VIBRATING TELEPHONE DIAPHRAGMS. 4i7 



frequencies (obtained from a Vreeland oscillator and Rayleigh 

 bridge), between 980-—' and 1,020 '—'. It will be observed that the 

 maximum impedance of the instrument Z„,, at resonance, was the 

 diametral resistance OR = it,.S ohms, or 13.8 X lo** absohms. The 

 R.M.S. current strength in the instrument was 0.55 milliampere 

 = 5.5 X io~^ absampere. The maximum cyclic current Im was thus 

 7.78 X lO"^ absampere. At the impressed resonant frequency of 

 1,000.5 ^~"> the angular velocity would be Wq^ 6,286 rad./sec. Sub- 

 stituting in (7) 



7.78 X 10-^ X 13-8 X lo^ 107.4 X lo^ 



6.286 X 10^ X 0.61 1 X 10-^ 3.83 X lo^ 



dyne perp. cm. 



= 2804 : . 



absampere 



The lower circle in Fig. 19, Oa and b shows the magnitudes of 

 the deflections, each side of the scale zero, in radians of arc. The 

 maximum observed deflection at Or ^0.0611 radian, was obtained, 

 within the limits of experimental error, at the same frequency as 

 the maximum resistance OR of the motional-impedance circle. Sub- 

 stituting the value of A just found in (9) we obtain 



_ 2.804 X 10^ X 778 X io ~^ _ 21.82 X io~^ 



^ ~ 0.61 1 X io~^ X 6.286 X 10^ ~ 3.83 X 10- 



, dyne perp. cm. 



= 5.697 X io~^ . . 



rad. per sec. 



The maximum cyclic displacing torque was by ( i ) 



7.78 X lO"'^ X 2.804 X 10^ = 0.2182 dyne perp. cm. 

 The quadrantal points B and A on the motional-impedance circle 

 are at 996 '— ' and 1,005 ^~'' making the damping constant A ^3.142 X 

 9 = 28.3; so that the oscillations of the instrument would naturally 

 fall to i/eth, or to 36.8 per cent, of the initial amplitude, in a time 

 constant of 1/28.3 = 0.0353 second. Substituting this value of A in 

 (11), we obtain 



5.697 X io~^ _. „ dynes 



m = ^ -^-^ = 1.006 X 10 ^ gm.-cm.-; or 



56.6 ' • • ' j.^^ pgj. gg^ 2 



PROC. AMER, PHIL. SOC, VOL LV, BB, JULY lO, I916. 



