236 MAGNETISM however many poles of the same kind there may be, true and false, the whole number must be odd. This of course disposes of the notion formerly held by some physicists that the earth actually had two north poles. As already indicated, Gauss concluded from his reduction of the magnetic observations at his disposal that, apart from purely local disturbances, the earth has, as a matter of fact, only one north and one south pole. Local The effeet of a deposit of magnetic ore, or other cause disturb- of the kind, might of course produce a disturbance, within ances of & ij m jted area, of the equipotential lines. It may assist the practical magnetist to indicate the nature of this disturbance in a particular case. Let us suppose that a magnet is placed some distance underground, vertical, with its north pole uppermost. Then, if its moment be sufficiently great, the equipotential lines will be as in fig. 27. l The upper side of the figure is supposed to be magnetic north, and it is supposed that the undisturbed lels. Fig. 27. parallels would be straight lines running magnetic east and west, which is sufficiently near the truth in most cases. It should be observed that fig. 27 is in reality a transformation of figure 26, one of the poles being projected to infinity. The reader should notice that the double point F, due south of the point a vertically over the disturbing magnet, is a point of equilibrium at which the horizontal components of the forces of the earth and the magnet destroy each other ; it will be a false pole, south or north according as the magnet or the earth prevails. EXPERIMENTAL FOUNDATION FOR THE LAW or THE INVERSE SQUARE. Difficul- From what has already been laid down, it will be ties of se en that the determination of the elementary law of tlie magnetic action is a very complex problem. The action as 1 to the between two magnets depends, not only on their distance elemen- apart, but also on their relative angular position. Then tarylaw. we have to distinguish force of translation, which varies inversely as the fourth power of the distance, and directive couple, which varies inversely as the third power. It must also be remembered that the elementary law results in part from an hypothesis as to the nature and distribution of the cause of the magnetic action, for, until some such hypothesis is made, no clear conception is possible of what is to be understood by elementary action. Lastly, we have the disturbance which arises from magnetic induction, the consequence of which is that magnetically speaking two magnets are not the same at different distances apart. When all these circumstances are considered, it is not surprising to find considerable uncertainty and difference of opinion among the earlier magnetic philosophers. The truth is that the law as now established owes quite as 1 Gauss, I.e., 13. much to the development of magnetic theory as to tho work of magnetic experimenters. The question attracted the notice of Huygens and Huygens Hooke, but Newton seems to have been one of the first Hooke, who propounded any law on the subject. He says Newton - (Principia, lib. iii. prop. 6, cor. 5) that some rough experiments had led him to the conclusion that the magnetic force (vis magnetica) decreases according to the law of the inverse cube of the distance. No account of the experiments is extant, and it does not appear what he means exactly by vis magnetica. If the directive couple is meant, and the action of the entire magnet is intended, then, as we have seen, this is in agreement with modern theory. In a remarkable note in the annotated edition of the Principia by Le Sueur and Jacquier (assisted by Le Sueui Calandrini ?) (1742) on the passage in question, a series an(l of deflexion experiments are described, and an accurate ac( l ui discussion is given, from which results the law of the inverse cube for the deflecting couple. Hawksbee 2 made Hawks- experiments with a view to determine the law of magnetic l > ee arul action, in which a deflecting magnet was moved at various ay or distances round a compass, and the corresponding deflex ions noted. A few years later Brook Taylor 3 and the same experimenter made a series of observations in which the "end on" method of deflexion still in use was adopted. But in neither case was any definite result arrived at. A similar uncertainty appeared in the experiments of Winston, Wliiston who indicates the inverse -|th power of the distance as the law of decrease. Musschenbroek s experiments, which were Mussclie extensive, also led to no final result. He used the method of ^ roek - Hooke, in which the attraction of a vertical bar magnet upon another suspended from one arm of a delicate balance is balanced by weights attached to the other arm. From some of his experiments he deduces as low a power as the inverse 1st, from others the |th, and so on ; but no attempt is made to analyse the phenomena. Michell, in his treatise on artificial magnets (1750), however, deduces the law of the inverse square from Musschenbroek s results. Although TEpinus does not arrive at any definite result as to the elementary law, there can be no doubt that his Tenlamen Theorist Electridtatis et Magnetismi (1759) contributed powerfully towards the solution of the question. Tobias Tobias Mayer seems to have been the first to publish the law of Mayer, the inverse square as the actual result of an experimental investigation. His paper was read before the Royal Society of Gottingen, and was referred to in the Goftinger Gelehrter Anzciger for 1760, but never fully published ; it is best known from the criticism of ^Epinus, " Examen Theorias Magneticse a Tob. Mayero propositae " (Nov. Comm. Acad. Petrop., 1768). 4 The most important of the earlier contributions was undoubtedly that of Lambert. 5 Lamber He seems to have been the first to analyse the physical circumstances of the problem in a thorough manner, and to point out the various elements of disturbance to be provided for. We regret that we are unable to devote space to an exhaustive account of his memoirs, 6 which are most instructive reading even now. He showed that the effect of an oblique magnetic force on the needle varies as the sine of the inclination ; and, making allowances for this, he deduced the law of the inverse square from de flexion experiments made at different distances. He also described the method of oscillations, but found difficulties in its practical application. It is upon his theoretical work, however, rather than upon his experiments, that his claim to be remembered rests. About the same time as Lambert, 8 Phil. Trans., 1712. 3 Phil. Trans., 1715 and 1721. 4 Comp. Hansteen, Mag. d. Erde, p. 283, 1819. 5 Hist. d. I Acad. Roy. d. Sc. Berlin, 1766. 6 An excellent one will be found in Hansteen, Maynetismus der
Erde, pp. 295 sq.