150 PROCEEDINGS OF THE AMERICAN ACADEMY. 



determination of the points of the circular graph, the writers beHeve 

 that the departure of a degree or two in the value of /?, as obtained 

 by direct measurement from its value as obtained by the circular 

 graphs, is not unsatisfactory. 



VII. Summary of Results. 



1. The resistance and inductance of several telephone receivers 

 were measured over a wide range of frequencies with their diaphragms 

 both free and damped. 



2. The damped resistance is approximately a quadratic function 

 of the angular velocity of impressed e. m. f. (see equations (1) and (2) ). 



3. Although the damped resistance and the damped inductance 

 both change with the frequency of e. m. f., their product is approxi- 

 mately constant, independent of the frequency, over a considerable 

 portion of the range of audible frequencies (see eq. (3) and (4) and 

 Table VII). 



4. The damped reactance of one form of standard bipolar Bell 

 receiver is approximately equal to its damped resistance, over a con- 

 siderable range of frequency; so that the current lags the e. m. f. by 

 45° (see Figure 2). 



5. The free resistance and reactance of telephone receivers go 

 through marked changes with changes in frequency of constant e. m. f. 

 in the neighborhood of the natural frequency of their diaphragms 

 {cf. Figures 4-6). 



6. The motional resistance and motional reactance (by which is 

 meant excess of free resistance of reactance over damped resistance 

 or reactance) conform accurately to certain simple laws as follow: 



I. The motional reactance plotted as ordinates against the 

 motional resistance as abscissas, as the frequency of constant 

 impressed e. m. f. is changed from zero to infinity, gives a 

 circular locus, with various interesting characteristics 

 (c/. Figures 7-12). 

 II. The rectangular plots of motional reactance and motional 

 resistance against angular velocity of constant impressed 

 e. m. f. give curves somewhat analogous to the curves of 

 index of refraction and absorption of light in an optical 

 medium in the neighborhood of an absorption band {cf. 

 Figures 4-6). 



7. The power taken by a telephone receiver when sounding at 0.3 

 volt applied voltage may exceed by 68% the power taken from the 



