VIBRATING TELEPHONE DIAPHRAGMS. 445 



where n^ and 11.-, are the corresponding impressed frequencies ; whence 



r r 

 W7 = — r = , gm.-cm.-. (ii) 



At these quadrantal frequencies, the deflection amphtudes will be 

 very nearly (9,„/V2 radians. Finally, by observing the angular 

 velocity w^ of resonance, when 9m becomes a maximum, we obtain 



coo = \/— , radians/sec, (12) 



\ m 



whence 



, dyne perp. cm. 



5 = wcoo^ -r. . (13) 



radian 



Consequently, all four constants A, m, r and .$• can be found for any 

 assigned adjustment of the vibration galvanometer, by measuring 

 (a) its motional-impedance Zm in a Rayleigh bridge, to a measured 

 alternating current /,„ maximum cyclic absamperes, {b) noting the 

 deflection 9m in radians, at resonance, on either side of the scale zero, 

 (c) the resonant angular velocity oj„ and {d) the impressed fre- 

 quencies at the quadrantal points fio, «i cycles per second. 



Two additional checks on the above results can be obtained, if 

 desired, (i) by passing a small measured continuous current h ab- 

 samperes from a storage cell and measuring the steady deflection 

 produced. If 9s is the corresponding steady deflection obtained, in 

 radians ; then 



sds = IsA, dyne perp. cm., (14) 

 whence 



IsA dyne perp. cm. 



^^~d7' radian ' ^^^^ 



It should be noted, however, that the value of ^, obtained in this 

 continuous-current test, is found to differ slightly from that found 

 by A.C. measurements. The latter are to be preferred when avail- 

 able. (2) By disturbing the vibratory system, and allowing it to 

 oscillate freely to rest, according to the formula. 



— = e , numeric, (16J 



Vn 



