74 ELECTRICITY [ELECT UOMAQNETISM. Action of magnet on elec tric dis charge. liquid therefore rotates in the direction of the hands of a watch. Magnetic Action on the Electric Discharge in Gases. A. large number of very interesting results have been obtained concerning the behaviour of the electric discharge in a field of magnetic force. We can only make a brief allu sion to the matter here. The key to the phenomena lies in the remark that the electric discharge in vacuum tubes may be regarded as an electric current in a very flexible elastic conductor. It is clear that such a conductor would be an equilibrium if it lay in a line of magnetic force passing through both its fixed ends. Again, if the flexible conductor be constrained to remain on a given surface, it will not be in equilibrium until it has so arranged itself that the resultant electromagnetic force at each point is perpendicular to the surface. At each point, therefore, the magnetic force must be tangential to the surface. 1 A perfectly flexible but inexteusible conductor, two points of which are fixed, will tuke such a form that the electromagnetic force at each point is balanced by the tension. Le Iloux fastened a thin platinum wire to two stout copper terminals, and caused it to glow by passing a current through it. When the terminals were placed equatorially between the flat poles of an electromag net, the wire bent into the form of a circular arc joining the terminals. When the terminals were placed axially, it assumed a helical form. (See also Spottiswoode and Stokes, Proc. R. S., 1875.) The behaviour of the light emanating from the positive pole may be explained in general as lying between the two cases which we have just discussed. One of the most remarkable of these phenomena is the rotation of the discharge discovered by Walker, and much experimented on by De la Rive. This may be exhibited by means of the apparatus shown in fig. 44, consisting essentially of an exhausted vessel, one of the electrodes in which is ring-shaped; a bar of soft iron, covered with some insulating material, is passed through the ring and fixed to the stand. When this apparatus is placed on the pole of a powerful magnet, the discharge ro tates as a wire hinged to the upper elec trode would do. Fig. 44. Owing to the distinct character of the negative light, the action of the magnet on it is different from that on the positive light. Pliicker found that the general character of the phenomena may be thus described : The negative light is bounded by magnetic curves that issue from the electrode and cut the walls of the tube. The two diagrams in fig. 45 will convey an idea of the to follow the subject further, we must be content to refer the reader to the interesting papers of Pliicker 2 and Hittorf. 3 An excellent summary will be found in Wiede- mann. Ampere s Method. Before quitting the subject of Am- electromagnetism, it will be useful, for the sake of com- P^e s parison, to give a brief sketch of the method of Ampere, ieory or rather of that modification of the original method now commonly found in Continental books, which was suggested by Ampere himself, in a note to the Theorie dcs Pheno- menes filectrodynamiques. Ampere starts with the idea that the electrodynamic action of two circuits is the sum of the actions at a distance between every pair of their elements. He supposes, as the simplest and most natural assumption, that the force between two elements is in the line joining them. Besides this assumption, his theory rests on four ex periments. 4 The first of these shows that, when a wire is doubled on itself, the electrodynamic action of any current in it is nil, The second experiment shows that this is also true, even if one of the halves of the wire be bent or twisted in any way, so as never to be far removed from the other. The third experiment proves that the action of any closed circuit on an element of another circuit is perpendicular to the element. In the fourth experiment it is shown that the force between two conductors remains the same when all the lines in the system are increased in the same ratio, the currents remaining the same. From the assumption, together with the first experiment, it fol lows that the force between two elements is proportional to the product of the lengths of the elements, multiplied by the product of the strengths of the currents and by some function of the mutual distance and of the angles which determine their relative position. Hence it may be shown, from the fourth experiment, that the force between thu elements must vary inversely as the square of the distance between them. The second experiment shows that wo may replace any element of a circuit by the projections of the element on three rectangular axes. From these results it is found that the force between ds and da- must be Fig. 45. appearance of the phenomenon. Although much tempted 1 Loci having this property were called by Pliicker epipolic curves. The constant k is then determined from the result of the third experiment ; and it is found that k must be equal to f . The formula is thus completely determined, with the exception of A, which depends on the unit of current which is chosen. The action of a closed circuit on an element is then calculated, and a vector found, which Ampere calls the " directrix," from which this action can be found in exactly the same way as we derived this same action from the magnetic induction. The theory is then applied to small plane circuits, solenoids, and so on. As was remarked in the historical sketch, a variety of other elementary laws may be substituted for that of Ampere, all of which lead to the same result for closed . circuits. Maxwell has presented Ampere s theory in a more general Genei form, in which the assumption about the direction of the tzail elementary action is not made. Neglecting couples, he l finds for the most general form of the components of the force exerted by da- on ds, l_(d_D d_D_ d*D R = IP V ds da- in the direction of D, -,- , I ii dsda + D jf : ii dsda dada I . dsda dQ ;..,, , S = - 3 n dsda- > da 22). and S= - ii dsda- > S = -r da 0" in the direction of ds and da respectively. 2 Pogg. Ann., ciii., civ., cv., cvii., cxiii., 1858, &c. 3 Pogg. Ann., cxxxvi., 1869.
4 Details respecting these experiments, and other matter connected