CHAPTER VI.

THEORY OF ELECTRODYNAMICAL ACTION.

AMPÈRE'S Theory. Nothing can show in a more

striking manner the advanced condition of physical speculation in 1820, than the reduction of the strange and complex phenomena of electromagnetism to a simple and general theory as soon as they were published. Instead of a gradual establishment of laws of phenomena, and of theories more and more perfect, occupying ages, as in the case of astronomy, or generations, as in the instances of magnetism and electricity, a few months sufficed for the whole process of generalization; and the experiments made at Copenhagen were announced at Paris and London, almost at the same time with the skilful analysis and comprehensive inductions of Ampère.

Yet we should err if we should suppose, from the celerity with which the task was executed, that it was an easy one. There were required, in the author of such a theory, not only those clear conceptions of the relations of space and force, which are the first conditions of all sound theory, and a full possession of the experiments; but also a masterly command of the mathematical arms by which alone the victory could be gained, and a sagacious selection of proper experiments which might decide the fate of the proposed hypothesis.

It is true, that the nature of the requisite hypothesis was not difficult to see in a certain vague and limited way. The conducting-wire and the magnetic needle had a tendency to arrange themselves at right angles to one another. This might be represented by supposing the wire to be made up of transverse magnetic needles, or by supposing the needle to be made up of transverse conducting-wires; for it was easy to conceive forces which should bring corresponding elements, either magnetic or voltaic, into parallel positions; and

then the general 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 electro-magnetic 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 designated1 by the

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

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. 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 formule, 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 well-known 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 whatBut it still remained necessary to determine two fundamental quantities; one of which expressed the power of the distance according to which the force varied; the other, the degree 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; 2 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.

ever.

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.3 And throughout his labours, we find reason to admire, both his mathematical skill, and his steadiness of thought; although these excellencies 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

2 Communication to the Acad. Sc., June 10, 1822. See Ampère, Recueil, p. 292. 3 Recueil, p. 314.

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 honour 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, endeavoured to reduce the electromagnetic 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 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

4 Ampère, Théorie, p. 154.