The needles were then moved a little closer to the spheres, In all these cases, the first column gives the readings when the spheres directly under the magnetometer are positively charged, and the second column when they are negatively charged. In No. 1, the successive deflexions are: 3, 6, 2, 12, 5, 8, 10, 7, 7; giving an average of 67. In No. 4 they are: 21, 13, 0, 8, 18, 18, 9, 19, -6, 10, -8, 7, 9; giving an average of 9.0. It is evident that with variations such as are present here the measurements can be regarded only as a rough approximation. But the most important fact to be observed is that when the spheres directly under the magnetometer are changed from negative to positive a deflexion towards the small figures of the scale takes place; and when changed from positive to negative a reverse deflexion takes place. When on account of changes in the zero-point some of the deflexions do not apparently follow this rule they are entered with a negative sign in finding the average deflexion. There has invariably resulted a positive deflexion on taking the average. Earlier experiments were made with four spheres in each set. With this number it was possible to get much higher speeds-75-85 revolutions per second. Similar qualitative results were observed, but when comparison with theory was attempted it appeared that fair agreement could be obtained if the maximum value of the magnetic force were used instead of the average. This was largely an accidental result, a sufficient number of reversals not having been made. It would have been desirable to have made a larger number of reversals in each series, but after the apparatus had been running for some time the bearings became so much heated that it was impracticable. The following table gives the values of the ratio of the units obtained from the above readings: These results may be taken as fairly representing all that have been obtained. The agreement between theory and experiment is fully as good as could be expected when all the uncertain elements in the determination are taken into consideration. These uncertain elements are (1) The actual charges carried by the spheres and the effect of surrounding bodies, especially the plate coated with tinfoil covering the lower end of the magnetometer-tube. This tinfoil is cut into strips about 1 millimetre in width, and its effect must be small. (2) The non-uniformity of distribution of electricity upon the spheres so that the charges cannot be regarded accurately as concentrated at their centres. (3) Errors in reading the deflexion of the needle due to outside disturbances. Experiments have also been made with the direction of motion of the spheres reversed. The results obtained are similar in every respect to those given above, except that they are reversed. Experiments using only a portion of the 10,000 cells of the storage-battery gave results which agree fairly well with the preceding. The deflexions were too small, however, to expect very close agreement. Jefferson Physical Laboratory, Harvard University, Cambridge, Mass. XXVII. On the Electrical Resistance of Bismuth to Alternating Currents in a Strong Magnetic Field. By GEORGE C. SIMPSON, B.Sc., Scholar of the Victoria University*. ONE NE of the many anomalous properties of bismuth is the change which the resistance of a filament undergoes when placed perpendicular to the lines of force in a strong magnetic field; not only does its resistance very much increase, but, as discovered by Lenard, its resistance to alternating currents under these conditions is apparently different from its resistance to direct currents. Many experimenters have studied this difference, and although nearly all are agreed as to the way in which it varies with the strength of the field -the frequency remaining constant-each experimenter seems to have arrived at a different conclusion as to the way it varies with the frequency-the field remaining constant. Lenard (who measured the resistance of the bismuth by means of a Wheatstone-bridge, using an induction-coil to supply the alternating current, and a telephone in place of the galvanometer) concluded that the resistance of bismuth in a strong field is the same for alternating as for direct currents until frequencies of the order of magnitude of 10,000 per sec. are used. On the other hand M. Sadovsky ‡, working at St. Petersburg, showed that with the bismuth in a strong field, an alternating current having a frequency of three or four alternations per second produced a change in the resistance of the bismuth. In M. Sadovsky's apparatus an alternating current from a dynamo was supplied to a Wheatstone-bridge containing the bismuth. On the shaft of the dynamo three segments of brass, each extending over 60° of the circumference, were fixed. By pressing a spring into contact with the first segment, the galvanometer-arm was closed for of an alternation; on pressing another spring, the galvanometer arm was closed for the next; and a third spring closed it for the next of an alternation. In this way the galvanometer was connected to the bridge, 1st, when the current was rising in the bismuth; 2nd, when it was at the crest of a wave (current maximum); 3rd, when it was decreasing. M. Sadovsky did not aim at quantitative results, but he obtained *Communicated by Prof. A. Schuster, F.R.S. + Wied. Ann. xxxix. p. 619 (1890). Journal de la Société Physico-Chimique Russe, vol. xxvi. no. 2 (1894). the following qualitative ones :-If Rr, Rm, Ra, and R. are the resistances of the bismuth to a rising, maximum, decreasing, and constant current respectively, then Rr>Rm>Re>Rd. * More recently R. Wachsmuth and C. Bamberger found the resistance in strong fields to be quite independent of the frequency. As these results are so mutually contradictory, Dr. Schuster suggested that I should undertake a research on the subject; my aim being to find how the resistance of bismuth to alternating currents depends on the frequency of the current if the field is kept constant and large. In all my experiments a Hartmann and Braun bismuth spiral (having a resistance of 17.88 ohms at 21° C. in zero field) was placed perpendicular to the field produced by a large electromagnet, the field-strength being about 17,000 per sq. cm., so that the resistance of the bismuth in the field was double its value outside. The alternating current used was generally obtained from a small dynamo which gave a current curve approximately sinusoidal in shape. lines The method of experimenting was based on the following considerations :-As any small change in the resistance of a wire carrying a current may be considered as the result of an E.M.F. set up in the wire, whatever the changes in the bismuth may be due to they can be regarded as arising from an electromotive force set up in the bismuth itself. If on examination this E.M.F. (called in this paper the "bismuth E.M.F.") should prove to be opposite in phase to and of the same wave-form as the-say simple harmonic-current causing it, it may safely be inferred that the change in the bismuth is really a change in the resistance pure and simple. But if the "bismuth E M.F.," while still possessing the proper wave-form, should be displaced 90° ahead or 90° behind, it would be necessary to conclude that in the one case there exists something of the nature of capacity, in the other something of the nature of self-induction in the bismuth. There is the further possibility of the "bismuth E.M.F." having a different wave-form from that of the current. Two methods of experimenting were used. A direct method of obtaining the wave-form of the "bismuth E.M.F." and of the current producing it will be first described. * Physikalische Zeitschrift, I. ii. p. 127 (1899). A Wheatstone-bridge (fig. 1) containing the bismuth, S, was balanced for steady currents, and then an alternating current supplied instead. The "bismuth E.M.F." which this alternating current set up caused an alternating difference Fig. 1. R 3000 ohms 100 ohms I DANIELL of potential across the galvanometer-arm AB in phase with, and of the same wave-form as, itself. An adjustable contactmaker, M, on the dynamo-shaft closed the galvanometer-arm for an instant at any required phase of an alternation; the result being a deflexion of the galvanometer which varied in magnitude and sign with the phase of the "make." The "make" having been set at a known phase, a potentiometer, connected to the ends of the galvanometer-arm, AB, was then adjusted until there was no deflexion of the galvanometer, in which case the potentiometer-reading gave the value of the "bismuth E.M.F." at the instant of the make. Curve I. (fig. 2) shows the form of the "bismuth E.M.F." obtained in this way. In order to compare this "bismuth E.M.F." with the curve of the current producing it, the bismuth spiral was |