430 KENNELLY AND AFFEL. 



edge, is subject to distributed attracting electromagnetic and opposing 

 resilient forces, with distributed mass or inertia, and distributed 

 frictional resistance to motion. In Figure 7, the system is simplified 

 to an equivalent central particle, of mass m, attracted electromagneti- 

 cally, and having its motion opposed by a localized elastic tension of «■ 

 dynes per cm. of displacement, together with a localized frictional 

 opposing force ^ of r dynes per kine (dynes per cm per sec) . 



The justification for the above simplifying substitution, lies in the 

 fact that the observed " motional-impedance circle," and its associated 

 phenomena, are found to be in satisfactory accordance with the simpli- 

 fied theory. 



Deductions from the Motional-Impedance Circle taken 

 separately. 



It was shown in the paper of 1912, that from an inspection of the 

 motional circle, it is possible to obtain the following data: 

 (1) The resonant angular frequency of the diaphragm * 



=J 



Wo = radians per second (1) 



This frequency is found at the maximum motional impedance, i. e. 

 at OP, Figure 4, the diameter of the motional-impedance circle. 



(2) The damping constant, or logn decrement per second of the 



r 

 diaphragm: A = — numeric per second (2) 



This damping constant is a function of the distribution of frequencies 

 around the motional-impedance circle. It is equal to half the differ- 

 ence between the angular velocities at the cjuadrantal points QQ', 

 Figure 4. In t seconds after the release of the diaphragm from a dis- 

 turbed position, the amplitude of residual disturbance is €~^' times 

 the initial amplitude. 



(3) At resonance, i. e., at the natural frequency of the diaphragm, 

 the magnitude of the motional impedance, or the diameter of the 

 motional impedance circle, is defined by 



A- 

 Zm = — absohms (3) 



3 The "kine" is a name for the C. G. S. unit of velocity, originally proposed- 

 by the B. A. 



4 See Appendix I. 



