strictly synthetical investigation, cor- 

 responding closely with that investigation of " the equation of con- 

 tinuity" in fluid motion which is analogous to Fourier's investigation 

 of the equation of motion of heat in a conducting solid, a certain distri- 

 bution of" imaginary magnetic matter" consisting of equal quantities 

 of positive and negative, or northern and southern matter each occu- 

 pying finite portions of the body or of its surface separated from those 

 occupied by the other, is shown to represent the polarity of a magnet 

 according to the assumed properties of this magnetic matter. The for- 

 mulae by means of which the resultant action between two entire mag- 

 nets of finite dimensions is determined are much simplified by this con- 

 ventional method of representing polarity. The result of the inves- 

 tigation agrees with what is expressed by a certain formula of Pois- 

 son's, deduced by a process of integration hy parts, from his elemen- 

 tary expression for the function since called by Green the " potential," 

 at any point in the neighbourhood of a magnet. Hence the investi- 

 gation of Chap. HI. leads, as is shown at the commencement of 

 Chap. IV., to a strictly synthetical proof of that remarkable formula. 



The fourth chapter contains, in the first place, formulae for the r 

 potential," and for the " magnetic force/' at any point in the neigh- 



