474 KENNELLY AND AFFEL. 



where A is the same force-constant as is defined in (34) and (35); 

 or, substituting from (37) : 



AH 

 ex = — 



2; 



\|8i + i82 ab volts Z (39) 



From such experimental observations as have yet been made, it 

 appears that jSi = /32 = |8, say; or that the lag of flux in the a.c. 

 magnetic circuit, associated with the alternation of air-gap reluctance, 

 is nearly the same as that associated in the same magnetic circuit with 

 alternation of current. It is hoped to make further investigations on 

 this point. In any case, however, if we consider that /3i + /So = 2jS, 

 we have for the motional impedance 



Br 



A . , AH , A2 



Z = ^ = V .r \02 = ^- \2i8 = — \2|8 absohms Z (40) 



This is the vector change in the impedance of the receiver winding, 

 occurring at any assigned frequency, between the conditions of free 

 vibration and suppressed vibration. Since in (40) the denominator z, 

 the mechanical impedance, follows a straight-line locus (Fig. 5), as 

 the frequency is varied, the system otherwise remaining constant, the 

 motional impedance Z must follow a circular locus, similar to that of 

 Figure 29, except that the diameter of the circle will be depressed be- 

 low the axis of reals by the angle 2/3. From this circle, corrected 

 when necessary for the effect of change in impressed frequency on 

 A, the natural frequency coo and the damping constant A can be 

 determined according to formulas (20) to (23). 



Solution for Diaphragm Constants .1, m, r and s, when x^ is 



GIVEN. 



From (36) and (38), taking current phase as standard, 



. ^ fi ^^^ ^frn^ ej^'i ^ e:cm dyues ,^j. 



i Im X Xm absampere 



and from (18), at resonance. 



fm = rxm dynes (42) 



where /m is the maximum cyclic value of the impressed force; and x^ 

 the maximum cyclic velocity in phase therewith, also from (40) 



Cxm = Im T^m abvolts (43) 



