TELEPHONE DIAPHRAGMS. 475 



where em is the maximum cycHe induced voltage, I^ the maximum 

 cycHc current at resonance and Z^ the maximum motional impedance, 

 or the diameter, in ohms, of the motional impedance circle. Substi- 

 tuting in (41) we have 



XmT ImZm dynes ,^^. 



or 



T 2 'Z J. 



(45) 



and Im^Zm = (i'm)"^ = Pm abwatts (46) 



where P„ is the maximum cyclic mechanical power at resonance. In 

 these last equations the phase angles disappear and the magnitudes 

 or vector moduli only are presented. The maximum cyclic velocity 

 has a magnitude represented by 



Xm = oooXm kines (47) 



Xjn being the maximum cyclic displacement as measured at the resonant 

 frequency coo over an air-gap i. e., near the center of the diaphragm. 

 Consequently, 



_ Im^Zm dynes , , 



Xm^ oi<? kine 



This determines the value of the mechanical resistance r in terms of 

 measured quantities. 



From the motional impedance circle, we can obtain the damping 

 constant A = r/{2m), by any of the formulas (20) to (23) ; so that 



m = — gm (49) 



From the observed resonant angular velocity at the extremity of the 

 motional impedance diameter, we have from (19) 



* = mw^ dynes /cm (49a) 



Finally, from the relation Zm = ' by (40), we have 



A = Vz;::; = 1^"^ dyne^ 



Xm 0)0 absampere 



which completes the series of constants. The working formulas are 

 thus (48) to (50) inclusive. 



