ON THE DETERMINATION OF THE QUANTITY OF MAGNETISM OF A MAGNET. BY R. BLONDLOT. The notion of instituting a method of magnetic exploration based on the production of induced currents has long been entertained. In 1849 Van Rees published* the result of researches on the distribution of magnetism, the principle of his process being as follows:-The wire of a much-flattened induction-coil is connected with a galvanometer; the bar to be examined is introduced into the coil up to a fixed point of the latter, and is then briskly withdrawn to a great distance: this gives rise to an induction-current, which deflects the needle of the galvanometer a certain angle. Van Rees lays down a simple proportionality between the intensity of the current and the inducing magnetism, from which it follows that the current observed is a measure for the sum of the free magnetism over which the coil glides; and he concludes, from a known relation, that that sum is equal to the actual magnetism at the place from which the withdrawal of the coil started. Subsequently, in 1861, in a memoir an abstract of which appeared in Poggendorff's Annalen†, M. Rothlauf treats the same subject, commencing with a critical examination of Van Rees's memoir. The theory of the latter is faulty in two points; the principal charge against it is that it suppcses the experiments to be made with a coil formed of one circumvolution only, and that the points situated beneath it are the only ones which act by induction. We refer for the details of the criticism to M. Rothlauf's memoir‡. Finally, M. Gaugain has recently taken up Van Rees's method, and made it the foundation of researches, which he is pursuing with success, on magnetism. It appeared to us important to examine Van Rees's method from the theoretical point of view, to seek the exact signification of the numbers given by it, and to treat in particular a case in which, though generally inaccurate, its application does not involve any appreciable error. The first impulse measured represents, with respect to the induced current, the integral dt, i denoting the variable intensity to of the current, and t the time, the limits of which are to and t1. Let us go back to the theory of induction-currents given by Neumann. If we have a fixed pole P, and a closed circuit B moving in relation to the pole, there is produced in the circuit an induction-current in the inverse direction of the current which would give to the circuit the motion which it actually has (Lenz's law). Let ds be an element of the circuit; this element is the seat of an electromotive force e ds. If the circuit B were traversed by a * Pogg. Ann. vol. lxxiv. p. 217. +"Bestimmung der magnetischen Vertheilung mittelst Magnet-Induction," Pogg. Ann. vol. cxvi. p. 592. See also G. Wiedemann, Die Lehre von Galvanismus, vol. ii. p. 321, note. 482 Intelligence and Miscellaneous Articles. ON THE DETERMINATION OF THE QUANTITY OF MAGNETISM OF The notion of instituting a method of magnetic exploration based Van Rees lays down a simple proportionality between the inten- Subsequently, in 1861, in a memoir an abstract of which appeared Finally, M. Gaugain has recently taken up Van Rees's method, It appeared to us important to examine Van Rees's method from the theoretical point of view, to seek the exact signification of the numbers given by it, and to treat in particular a case in which, though generally inaccurate, its application does not involve any appreciable error. The first impulse measured represents, with respect to the induced current, the integral ("dt, i denoting the variable intensity of the current, and t the time, the limits of which are t, and t Let us go back to the theory of induction-currents given by Neumann. If we have a fixed pole P, and a closed circuit B moving in relation to the pole, there is produced in the circuit an induction-current in the inverse direction of the current which would give to the circuit the motion which it actually has (Lenz's law), Let ds be an element of the circuit; this element is the seat of an electromotive force eds. If the circuit B were traversed by a *Pogg. Ann. vol. lxxiv. p. 217. Vertheilung mittelst Magnet-Induc tion," See also G. Wiedemann, Die Lehre von Galvanismus, vol. ii. p. 321, note, current of the intensity m in absolute measure, ds would be acted on by a certain force from the pole P. Let Y be the component of that force along the direction of the motion; the elemental law given by Neumann is the following:e ds=—evy, v designating the velocity of the element ds, and e being a constant. Let us consider what takes place in the time dt for the entire circuit. Let R be the resistance; the elementary current produced will be, according to Ohm's law, € i dt: Συγdt, the symbol extending to the entire circuit B. dw But we have v=t, du representing the element of the trajectory of ds; therefore € dw idt= = Σγ R dt i dt: = which gives the following enunciation: The differential current is equal, except a factor, to the sum of the elementary work of the forces to which the pole is subjected on the part of the elements of a current 1 supposed to traverse the circuit B. Integrating between the corresponding limits, we get (A) 0 It follows that, for a given circuit, the first impulse of the galvanometer is proportional to the work which would be necessary to produce the relative motion of the pole and the circuit supposed to be traversed by the current 1. If we wish to pass to the case of the true magnet, it suffices to consider any number of poles; and it is seen, by a series of summations, that the theorem applies in the case of distribution as any in that of a single pole. We have now to estimate the work as a function of the data of experiment. Let V be the potential, relative to the circuit, of any pole P, and μ the magnetism of the pole; the work in order that the system may from one state to the other, taking into account this pole only, pass is equal to the corresponding variation of the quantity μV; let it (V-V). We shall therefore have, by substitution in equation (A), be w1 RS" Zydw. the summation here extending to all the poles of the arrangement*. *This equation agrees with the calculation given by G. Wiedemann, l. c. vol. iii. p. 80. This relation, in general very complicated, is simplified in a special case, as we will show. Let us consider the potential V of a pole P. It is known that this potential has for its value in absolute measure the opening of the cone under which the pole P regards the current. If, then, the circuit B starts from negative infinity to reach the pole and then remove thence to positive infinity, the potential varies by the quantity 4π. From this it follows that, in the above-indicated conditions of displacement, V,-V, is a constant quantity, and equal to 4 for all the poles; consequently it can be put as a factor, which gives designating by M the total magnetism of the arrangement. In a long magnet the magnetism can be regarded as collected in the vicinity of the extremities; therefore if the coil be placed on the middle portion of such a magnet and the latter be afterwards removed to a great distance, the conditions will be sensibly those of the preceding theory. It hence follows that the quantity of the current can serve for measuring the total magnetism of the half of a bar, provided that the bar be not too short-that is to say, that its polar distance be not less than 8-10 centims. We see also that the current is independent of the diameter of the coil, if this diameter is a small fraction of the length of the bar. The last proposition was experimentally verified by Faraday and Lenz, and more recently by M. Gaugain.-Comptes Rendus de l'Académie des Sciences, vol. lxxx. pp. 653-656. ON CAMACHO'S NEW ELECTROMAGNET. To the Editors of the Philosophical Magazine and Journal, In the April Number of your Magazine Mr. R. S. Culley states that he had in his possession, in 1852, a magnet similar in principle to that of M. Camacho, which was invented by the late Richard Roberts. I take the following extract from a paper on the Construction of Galvanic Magnets, by John B. Zabriskie, M.D., published in the American Journal of Science and Arts for July 1839. After dwelling upon the difficulty of "saturating with magnetism large masses of iron," he continues, "but if we divide perpendicularly each extremity of a large magnet into four equal parts and wind each part separately, there will be no difficulty in completely saturating the whole." This seems to me to be the same idea upon which both Mr. Roberts and M. Camacho proceeded to construct their magnets. Cambridge, U. S. Yours sincerely, JOHN TROWBRIDGE, S.D. Harv. Coll. INDEX TO VOL. XLIX. 485 Bosanquet (R. H. M.) on the mathe- Bouty's (Prof. E.) studies on mag- Broun (J. A.) on the sun-spot period Camacho (J.) on a new electromag- Capron (J. R.) on the comparison of some tube and other spectra with 134. Colour, on combination of, by means Curtis (Prof. A. H.) on extraordinary Diamagnetism, on the experimental Diamond, on the specific heat of, Diffraction, on the projection of the Dolerites, on the microscopic struc- Draper (Prof. J, C.) on the projec- Electric conducting-power of the 484. Equilibrium and initial and steady Etna, on the eruption of, on the 29th tion of certain, 157. Flames, on the reflecting-power of, Force, on Helmholtz's memoir on methods of solving certain electri- from their supersaturated solutions Glaisher (J.W. L.) on partitions, 307. Goldstein (E.) on the spectra of gases, Grotrian (O.) on the electric conduct→ attached water, 1, 206, 266. thematical theory of, 98. trum of the aurora, 65. Hydrogen, on the solution of, in Ice, on permanent, in a mine in the Kohlrausch (Prof. F.) on the electric Light, on polarization by diffusion of, 50. Liquids, on some phenomena con- nected with the boiling of, 432. Lodge (O. J.) on the flow of electri- quantity of magnetism in a, 482. 243. Mallet (R.) on volcanic energy, 144; on expansion by refrigeration, 231. site nature of the electric discharge, |