KENNELLY AND PIERCE. 



TELEPHONE RECEIVERS. 



145 



diameter of len2;th ^— depressed 2/? below the axis of reals. Equation 



r 



(31) is the theoretical equation to the circular graphs of Figures 7 to 12. 



Replacing the vector z of equation (31) by its absolute value |z| 



and angle a, we have 



A" 



Z' - Z = rj '2/3 + a 

 \z\ 



absohms Z (32) 



Equation (32) ma}' be analysed into 



A 



R' — R= rr cos {2^3 + a) 



X = -r^'sin (2^9 + a) 



in which 



and 



M=J 



r~ + 'moo 



a = tan 



moo 



s 



3 

 0} 



absohms (33) 

 absohms (34) 



absohms (35) 



radians (36) 



are functions of 00. The quantity A, involving SJq ^^^ "^^^ might be 

 expected to vary with variation of w, but an examination of the 

 experimental results shows that, with the excitations employed, not 

 much error is introduced by considering A and also /? independent of 00. 



Equations (32), (33), and (34) are in convenient form for computa- 

 tion, and permit an easy determination of some of the important 

 mechanical constants of the diaphragm. 



For example, if we let coq be the angular velocity of impressed 

 mechanical force for which the sustained vibration of the diaphragm 

 is in resonance, we see from equation (6) above that 



ooo 



=4 



s 



m 



radians /sec. (37) 



Now, if CO, the angular velocity of the impressed electromotive force in 



the telephone circuit, is equal to coq = — , it is seen by equation (36) 



\m 



