ral phenomena above stated would be accounted for. And the choice between the two modes of conception, appeared at first sight a matter of indifference. The majority of philosophers at first adopted, or at least employed, the former method, as Oersted in Germany, Berzelius in Sweden, Wollaston in England.

Ampère adopted the other view, according to which the magnet is made up of conducting-wires in a transverse position. But he did for his hypothesis what no one did or could do for the other: he showed that it was the only one which would account, without additional and arbitrary suppositions, for the facts of continued motion in electromagnetic cases. And he further elevated his theory to a higher rank of generality, by showing that it explained,-not only the action of a conducting-wire upon a magnet, but also two other classes of facts, already spoken of in this history, the action of magnets upon each other, and the action of conducting-wires upon each other.

The deduction of such particular cases from the theory, required, as may easily be imagined, some complex calculations: but the deduction being satisfactory, it will be seen that Ampère's theory conformed to that description which we have repeatedly had to point out as the usual character of a true and stable theory; namely, that besides accounting for the class of phenomena which suggested it, it supplies an unforeseen explanation of other known facts. For the mutual action of magnets, which was supposed to be already reduced to a satisfactory theoretical form by Coulomb, was not contemplated by Ampère in the formation of his hypothesis; and the mutual action of voltaic currents, though tried only in consequence of the suggestion of the theory, was clearly a fact distinct from electromagnetic action; yet all these facts flowed alike from the theory. And thus Ampère brought into view a class of forces for which the term "electromagnetic" was too limited, and which he designated' by the appropriate term electrodynamic; distinguishing them by this expression, as the forces of an electric current, from the statical effects of electricity which we had formerly to treat of. This term has passed into common use among scientific writers, and remains the record and stamp of the success of the Amperian induction.

The first promulgation of Ampère's views was by a communication to the French Academy of Sciences, September the 18th, 1820; Oersted's discoveries having reached Paris only in the preceding July.

1 Ann. de Chim., tom. xx. p. 60 (1822).

At almost every meeting of the Academy during the remainder of that year and the beginning of the following one, he had new developements or new confirmations of his theory to announce. The most hypothetical part of his theory,-the proposition that magnets might be considered in their effects as identical with spiral voltaic wires,he asserted from the very first. The mutual attraction and repulsion of voltaic wires,--the laws of this action,-the deduction of the observed facts from it by calculation, the determination, by new experiments, of the constant quantities which entered into his formula,followed in rapid succession. The theory must be briefly stated. It had already been seen that parallel voltaic currents attracted each other; when, instead of being parallel, they were situate in any directions, they still exerted attractive and repulsive forces depending on the distance, and on the directions of each element of both currents. Add to this doctrine the hypothetical constitution of magnets, namely, that a voltaic current runs round the axis of each particle, and we have the means of calculating a vast variety of results which may be compared with experiment. But the laws of the elementary forces required further fixation. What functions are the forces of the distance and the directions of the elements?

To extract from experiment an answer to this inquiry was far from easy, for the elementary forces were mathematically connected with the observed facts, by a double mathematical integration;—a long, and, while the constant coefficients remained undefined, hardly a possible operation. Ampère made some trials in this way, but his happier genius suggested to him a better path. It occurred to him, that if his integrals, without being specially found, could be shown to vanish upon the whole, under certain conditions of the problem, this circumstance would correspond to arrangements of his apparatus in which a state of equilibrium was preserved, however the form of some of the parts might be changed. He found two such cases, which were of great importance to the theory. The first of these cases proved that the force exerted by any element of the voltaic wire might be resolved into other forces by a theorem resembling the wellknown proposition of the parallelogram of forces. This was proved by showing that the action of a straight wire is the same with that of another wire which joins the same extremities, but is bent and contorted in any way whatever. But it still remained necessary to deter· mine two fundamental quantities; one which expressed the power of the distance according to which the force varied; the other, the de

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gree in which the force is affected by the obliquity of the elements. One of the general causes of equilibrium, of which we have spoken, gave a relation between these two quantities; and as the power was naturally, and, as it afterwards appeared, rightly conjectured to be the inverse square, the other quantity also was determined; and the general problem of electrodynamical action was fully solved.

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If Ampère had not been an accomplished analyst, he would not have been able to discover the condition on which the nullity of the integral in this case depended. And throughout his labors, we find reason to admire, both his mathematical skill, and his steadiness of thought; although these excellences are by no means accompanied throughout with corresponding clearness and elegance of exposition in his writings.

Reception of Ampère's Theory.-Clear mathematical conceptions, and some familiarity with mathematical operations, were needed by readers also, in order to appreciate the evidence of the theory; and, therefore, we need not feel any surprise if it was, on its publication and establishment, hailed with far less enthusiasm than so remarkable a triumph of generalizing power might appear to deserve. For some time, indeed, the greater portion of the public were naturally held in suspense by the opposing weight of rival names. The Amperian theory did not make its way without contention and competition. The electro-magnetic experiments, from their first appearance, gave a clear promise of some new and wide generalization; and held out a prize of honor and fame to him who should be first in giving the right interpretation of the riddle. In France, the emulation for such reputation is perhaps more vigilant and anxious than it is elsewhere; and we see, on this as on other occasions, the scientific host of Paris springing upon a new subject with an impetuosity which, in a short time, runs into controversies for priority or for victory. In this case, M. Biot, as well as Ampère, endeavored to reduce the electro-magnetic phenomena to general laws. The discussion between him and Ampère turned on some points which are curious. M. Biot was disposed to consider as an elementary action, the force which an element of a voltaic wire exerts upon a magnetic particle, and which is, as we have seen, at right angles to their mutual distance; and he conceived that

2 Communication to the Acad. Sc., June 10, 1822. See Ampère, Recueil, p. 292.

3 Recueil, p. 314.

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the equal reaction which necessarily accompanies this action acts oppositely to the action, not in the same line, but in a parallel line, at the other extremity of the distance; thus forming a primitive couple, to use a technical expression borrowed from mechanics. To this Ampère objected, that the direct opposition of all elementary action and reaction was a universal and necessary mechanical law. He showed too that such a couple as had been assumed, would follow as a derivative result from his theory. And in comparing his own theory with that in which the voltaic wire is assimilated to a collection of transverse magnets, he was also able to prove that no such assemblage of forces acting to and from fixed points, as the forces of magnets do act, could produce a continued motion like that discovered by Faraday. This, indeed, was only the well-known demonstration of the impossibility of a perpetual motion. If, instead of a collection of magnets, the adverse theorists had spoken of a magnetic current, they might probably interpret their expressions so as to explain the facts; that is, if they considered every element of such a current as a magnet, and consequently, every point of it as being a north and a south point at the same instant. But to introduce such a conception of a magnetic current was to abandon all the laws of magnetic action hitherto established; and consequently to lose all that gave the bypothesis its value. The idea of an electric current, on the other hand, was so far from being a new and hazardous assumption, that it had already been forced upon philosophers from the time of Volta; and in this current, the relation of preceding and succeeding, which necessarily existed between the extremities of any element, introduced that relative polarity on which the success of the explanations of the facts depended. And thus in this controversy, the theory of Ampère has a great and undeniable superiority over the rival hypotheses.

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CHAPTER VII.

CONSEQUENCES OF THE ELECTRODYNAMIC THEORY.

T is not necessary to state the various applications which were soon made of the electro-magnetic discoveries. But we may notice one

4 Ampère, Théorie, p. 154.

of the most important, the Galvanometer, an instrument which, by enabling the philosopher to detect and to measure extremely minute electrodynamic actions, gave an impulse to the subject similar to that which it received from the invention of the Leyden Phial, or the Voltaic Pile. The strength of the voltaic current was measured, in this instrument, by the deflection produced in a compass-needle; and its sensibility was multiplied by making the wire pass repeatedly above and below the needle. Schweigger, of Halle, was one of the first devisers of this apparatus.

The substitution of electro-magnets, that is, of spiral tubes composed of voltaic wires, for common magnets, gave rise to a variety of curious apparatus and speculations, some of which I shall hereafter mention.

[2nd Ed.] [When a voltaic apparatus is in action, there may be conceived to be a current of electricity running through its various elements, as stated in the text. The force of this current in various parts of the circuit has been made the subject of mathematical investigation by M. Ohm.' The problem is in every respect similar to that of the flow of heat through a body, and taken generally, leads to complex calculations of the same kind. But Dr. Ohm, by limiting the problem in the first place by conditions which the usual nature and form of voltaic apparatus suggest, has been able to give great simplicity to his reasonings. These conditions are, the linear form of the conductors (wires) and the steadiness of the electric state. For this part of the problem Dr. Ohm's reasonings are as simple and as demonstrative as the elementary propositions of Mechanics. The formula for the electric force of a voltaic current to which he is led have been experimentally verified by others, especially Fechner, Gauss, Lenz, Jacobi, Poggendorf, and Pouillet.

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Among ourselves, Mr. Wheatstone has confirmed and applied the views of M. Ohm, in a Memoir On New Instruments and Processes for determining the Constants of a Voltaic Circuit. He there remarks that the clear ideas of electromotive forces and resistances, substituted by Ohm for the vague notions of quantity and intensity which have long been prevalent, give satisfactory explanations of the most important difficulties, and express the laws of a vast number of phenomena

Die Galvanische Kette Mathematisch bearbeitet von Dr. G. S. Ohm, Berlin, 1827.

2 Mass-bestimmengen über die Galvanische Kette. Leipzig, 1831.

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3 Results of the Magnetic Association. 4 Phil. Trans. 1843. Pt. 11.