KENNELLY AND PIERCE. — TELEPHONE RECEIVERS. 143 



bipolar and for the monopolar receiver, and in order to simplify the 

 equations, let us write 



A = ^"^° for the bipolar receiverj and dynes /absampere (17) 



A = — ^ for the monopolar receiver; dynes /absampere (18) 



C't- 



then, for either instrument, 



./;• = Ai dynes Z (19). 



Equations (15), (16) and (19) assume that the pull on the diaphragm 

 due to i is in the phase with i; but with hysteresis and eddy currents 

 present, the electromagnetic force will lag^ behind the current i by an 

 angle /?i; whence the force on the diaphragm due to the current i 



becomes, by eq. (19), 



fi = A i i3, dynes Z (20) 



Consequently, by equation (6), 



X = ^-^ cm/sec Z (21) 



z 



The e. m. f. induced in the coils by the motion of the diaphragm 

 will be, in the absence of hysteresis, 



e;c=iV^ = iV^i: ab volts, Z (22) 



and by differentiating equation (10) or (11), equation (22) gives 



to a first approximation 



2N?Q'ox .. , , . . 



ex = — — — = Ax ab volts, Z (22a) 



and by substitution from equation (21) 



e, = tt±^. abvolts Z (23) 



z 



However, it should be noted that there is also a hysteretic lag of 

 flux with change of gap, and this will cause the induced e. m. f. to lag 

 by a certain angle /?2 behind x, so that equation (23) should be changed 

 to 



^^^^i%±h ,b,„to^ (24) 



3 On the question of Constancy of 0i see VI below. 



