1915.] SURFACES OF TELEPHONIC DIAPHRAGMS. 129 



Equation (4) shows that the displacement velocity w is equal to 

 the impressed vibro-motive force /, divided by the impedance 2. 

 The locus of this velocity, as o varies from o to co with constant F, 

 becomes a circle OMP, the diameter OM of which is equal to F/r 

 cm. per sec, while the angle a of the chord OP, measuring the 

 velocity, is equal and of opposite sign to the angle a of the im- 

 pedance 5. In the case represented by Fig. 1\A, the telephone dia- 

 phragm No. 2 was actuated electromagnetically at constant alternat- 

 ing-current strength, under varying frequency. At the frequency 

 71 = 992 —', the vibratory velocity OM = 4.8 cm. sec, was a maxi- 

 mum, and was in phase with the impressed vibro-motive force F. 

 At M = 994'~-', the mechanical impedance had increased to op at the 

 angle a =^14°, and the vibratory velocity had fallen from OM to 

 OP or from 4.8 to 4.65 cm. per sec. lagging in phase behind the 

 impressed vibro-motive force by 14°. The diagram shows that 

 between the frequencies of 923 and 1,074.—', the vector displace- 

 ment velocity w had moved over nearly the entire circumference of 

 the velocity circle OMP, and from a phase nearly 90° ahead of the 

 impressed vibro-motive force to nearly 90° behind it. 



If we integrate (4) with respect to time, we obtain, for the steady 

 state of motion, 



= I wdt = I dt = — — = — , cm. Z . (5) 



This shows that the instantaneous displacement is m times less than 

 the corresponding instantaneous velocity, and is 90° behind it in 

 phase. If we consider the maximum displacement, we have 



^m..= -'- cm. (6) 



The locus of zVmux is therefore a closed curve distorted from a circle 

 by the effect of varying w in the denominator. Considering it as 

 an approximate circle for this case, the diameter OM' correspond- 

 ing to M=:992'— ^ represents a displacement amplitude of J.'/fj'', 

 lagging approximately 90° behind the maximum velocity OM. At 

 the frequency 994 '—', the displacement would be OP' = 7.48 /x. 



