Measurement of Inductance by Anderson's Method, using Alternating Cur- E. B. Rosa 383 The Relative Intensities of Metal and Gas Spectra from Electrically Conducting Gases. . P. G. Nutting 399 The Use of White Walls in a Photometric Laboratory. . . E. B. Rosa, M. G. Lloyd, and C. E. Reid 421 Detector for small Alternating Currents and Electrical Waves. L. W. Austin 435 The Positive Charges carried by the Canal Rays L. W. Austin 439 G. K. Burgess 443 DEPARTMENT UNITED AND LABOR AMERICA STATES OF WASHINGTON GOVERNMENT PRINTING OFFICE MEASUREMENT OF INDUCTANCE BY ANDERSON'S METHOD, USING ALTERNATING CURRENTS AND A VIBRATION GALVANOMETER. By EDWARD B. ROSA and FREDERICK W. GRover. 1. HISTORY OF THE METHOD. Several modifications of Maxwell's method" of comparing an inductance with a capacity have been proposed in order to obviate the double adjustment of resistances necessary in that method. Maxwell showed that if (1) the bridge is balanced for steady currents and at the same time (2) the resistances are so chosen that there is no deflection of the galvanometer when the battery current is suddenly closed or broken, then L=CRQ=CPS (1) where L is the inductance in the arm A D, the resistance of which is a Eléctricity and Magnetism, § 778. Q, C is the value of the capacity in parallel with R, and P, R, and S are noninductive resistances. In order to satisfy both of these conditions two of the arms of the bridge must be varied simultaneously, so that the balance for steady currents may be maintained while the balance for transient currents is sought. This is generally a tedious process, although by means of a small variable inductance in Q, in addition to the inductance to be measured, and a multiple valued condenser the process might be considerably accelerated. In 1891 Professor Anderson proposed an important modification of Maxwell's method, which consisted in joining the condenser to a point E, separated from C by a variable resistance r. The bridge being balanced for steady currents by varying any one of the four arms of the bridge, the balance for transient currents is then made by varying, which does not disturb the balance of the bridge for steady currents. This change, which rendered the two adjustments independent, removed at once a most serious difficulty and made the method thoroughly practicable. Anderson's demonstration for the case of transient currents gives for the value of the inductance (changing the letters to correspond to fig. 2) L=C [r (Q+S)+PS] If r=0, LCPS, as in Maxwell's method. (2) In the use of Anderson's method r may be small, so that CPS is the principal part of the expression for the inductance, or it may be larger, and the first term, Cr (Q+S), represents the larger part of L. Thus a considerable range of values of inductance may be measured a Phil. Mag., 31, p. 329, 1891. without changing the arms of the bridge or the capacity of the condenser. Stroud and Oates" have proposed another modification of Maxwell's method, which they have used with much success in measuring inductances. Instead of employing an interrupted current from a battery, as Anderson had done, they used an alternating current and an alternating-current galvanometer, the latter being essentially a d'Arsonval galvanometer, with the field magnet laminated and strongly excited by an alternating current from the generator. The galvanometer was thus made very sensitive, and to increase the sensitiveness still further the resistance was placed outside the bridge, as shown in Fig. 3. It will be seen that this arrangement differs from Maxwell's only in separating the point B from the terminal of the condenser by the auxiliary adjustable resistance r, which in Anderson's method is in the galvanometer circuit between Cand D. As the resistance is sometimes several hundred ohms, it reduces the sensibility when in the galvanometer circuit, whereas in the arrangement of Fig. 3 the electromotive force can be increased if r is large, and so keep the same current in the bridge as when r is small, and thus maintain the sensibility. The expression for the inductance L in Stroud's method (changing the letters to correspond with Fig. 3) is L=C[r (Q+P)+PS], (3) which closely resembles the formula for Anderson's method, but differs in having Q+Pin the first term instead of Q+S. a Phil. Mag., 6, p. 707, 1903. |