KENNELLY AND PIERCE. — TELEPHONE RECEIVERS. 125 



When, however, the computation is extended to a single observation 

 at 24G4 cycles per second, a departure of 5% is obtained. 



A third interesting fact shown by the experimental tal)les is that 

 the damped reactance is approximately equal to the damped resis- 

 tance for the telephone "Rb" over a wide range of frequency. This 

 may be seen, for this telephone, at 0.3 volt, by a reference to Figure 2 

 and by a comparison of the observed reactance values, marked by 

 crosses, with the observed points on the resistance curve marked by 

 black dots. The damped reactances and damped resistances are seen 

 to be nearly the same throughout the range of frequencies between 

 451 cycles per second (co = 2834) and 1250 cycles per second (co = 

 7850). Within this range the damped resistance and the damped 

 reactance both nearly double and yet remain within a few percent 

 of equality with each other. For the telephone Rb at 0.42 volts, the 

 same approximate equality holds within the range of frequencies 

 between 428 and 2464 cycles per second, as may be seen by a reference 

 to the fourth and seventh columns of Table III. It is to be noted, 

 however, that this same equality cannot persist at low frequencies, 

 for the damped reactance at zero cycles is zero, while the resistance 

 of this instrument at zero cycles is 71 ohms. As a corollary, it may be 

 observed that within the range of equality of damped resistance and 

 damped reactance, the damped angle of lag of current behind impressed 

 e. m. f . is 45°, and the damped impedance is V2 R. With the other 

 instruments tested, the equivalence of damped reactance and damped 

 resistance was not obtained ; but, as may be seen by reference to Figure 

 3, the curves of damped reactance and damped resistance for the 

 watch-case instrument run nearly parallel and within 10 ohms of each 

 other, for a considerable range of frequencies. 



It would be interesting to discuss the relations expressed in equations 

 (1), (2), (3), and (4). Since, however, at this time the primary pur- 

 pose of the writers is to present an account of the effects of the motion 

 of the diaphragm in modifying the resistance and reactance of the 

 telephone receivers, a further discussion of the relations (1) to (4) 

 will be deferred. 



The Effects of Motion of the Diaphragm on the Resistance 

 and Reactance of the Receivers. — As stated in the introduction, 

 the motion of the diaphragm of a telephone receiver has a marked effect 

 on its resistance and reactance. This effect is best shown by sub- 

 tracting the damped resistance from the free resistance, and the 

 damped reactance from the free reactance and plotting the differences, 

 called respectively motional resistance and motional reactance, against 



