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whole, in consequence of the great obliquity of their actions, much less powerful than the attractive portions, which act at a greater angle. This inequality diminishes as the middle parts of each magnet are brought to each other, until the repulsion predominates ; and this repulsion arrives at its maximum when the two magnets are opposite each other in parallel lines. It was in consequence of his having neglected to take the whole of these forces into account, that Mr. Barlow advanced objections to Ampère's theory, derived from the above fact; which objections, when accurately examined, appear to be without foundation.*

The most satisfactory answer to all the objections that can be made to the adequacy of the theory to explain the phenomena of magnetism, is to show that the very same phenomena may be produced by substituting for the magnets, in each experiment, actual voltaic currents by heliacal arrangements of wires, constructed in the way already described. On this subject Ampère has arrived at the following general conclusion :

"Lorsqu'on a ainsi ramené l'action des aimans aux loix générales de celles des conducteurs voltaïques, on peut en déduire différens phénomènes, dont nous n'avons pas encore parlé et qui ont lieu lorsqu'on fait agir l'un sur l'autre un conducteur voltaïque et un aimant, tels que la révolution d'un aimant autour d'un conducteur, la rotation d'un de ces corps sụr son axe par l'action de l'autre, celle qu’un aimant produit dans le mercure que traverse le courant électrique et qu'a découverte Sir H. Davy, les divers mouvemens du conducteur annulaire flottant de M. de la Rive, et toutes les autres conséquences de ce genre que l'expérience confirme.

. C'est aussi alors qu'on peut appliquer la formule aux phénomènes que présentent l'action mutuelle d'un conducteur voltaïque et d'un aimant et celle de deux aimans, en calculant les effets que doivent produire, d'après cette formule, les courans électriques disposés autour des particules des aimans. Ce nouveau progrès d'une branche si intéressante de la physique est dû à M. Savary ; voici les principaux résultats qu'il a obtenus, en appliquant la formule au calcul de l'action exercée par des cylindres électro-dynamiques d'un très petit diamètre, les seuls auxquels on doive comparer les aimans quand on les considère comme des assemblages de courans électriques tournant autour de leurs particules.'-p. 341.

L'action mutuelle d'un fil conducteur d'une forme et d'une grandeur quelconques, et d'un cylindre électro-dynamique, lorsqu'on suppose que ce cylindre est assez long pour que l'une de ses extrémités soit très loin du conducteur, ne dépend que de la situation de son autre extrémité relativement à ce conducteur, et reste la même quelle que soit la direction de l'axe du cylindre.'

• L'action mutuelle de deux cylindres électro-dynamiques, quelles

* See page 298 of Mr. Barlow's work.

que

6

que soient les directions de leurs axes, se compose de quatre forces, deux attractives et deux répulsives, dirigées suivant les droites qui joignent deux à deux les extrémités des cylindres, et en raison inverse du carré des distances entre ces extrémités; ce qui donne, à l'égard de ces dernières, la formule que Coulomb avait trouvée par expérience pour les pôles de deux aimans, en observant la direction qu'un de ces aimans prend par l'action de l'autre.'-p. 343.

One difference, indeed, has been observed between the actions of the voltaic and the ordinary magnet. In the former, the poles are at the very extremities of the cylinder ; in the latter, they are found to be at points at a small distance from the ends and nearer to the centre. This circumstance has been often adverted to by writers on magnetism, and has been particularly noticed by Mr. Faraday.* It would indicate either some degree of obliquity in the currents, or a greater condensation of those near to the centre: effects which are not only quite consistent with Ampère's hypothesis, but which might have been predicted as the natural consequences of the known laws of electro-dynamic action.

• D'après les calculs de M. Savary, confirmés en ce point par les expériences de M. Faraday sur les fils conducteurs pliés en hélices, que ce célèbre physicien a consignées dans son mémoire du 11 Septembre 1821, les points auxquels on donne dans l'aimant le nom de pôles, devroient être situés précisément à ses extrémités, quand on suppose que tous les courans électriques d’un aimant sont situés dans des plans exactement perpendiculaires à son axe, et qu'ils oột tous la même intensité. C'est ce qui n'a pas lieu pour les aimans ordinaires, mais seulement pour ceux qu'a construit, avec des fils d'acier extrêmement fins, un jeune physicien de Paris, déjà célébre par ses belles recherches sur l'électricité développée par la pression ; or, il est aisé de voir qu'indépendamment de ce que cet effet seroit produit par une intensité variable des courans, qui seroit d'autant plus grande que ces courans seroient plus près du milieu de l'aimant, ainsi que je l'ai admis d'abord, ce même effet est une suite nécessaire de l'inclinaison des plans des mêmes courans dans le sens que je viens d'indiquer. Il l'est également de voir que le même conducteur qui est attiré dans l'intervalle des deux pôles doit être repoussé au-delà ; que les deux extrémités de deux aimans qui portent les noms contraires, doivent s'attirer non-seulement quand les axes des deux aimans sont en ligne droite, mais encore quand ils sont dans la position représentée dans la figure.'-p. 257.

• Cette inclination des plans dans lesquels sont situés les courans des particules des aimans paraît etre la cause de la différence que M. Faraday a remarquée entre la manière d'agir des aimans et des cylindres électro-dynamiques ; elle consiste en ce que les pôles proprement dit d'un aimant ne sont pas situés exactement à ses extré

* Quarterly Journal of Science, xij. 76.

mités,

mités, au lieu que les points qui présentent les mêmes propriétés dans un cylindre électro-dynamique. sont précisément à ses extrémités, conformément aux calculs déduits de la formule.'--p. 340.

We come now to the subject of terrestrial magnetism. If we assume that the action of the solar rays on successive parts of the torrid zone, from east to west, produces currents of positive electricity in that direction, and which may be regarded as collectively circulating in what may be called the magnetic equator; attended, as they must always be, by counter-currents of negative electricity in the same equator, but in the opposite direction ; and also that these currents have the same properties and modes of action with all other electrical currents,—then there must result, as a necessary consequence, a two-fold polarity, apparently belonging to the earth, and directed to the poles of this magnetic equator.

It is to be observed, that as that polarity, which is situated near the north pole of the earth, results from a current moving in a direction similar to that of the hands of a watch, it will have the properties of a southern polarity, in the sense in which we have invariably used the term; that is, it will attract the north pole of a magnet, and repel the south pole; while actions the reverse of this will take place in the southern hemisphere. It is unnecessary to remark, how exactly this theory accords with all the known facts relative to the action of the earth on magnets. The directive power which acts on magnets on the surface of the earth, is the result, not of any real influence proceeding from that part of the earth to which their poles point, but of the action of the currents at the magnetic equator, and the tendency of the currents in the magnet itself to turn it, so that they shall attain the position of equilibrium we have already adverted to, in considering the mutual action of two circular currents. This position is precisely the plane which is perpendicular to the line of magnetic direction; that is, to the axis of the dipping needle: for as the electric currents in the needle are at right angles to its axis, it follows that when they arrange themselves in conformity with the equatorial currents of the earth, that are circulating east and west, that axis and the whole needle will point to the north and south-as we find they actually do.

The nature of this influence is more clearly discernible when it is exhibited in its simplest form, on a single circular current, which, as we have seen, may be regarded as the element of a mag

A conducting-wire bent into the form of a circle, when free to move, always assumes, by the electro-magnetic action of the earth, a position in a plane descending to the south, intersecting the horizon in a line passing east and west, and inclined to it at an angle which is the complement to the dip; that is, in a plane

net.

Tu

which is perpendicular to the magnetic meridian. Its northern

and southern polarities are equally real with that of a magnetic needle; but apper

tain to an imaginary axis passing through ď

the centre of the circle and perpendicular to its plane. The direction of the currents on its south side, or that nearest the

equator, is similar to those in the earth's equator —that is, from east to west, (the positive

current being always understood as defining the direction). All these circumstances are shown in the diagram annexed, in which N S, representing the north and south poles of the earth, the directions of the equatorial currents are denoted by the arrows; and the position assumed by the currents of a magnet is shown at m; its poles acting in the direction of the line dd.

The same phenomena are observed, if the course of the moveable wire be that of a parallelogram ; or, indeed, any plane figure which returns into itself, as well as if it were a circle. By varying these forms, we are enabled to observe and distinguish the effects of the earth's influence on wires which are parallel to the direction of the dip, and on such as are at right angles to it. The experiments of De la Rive on these subjects deserve notice, as a beautiful specimen of philosophical analysis ; but any detailed account of them would extend this Article to too great a length.

The action of the earth on spiral conducting wires is precisely similar in kind to that on single circles, but it is more powerful in degree. Helices are, in like manner, found to obey the terrestrial influence, just as magnets do when placed in similar circumstances as to freedom of motion, provided the electrical currents which they convey are of sufficient intensity. Continued progressive, or even rotatory motion may be obtained by the same intluence, in conductors whose motions are limited to certain planes, either in parallel directions, or round an axis. So that, in fact, every experiment that has been tried, and a great variety has been devised by the ingenuity of numerous experimentalists, has served but to confirm the correctness of Ampère's views of the theory of magnetism. It is easy to distinguish whether the motion of any part of a voltaic circuit is the effect of the influence of the earth, or merely of the other portions of the same circuit, by reversing the communications with the ends of the pile or battery employed : in the former case, the direction of the motion is immediately reversed by this change; and in the latter case, the action continues the same as before. Ampère is far from supposing that the successive action of the

solar

solar rays on the equatorial regions of the earth is the sole cause of the electric currents that circulate in them. Internal changes taking place in the earth itself, must also concur in producing them; for it would otherwise be impossible to account for the observed variations in their effects. The diurnal variations may, however, fairly enough be attributed to the alternate changes of temperature occurring in different parts of the torrid, and even of the temperate zones.

The phenomena of magnetic induction, whether effected by currents of electricity passing through a conducting body, or by a magnet in which such currents are assumed to exist, are also in perfect conformity with this hypothesis. A conducting wire tends to the determination of currents in the same direction as those. which it conveys itself, in all the magnetisable bodies in its vici nity: these currents continue to circulate with more or less per manency, after the removal of the current which originally determined them. In soft iron they soon disappear: in steel they continue to maintain themselves, and give rise to permanent magnets. The polarities thus induced will have transverse directions with respect to that of the current to which they owe their origin, for the reasons we have already so fully explained.

Numerous facts have induced Ampère to conclude, that the circulation of electric currents peculiar to magnets, takes place round each particle of the magnetic body; he has also adopted the opinion, that these currents pre-existed in the bodies susceptible of magnetism, before this property was imparted to them; but as they were moving in every variety of direction, they neutralised each other, and could produce no external effect. It is only when a determinate direction has been given to them, either by another magnet, or by a voltaic current, that they become capable of exerting any magnetic action.

By a very curious experiment, Ampère has proved, that a powerful electric current has a tendency to excite similar currents in neighbouring bodies, not generally susceptible of magnetism. A copper wire of considerable length was rolled round a cylinder, so as to form a coil, all the turns of which were separated from each other by silk riband. Within this spiral coil, a ring of brass was freely suspended by a fine metallic thread, passing through a small glass tube, which was placed between the threads of the copper coil. The circumference of the ring, in every part, was thus brought very near to the copper wire, through which a powerful voltaic current was made to pass. Under these circumstances, the brass wire was attracted or repelled by a magnet, in the same way as it would have been, had it formed part of the same voltaic circuit. The action, indeed, was but feeble, and

Ampère,

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