148 PROCEEDINGS OF THE AMERICAN ACADEMY. 



Having now obtained the constants of Table XI, the theoretical 

 distribution of angular velocities around each of the circular graphs 

 of Figures 7 to 11 were calculated by equation (39), and these theo- 

 retical values are designated by numerals on the inside of the circular 

 graphs. 



The values of R'—R and of X'—X corresponding to these theo- 

 retical values of co were then plotted as the circles on the rectangular 

 graphs of motional resistance and motional reactance in Figures 4, 5, 

 and 6. It is seen that the agreement of the computed and observed 

 points in these Figures 4 to 6, while not exact throughout the entire 

 range, is yet sufficiently good to show that the theory is essentially 

 correct. 



Another significant point in the theory is the interpretation we have 

 gi\'en to the depression angle 2 /? of the circular graphs. We inter- 

 preted /? to be the angle by which the magnetic flux lags behind the 

 magnetizing current in the telephone receivers. To test this point, 

 this angle of lag of magnetic flux behind magnetizing current was 

 independently measured with the experimental bipolar receiver. 

 This receiver had a separate secondary, or exploring, coil wound 

 around the ends of its poles, near the diaphragm. The e. m. f. gen- 

 erated in this exploring coil is in phase with the time rate of change 

 of flux; and the phase of this e. m. f. was compared with the phase 

 of the alternating current in the exciting coils in two ways (1) by a 

 three-voltmeter method and (2) by an alternating current potentio- 

 meter. 



In the three-voltmeter method, a known resistance was put in 

 series with the exciting coils, and one end of the exploring coil was 

 connected to the point between the exciting coil and the known resis- 

 tance. With the frequency and the e. m. f. about the telephone kept 

 the same as that used in the bridge measurements (i. e., the e. m. f. 

 of 1 volt, and the frequency near the resonant frequency of the dia- 

 phram) voltages were measured about the known resistance (20 ohms), 

 about the exploring secondary, and about the two in series. These 

 voltages, being small, were measured by a crystal rectifier in series 

 with a galvanometer,^ — the galvanometer and rectifier having been 

 calibrated immediately before and after the experiment by an a. c. 

 potentiometer operating at the frequency employed. 



The readings of voltage were very consistent, and were as follows 

 in a typical case: 



5 G. W. Pierce: Phys. Review, 25, p. 31, 1907; ibid., 28, p. 153, 1909. 



