186 Prof. Thomson on the Theory of Magnetic Induction. 



relations qui doiveut exister entre a!, 0, 7'*, et les quantites 

 ay, /3p 7yt> poui' qii'il n'ait pas lieu." — Ibid. p. 378. 



The following explanation may serve to give an idea of Pois- 

 son's mode of treating the subject of the last quotation, and to 

 show the relation it bears to the theory of which an outline has 

 been given above. 



Let X, Y, Z be the components, parallel to three fixed rect- 

 angular axes, of the magnetic force at any point in a uniform 

 field of force. A sphere of any homogeneous magnetizable 

 substance being placed in this field, let i be the intensity, and 

 /, in, n the direction cosines of the magnetization which is in- 

 duced in it. Poisson deduces, from his hypothesis of magnetic 

 fluids, equations % which are equivalent to the following : — 

 27=AX + BY + CZ-] 

 m=A'X + B'Y+C'Z L 

 m=A"X-fB"YH-C"zJ 



where A, B, &c. are coefficients depending solely on the nature 

 of the substance. These equations are deducible from the 

 axioms and the hypothetical principle of the superposition of 

 magnetic inductions, stated above, without the necessity of refer- 

 ring at all to the hypothesis of " fluids." All that remains of 

 Poisson's theory is confined to the case of non-crystalline matter, 

 with reference to which it is proved that A, B', and C" must be 

 equal to one another, and that each of the other six coefficients 

 must vanish ; and there is nothing to indicate the possibility of 

 establishing any relations among the nine coefficients which must 

 hold for matter in general. I have found that the following rela 

 tions,reducing the number of independent coefficients from nine to 

 six, must be fulfilled, whatever be the nature of the substance : — 



B" = C'; C = A"; A' = Bj 



the demonstration being founded on no uncertain or special 

 hypothesis, but on the principle that a sphere of matter of any 

 kind, placed in a uniform field of force, and set to turn round 

 an axis fixed perpendicular to the lines of force, cannot be an 

 inexhaustible source of mechanical effect. All the conclusions 

 with reference to magnecrystallic action enunciated in the pre- 

 ceding abstract are founded on these relations. 



* Component intensities of magnetization. 



t Components of the magnetizing force. 



J The products of the first members of Poisson's three equations in 

 p. 278 of his first Memoire, into k, the ratio of the sum of the volumes of 

 the magnetic elements to the whole volume of the body, are respectively 

 equal to the three components of the intensity of magnetization (il, im, in) ; 

 and if A, B, &c. be taken to denote the values of the products of k into Pois- 

 son's coefficients P, Q, &c. respectively, the equations m the te.\t coincide 

 with those of Poisson. 



