40 



MAGNETISM. 



city, but not sensibly adding to its bulk. 

 On bringing a body thus constituted near 

 an electrified body, every one of the 

 grains would immediately become elec- 

 trical by induction ; and, in this condition 

 of the body, it has been mathematically 

 proved that the attractions and repulsions 

 which the body would exert externally, 

 would be the same with those of a ho- 

 mogeneous conducting body of the same 

 form and size, subjected to the same ex- 

 ternal forces : although, in the latter 

 case, the two electric fluids would be 

 transferred to the opposite extremities 

 of the body, while, in the former, they 

 would be obliged to remain in the con- 

 stituent masses to which they originally 

 belonged. An electrical body, consti- 

 tuted in the manner here supposed, pre- 

 sents us with a disposition exactly analo- 

 gous to that of a magnetical body ; and 

 is therefore calculated to give us a very 

 distinct idea of the distribution of the 

 magnetic fluids when that body is mag- 

 netized. The electricity inherent in the 

 tourmaline appears to be disposed in the 

 manner above described ; and this stone 

 accordingly affords an excellent illus- 

 tration of the hypothesis under our con- 

 sideration. See Electricity, $ 197. 



(162.) Another general consequence 

 of the theory is, that a magnetic needle, 

 placed in the interior of a hollow sphere 

 of soft iron, and so small as not to exert 

 any sensible influence on the sphere, will 

 not be subject to any magnetic action 

 from a magnetic force proceeding from 

 a point external to the sphere ; or, in 

 other words, all magnetic action, whe- 

 ther of the earth or of any number of 

 magnets placed without the hollow 

 sphere, will be completely intercepted by 

 the sphere with reference to all magnetic 

 bodies contained in its interior. And 

 conversely, such hollow sphere will 

 totally prevent the action of a magnet 

 placed within it from being exerted on 

 any body placed without the sphere. 



(163.) The formulae derived from this 

 theory have been applied by Poisson to 

 another case, which, as we shall after- 

 wards find, is one of considerable prac- 

 tical importance in navigation, namely, 

 that of a hollow sphere of iron, magnet- 

 ized by the influence of the earth, that 

 is, by the action of a force of which the 

 origin is very remote, and which may, 

 therefore, be considered as uniform in 

 magnitude, and acting in parallel direc- 

 tions on all the points of the body in 

 question. From the resolution of the 

 equations of magnetic equilibrium ob- 



tained in this case, it appears that al- 

 though the magnetism is by no means 

 confined to the superficial strata of 

 the sphere, and although its intensity 

 may be determined for any particular 

 point of the solid mass of the shell, yet the 

 magnitude of the three component forces 

 produced by it is wholly independent of 

 the thickness of the shell, and is deter- 

 mined only by the radius of the external 

 surface, and by the co-ordinates belong- 

 ing to the position of the point on which 

 the forces act. When the distance of 

 this point from the centre of the sphere 

 is very great, compared with the radius, 

 each of the three forces is very nearly as 

 the cube of the radius directly, and as 

 the cube of the distance inversely. We 

 shall have occasion, in a future chapter, 

 to notice the remarkable coincidence of 

 the results of observation with the de- 

 ductions from this theory, affording a 

 very important confirmation of the ac- 

 curacy both of the analysis itself, and of 

 the theory from which it is derived. 



(164.) In a subsequent memoir*, M. 

 Poisson extends his researches so as to 

 obtain a more diversified comparison of 

 the theory with the phenomena; and 

 with this view resolves the general equa- 

 tions he had before established, in the 

 case of bodies having forms less simple 

 than that of the sphere. Such a resolu- 

 tion, however, is attainable only in a very 

 limited number of cases, of which the 

 elliptic spheroid is an example. After 

 giving the formulae relating to a spheroid 

 of which the axes have any imaginable 

 relations to each other, he particularly 

 considers the two opposite cases of 

 spheroids extremely flattened and ex- 

 tremely elongated. The former may re- 

 present a plate, of which the thickness 

 varies very slowly near the centre, and 

 decreases from the point to the circum- 

 ference ; for its action on points near its 

 centre must be sensibly the same as that 

 of any other plate of uniform thickness 

 and of very great extent. The latter, or 

 the extremely elongated spheroid, ap- 

 proaches very nearly to the form of a 

 needle or bar, of which the diameter 

 decreases from the middle to the extre- 

 mities, varying at first very slowly ; and 

 its action on points near its middle can 

 differ but little from that of a bar of 

 which the diameter is constant, and very 

 small in proportion to its length. The 

 consideration of these three cases, which 

 readily admit of the application of the 

 analytical formulae, is of considerable 



* Memoires de 1'Jnstitut, tome v., p. 481. 



