VIBRATING TELEPHONE DIAPHRAGMS. 443 



suspension carry the testing current, and are connected mechanically 

 by a small mirror, which optically serves to indicate the angular dis- 

 placement of the bifilar system at the mirror. It is further assumed 

 that the restoring torque is sO dyne-perpendicular-cm. ,^- proportional 

 to the angular displacement d radians ; that the resisting torque dis- 

 sipating the energy of motion is r9, or is proportional to the angular 

 velocity radians per second ; also that the inertia torque, resisting 

 change of angular displacement, is md, where nv is the equivalent 

 moment of inertia of the system at the mirror, and is the angular 

 acceleration in radians per sec.^. The impressed displacing torquCt 

 or vibromotive torque (V.M.T.), is assumed to be simply harmonic 

 of the type 



/ = ImAe^""' = iA, dyne perp. cm. Z , (i) 



where i is the complex instantaneous current passing through the 

 suspension, with maximum cyclic value /« absamperes. A is the 

 torque constant of the instrument, in dyne perp. cm. per absampere, 

 y= V — I, w= the impressed angular velocity, and t is the time in 

 seconds from the moment when the real component of f starts posi- 

 tively through zero towards its maximum cyclic value. The real 

 component of ( i ) is the instantaneous torque. The equation of 

 motion is 



md ~\- rO -\- s6 = f , dyne perp. cm. Z , (i) 



whence, in the steady state, i. e., neglecting the exponentially decay- 

 ing transient term, 



• / / radians 



. , 5 \ s ' sec. 



r -\- j\ moo — - I 



^. (3) 



Here s is the mechanical impedance of the vibratory system. In the 

 ordinary bifilar oscillograph, none of the four constants A, in, r and 

 ^ is supposed to change, except through accidental changes of tem- 

 perature. In a vibration galvanometer, however, the tuning of the 

 vibratory system imposes changes in the impedance s, and in its 



12 In a torque t, dyne-perp.-cm., the force /i dynes is assumed to act 

 perpendicularly to the radius arm i cm., at which it is applied. A torque is 

 therefore not properly expressible as dyne-cm., but as dyne perpendicular 

 cm. ; or dyne 1 cm. 



