has succeeded in determining accurately what function of the intensity of magnetization or of the induction the stress really is. In order to show how the methods of experimenting have developed, and how they have led to those of the present investigation, I will describe shortly the chief experiments that have so far been made*. As long ago as 1833 Fechner† made a series of measurements of the weight necessary to separate a horseshoe magnet and its keeper, measuring the current by swinging a magnetic needle within a coil through which the current passed. He found a rough proportionality between the limiting weight and the current. Somewhat more accurate experiments made in 1839 by Lenz and Jacobit showed that this proportionality did not exist. In the same year Joule §, measuring the magnetizing current with an ingenious "current-weigher," found that for small currents the lifting-power of an iron electromagnet was proportional to the square of the magnetizing current, but that for stronger currents the lifting-power increased more slowly and ultimately reached a maximum value of 140 lb. per square inch; twelve years later, however, using a more powerful electromagnet, he found the maximum value to be 175 lb. per square inch. In 1852 Dub¶ found that the lifting-power was proportional neither to the current nor to the square of the current, but to some intermediate function, and for strong currents reached a maximum. Much more accurate experiments were made in 1870 by v. Waltenhofen**. Two similar bars of iron with plane ends were bent approximately to semicircles and wire wound evenly on both. One bar was fixed rigidly in a frame and the other one pulled up from it, the necessary force being measured by a spring-balance. A third bar and coil, similar to the other two but straight, was set up with a compensating-coil in the East and West line through a magnetometer-needle. these coils were in circuit with a galvanometer for indicating the current. All The stress between the bent electromagnets could thus be compared with the magnetic moment of the straight one, and * Cf. also Wiedemann, Elek. iii. Bd. 3, pp. 632-654; du Bois, Magnetische Kreise, sect. 105-110 (1894). + Schweigg. Journ. lxix. (1833). Pogg. Ann. xlvii. p. 415 (1839). ¶ Pogg. Ann. lxxxvi. p. 553 (1852). || Ibid. Jan. 1852, with the magnetizing current. With small currents the liftingpower increased more rapidly than the magnetometer-deflexion, but with stronger currents more slowly, the corresponding curve ultimately approaching a horizontal asymptote. Also the lifting-power was proportional neither to the current nor to its square, but was represented approximately by a function of the form b tan-1 (ac), where c is the current, and a, b constants. The magnetizing forces, however, used in these experiments could have been but small, since the straight magnet was never more than half saturated, and its magnetization was always nearly proportional to the current. The next experiments were made in 1881 by Werner v. Siemens. The electromagnets were made by cutting an iron tube in a plane through the axis, and winding both halves with wire. The interfaces were carefully ground together. A ballistic galvanometer and secondary coil were used to measure the induction. From the total induction"throw" was subtracted the throw caused by breaking the current in the coil after the iron was removed. The resulting differences are therefore proportional to the intensity of magnetization, not to the induction. The result showed that the lifting-power was approximately proportional to the magnetic moment per unit volume, but that the ratio somewhat increased as the current was increased. Similar results were obtained with electromagnets formed by cutting a circular iron tube in the plane through the greatest section. Siemens believed the above law to be established, and attributed the deviations to residual magnetism, and to imperfect contact of magnet and keeper due to bending, the imperfect state of the surfaces, and other mechanical causes. These were the probable causes of much greater errors than those believed to exist. In 1882 Wassmuth† experimented with magnets similar to those used by v. Waltenhofen. The induction was measured ballistically, and the ends of the magnets were ground plane and polished. The magnetic moment per unit volume was calculated from the induction-current and the results compared with a theory given by Stefan ‡, according to which the stress is proportional to the square of the magnetic moment per unit volume at the surface of contact. Wassmuth * Wied. Ann. xiv. p. 640 (1881). found, however, that the stress agreed better with an expression of the form where I is the magnetic moment per unit volume. Wassmuth's experiments are subject to the same objections as Siemens', viz., imperfect contact of magnet and keeper due to bending &c., and, in addition, to the difficulty of ensuring that the magnets separate at the two places of contact exactly simultaneously. If separation takes place at one place first, there will be an immediate diminution of the induction, and the limiting weights will generally be too small. Wassmuth further deduced from Siemens' numbers an expression for the lifting-power of the form a+bl2+cI1, which represented the latter's results fairly well. Neither Siemens nor Wassmuth appears to have thought of comparing his results with the theory given in sections 641-644 of Maxwell's Electricity and Magnetism,' which had been published several years before. Maxwell there arrives at the expression B2A/8π for the electromagnetic traction in air between two opposing, plane, infinitely near, and uniformly and normally magnetized pole-faces each of area A; where B is the induction. In 1886 Bosanquet* experimented with two straight iron electromagnets whose ends were ground together. One electromagnet was fixed vertically, and the other supported beneath it on the beam of a balance by which its weight was compensated, this allowing measurements with very small currents to be made. Weights were placed in a scale-pan suspended from the lower electromagnet, and the induction was measured by a small secondary coil near the surface of contact. For low and medium currents the weights supported were much greater than those given by Maxwell's theory, the values being better represented by an expression of the form aB+bB2; while with high currents the results appear to be very uncertain, most of the readings widely differing from the theoretical values. The mean results, however, agree to within about 5 per cent. In the same year Bidwell† made a series of measurements of the tractive force between two bar-magnets, and of the magnetizing current, but not of the induction, his object *Phil. Mag. xxii. p. 535 (1886). † Proc. Roy. Soc. xl. p. 486 (1886). being to measure the induction from the values of the tractive force, using Maxwell's expression. Quite recently an important paper has been published by Threlfall, giving an account of experiments made with apparatus essentially similar to Bosanquet's; but the interfaces of the electromagnets were carefully ground and polished, and the tractive force was measured by a spring-balance. The results for high inductions do not show better agreement than Bosanquet's with Maxwell's theory; but the author explains an important source of error which exists especially in working at low inductions, viz.-that the interfaces of the magnets do not generally remain in contact until the stress is completely overcome, but separate at one side first, thus enclosing a "wedge-shaped gap." The numbers given, however, only extend over a range of inductions from 11,000 to 16,000 C.G.S. units. Most of the paper deals with the case when the bars are separated by layers of nonmagnetic substance. It was clear, therefore, that more accurate experiments were necessary to determine whether Maxwell's expression represents exactly the tractive force, and if so, how apparatus is to be arranged so as to allow of the accurate measurement of induction by tractive experiments. Present Experiments. Apparatus. The following experiments were begun in October 1893. The apparatus was devised with a view to realizing as closely as possible the conditions under which the results could best be compared with Maxwell's theory, and was prepared and arranged as follows: A chosen bar of soft German iron was turned accurately to an ellipsoid of revolution of length 22.57 centim. and least diameter 15 centim. Its shape was tested by measuring its volume by weighing in air and water, and by calculating the volume from the above values of the axes. The two values agreed to within a tenth per cent. The ellipsoid was afterwards cut through in the equatorial plane, the diminution of length being measured by observing the distance between two marks on its surface. Two exactly similar magnetizing-coils were made, each 20 centim. long., and having 12 layers of 70 turns each of 2 millim. aluminium wiret. *Phil. Mag. July 1894. † Aluminium wire was used that the coils might be as light as possible, it being thought desirable not to use the compensating arrangement adopted by Bosanquet, as this probably introduced errors due to friction. The two halves of the ellipsoid were soldered into tubeswhich could be fitted tightly, axially, into the coils, the free ends projecting by amounts regulated by nuts, N (fig. 1), Fig. 1.-Longitudinal vertical section of Traction Apparatus. N P -R H running on the tubes. To secure good alignment of the halfellipsoids, a small brass ring, R, of 1 millim. width, was made to fit tightly on one half and loosely on the other at the plane of contact. This ring was afterwards found to be an important part of the apparatus, results obtained without it being very uncertain. To the absence of such a guide in Bosanquet's experiments may probably be attributed, to some extent, the uncertainty of his results, especially at high inductions. One coil was suspended from a tripod stand by two rods provided with nuts and screws, by which and two other screws (not shown in the diagram) the coil could be raised or lowered, levelled, and rigidly fixed. Below this was a platform, P, with |