& R2= 2 kзYE sin e cos € -R cos (pt-a) say; = {G_ k,YE sin2 e _ ¿G } + {k,YE sin ecos e 2k To make R a minimum, -be 2k -bE} + sin pt 2k 2 π If e is nearly equal to the result is very little influenced It has been already mentioned that experiments in which a galvanometer and an intermittent contact caused by a vibrating wire were employed gave results of little utility. An objection to the method is that the length of contact and the position of contact (so to speak) with regard to the phase of the alternating current are unknown. A well-designed alternator would provide a method of obtaining an alternating current almost perfectly harmonic in character, and by means of an intermittent contact arranged by the agency of the axis of the rotating armature the effect of the bismuth on the alternating current could be studied very efficiently. I employed a small alternator made from a motor, the character of whose alternating current I do not know. To make the tabulated results given later more clear, it may be mentioned that the wire of the bridge is divided into 1000 parts, and that increase in the reading means increase in the resistance measured. The alternator gave a current with a frequency of about 30 or 40 per second. With constant current and permanent contact, the reading was 489. The reading for minimum noise with the telephone was about 501. The readings obtained with an intermittent contact and a galvanometer are indicated in the table given below. I was assisted by a friend, and they were taken rapidly. What is called the lead is the angle between the point of intermittent contact and the point of zero current in other words, it is the angular distance the coil of the alternator has advanced beyond the position in which no current is produced before the galvanometer branch is made complete. 362 477 It may be of interest to examine, by means of an example, what sort of results one would expect from reasoning on the principles explained above, Let the E.M.F. acting at the extremities of the Wheatstone bridge be represented by Esin pt, and the back E.M.F. acting in the bismuth spiral by E sin (pt -45°). The adjoining figure represents a Wheatstone bridge. 30 The bismuth spiral is supposed to A be in the arm CD. CBA represents the bridge-wire divided into 1000 parts, the divisions counting from C to A. Let XY; this involves the assumption that the change in resistance of the bismuth is only apparent. B P The theoretical change in resistance of the bismuth spiral as determined by the telephone will first be calculated. Assuming that the current in BD is negligible, the current through the telephone varies as X X+Y or as Р {Esin pe-sin (pe-45)}-posin 1 30 sin (pt — 45°) —(1—r) sin pt 1 1 =sin pt (r-60) + cos pt (602) 2 =R sin (pt-a) say. pt, In the case of intermittent contact no current will go through the galvanometer when 1 1 (1− r) sin pt = { sin pt- sin(x)}, 30 Let pt+80, when 80 is infinitesimally small r=—∞, =-80, r = +∞; nothing corresponding to these results can be obtained in practice. In the above equation the contact is supposed to be of infinitesimal duration; as a matter of fact this is not the case : let T-time of contact, then a more correct equation would be However, this equation, integrated, would also give rise to expectations of discontinuity in r, when It will be interesting to find what would be the theoretical readings for various values of pt. The theoretical results indicate a sudden change at 0°, involving an impossibility of reading for small values of pt ( must lie between +1 and 0); later a gradual rise in reading to 180°, again a sudden change, and a repetition of the preceding. The measurements of the angles of lead are confessedly rough (they were made with the unassisted eye), theory would indicate an addition of 5° to each reading. I endeavoured to make more observations, but owing to difficulties decided to leave more accurate determinations to a future time. Theory indicates that difficulties might be expected at the position with which I always started, viz., a lead of about zero. I may mention that the telephones I employed were not nearly so useful with currents of low frequency as with higher. In fact a current from the alternator, which was none too powerful for use with the telephones and bridge, heated the bismuth spiral so as to perceptibly alter its resistance. I found that in a strong field the resistance of bismuth, as measured by a telephone, diminishes with increase of temperature: the same is true with a constant current, as, I found out after making my own experiments in May, was noticed by Van Aubel* a year or more ago, and later (with more detail) by Henderson †. That the resistance of bismuth in a strong field should diminish with increase in temperature is what one would expect if, as surmised, the increase of resistance is due to changes connected with the diamagnetism of bismuth. I do not know of any researches, but it is probable that the susceptibility of bismuth will diminish (numerically) with increase of temperature: assuming this, we should expect that the effect of an increase in temperature will be complex in character—that, so far as the effect of the demagnetization due to rise in temperature is concerned, the resistance will diminish; that, so far as the ordinary action of heat is concerned, the resistance will *Journal de Physique, September 1893, p. 108. |