MAGNETISM arly bration >serva- ons. oisson rst iggests bsolute lagnetic leasure- lents. so long that the magnetic potential of the body at its two ends may be neglected, then the integral electromotive force caused by the sudden removal of the body, or by the sudden destruction of its magnetism, is kirn times the component of the magnetic moment parallel to the axis of the coil, n being the number of windings per unit of length of the coil. Historical Remarks on the Progress of Magnetic Measure ments. The method of vibrations came very early into use in magnetic measurements. Winston and Graham made vibration observations with a dipping needle. Musschen- broek and Mallet also used a horizontal needle. Lambert appears, however, to have been the first to thoroughly understand and appreciate the method. For long it was the only accurate process in use for obtaining relative measures of the earth s force. It was so used by Rossel, D Entrecasteaux, and Humboldt. Coulomb, Hansteen, and Poisson, all contributed more or less to its improve ment ; and it finally reached perfection in the hands of G.iuss, 1 who gave the experimental process for obtaining the moment of inertia, investigated the correction for resist ance, and, by the introduction of the mirror and scale method, imparted astronomical accuracy to the determina tion of the period of vibration. The method of deflexion, in one form or another, is very old. Its existence as a thoroughly scientific method, however, dates from Hansteeu. The essential improve ment of eliminating the constants depending on the magnetic distribution by observations at different distances is due to Gauss. The advantages of the sine method were first pointed out by Lament in 184 1. 2 Poisson seems to have been the first to conceive the idea of absolute magnetic measurement. In a short but luminous article at the end of the Connaissance des Temps for 1828, he describes a method for obtaining the value of H in absolute measure. Horizontal vibration experiments are to be made with two magnets A and A , whose moments of inertia A and A are known. The times of vibration t and t of A and A , each suspended alone, are to be observed. Then both are to be placed in the magnetic meridian at a distance r apart in the same hori zontal line, and the periods 6 and & observed, of A when A is fixed, and of A when A is fixed. If r be very great compared with the linear dimensions of A and A , then lie recommends, however, that comparatively small values of r be taken, and the constants of distribution eliminated by experimenting at different distances. His fundamental units are the gramme, metre, and second. Nothing came of Poisson s proposal until Gauss took up the subject, both theoretically and experimentally, as above described. The first absolute measure of the earth s hori zontal force was made by him at Gottingen on the 18th September 1832; the value found was 1782 3 in milli metre milligramme second units. The magnet he used (about a foot long and weighing about 1 Ib) had for its moment 100877000 4 in the same units. Determi- The determination of the distribution of magnetism within iation of a lody, in other words, the determination of the magnetic nagnetic momen ts of its individual elements, by observations of bution. magnetic force at external points, is, as we have seen, an indeterminate problem. Nevertheless, a considerable part of the literature of magnetic science relates to it ; and we must give some account of what has been done, although 1 See his memoir, "Anleitung zur Bestimmung der Schwingungs- dauer einer Magnetnadel," in Res. d. Mag. Ver., 1837. 2 Ifandb. d. Magnetismus, p. 309. 3 -17821, C. O. S. * 100877, C. G. S. the results obtained are of comparatively slight physical interest, and of small practical value. Experimenters have been somewhat slow in recognizing " Free the essential indeterminateness of the problem. This no magnet- doubt has arisen from their imperfect analysis of the is . ni >" phenomena. Thus, although we cannot determine the actual internal distribution, yet the problem to determine phrase, the Gaussian surface distribution which will represent the magnetic action at all external points, however difficult, is quite determinate. This surface distribution has been called by some the "free magnetism " of the body ; and some, all the powerful contrary evidence notwithstanding, have imagined that this distribution has a physical existence, and have even spoken of the depth to which the free magnetism penetrates into the magnet. Others have con founded the free magnetism of Gauss s distribution with that of Poisson s ; and in many cases it is impossible to gather what the experimenter meant to indicate exactly by the phrase. The case in which, from the circumstances, the variation of the internal distribution is confined within the narrowest limits is that of bar magnets, whose length considerably exceeds their lateral dimensions ; and this is practically the only case that has been much studied. The most natural way of attempting to represent the action of such a magnet would be to suppose it replaceable by a fixed ideal magnet, and then to determine by experiment the strength and position of the poles of this magnet. The earliest notion was that the poles were situated exactly at the ends of the bar. It was soon found, however, that, if the poles did exist, they were not in general exactly at the ends. Lambert and Kupfer 5 concluded from their experi ments that in many cases the poles lay outside the bar, while in weak magnets they lay inside. Coulomb, as we have seen, and also Dalla Bella, inferred from their results that the poles fell within. Recent experiments have been made by Pouillet, 6 by Benoit, 7 by Petruscheffsky, 8 and by others on the same subject ; but it is needless to describe them here. The word "pole," like the phrase "free magnetism," has "Poles," been used by different writers in very different senses. Some have applied that name to the mass centres of the positive and negative magnetism of the actual molecules. But, although as a matter of convenience we have used these points in our theoretical development, they have, as far as physical observations are concerned, no existence. Others have defined the poles to be the mass centres of the positive and negative parts of Gauss s surface distribution. These might of course be determined, although the process would be extremely troublesome, and the result of no practical value whatever. In point of fact, if the magnet be in a uniform field, i.e., at a very great distance from the system that acts on it, the action depends solely on the magnetic moment, and the magnetic distribution has nothing to do with it ; the poles in this case are physically indeterminate. If, on the other hand, two magnets are within a moderate distance of each other, we may set to ourselves the problem to find two points in each of them such that the mutual action will be represented by quantities of positive and negative magnetism concentrated there. Then, in general, such points may or may not exist. Riecke has shown (see above, p. 233) that, if the distance between the magnets exceed a certain limit, then, as a matter of approximation, these equivalent poles, as he emails them, do exist. Except, however, in the case of magnets symmetrical about an axis, and also about an equatorial plane, they are not fixed in the magnets^but 5 See Lamont, Handb. d. Magnetismus, p. 294 sq. 6 Comptes Rend., 1868. 7 Comptes Rend., 1875. 8 Pogg. Ann., clii., 1874, andclx., 1877.
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