126 PROCEEDINGS OF THE AMERICAN ACADEMY. 



the frequency in radians per second (angular velocity). This is done 

 in Figures 4, 5, and 6. Taking Figure 4 plotted from Table IV 

 obtained with the watch-case receiver, as typical, it will be seen that 

 the Figure contains curves of motional resistance, motional reactance, 

 motional power, and phase angle of motional impedance, marked 

 respectively Resistance, Reactance, Power and Phase. These quantities 

 are all plotted against angular velocity. The black dots are observed 

 points, and the circles are computed values, or derived values. Begin- 

 ning with the resistance curve, and remembering that this curve 

 represents the excess of free resistance over damped resistance, that 

 is to say, the effect of the motion, it will be seen that, starting at a 

 value slightly below zero at 2834 radians per second, the increment 

 of resistance due to motion (motional resistance) increases up to 23 

 ohms at angular velocity 5674, then descends rapidly to minus 25 

 ohms at angular velocity 5938 and then increases again toward zero. 

 The motion of the diaphragm markedly increases the resistance at 

 certain frequencies and markedly decreases it at other frequencies. 

 The formulas for computing the motional resistance values are given 

 under heading V below. 



Next, let us examine the motional reactance curve. The effect of 

 the motion of the diaphragm is chiefly to decrease the reactance so that 

 the free reactance is less than the damped reactance, giving usually a 

 negative motional reactance, amounting to — 44.7 ohms at angular 

 velocity 5800. The motional reactance is not always negative but 

 shows small positive values in the neighborhood of angular velocities 

 4500 and 7000. 



The resemblance of the motional resistance curves and the motional 

 reactance curve of Figures 4, 5, and 6 to the curves of optical index 

 of refraction and optical absorption plotted against frequency, in the 

 neighboring of an absorption band, will at once strike the attention of 

 the reader familiar with theoretical optics. A difference, however, 

 exists on account of the hysteretic l)ehavior of the iron in the telephone 

 theory, as will be pointed out in the treatment under heading V below. 



Effect of Motion of Diaphragm on Draft of Power. — Attention 

 is next directed to the curve marked Power in Figure 4. This curve 

 shows the excess of power sent into the telephone when freely vibrat- 

 ing over the power sent into it under the same impressed e. m. f. when 

 damped. The excess of power (i. e. motional power) is plotted in 

 microwatts against angular velocity of impressed e. m. f., and is seen 

 to be different for different angular velocities corresponding to different 

 frequencies. The maximum of motional power is in the neighborhood 



