1908. 



KENNELLY AND UPSON— HUMMING TELEPHONE. 



357 



equations apply; but their real parts only are taken. In Fig. 15, the 

 projections of the vectors on a straight line through 0, are se- 

 lected. The dwindling vibrations of a tuning fork, or the oscillatory 

 discharge of a condenser through a circuit containing resistance and 

 inductance, obey this law. In the last named case, the inductance 

 corresponds to the mass m, the reciprocal of the capacity corresponds 

 to the elastic coefficient A, and the resistance corresponds to the 

 velocity-resisting coefficient F. The condenser-charge, or electric 

 quantity, corresponds to the vibratory displacement, the electric 

 current to the vibratory velocity, the discharging electromotive force 

 to the elastic force OF, the resistance e.m.f. to Of, the e.m.f. of 

 self-induction to Of, and the impedance of the discharging circuit 

 to the vector mw^ /_ ^, or ^J MA Z ^ = r/2 -f- jnna. 



Case of Retarded Free Vibration Reinforced. Restored Circu- 

 lar Orbit. — In order to sustain stable orbital motion in a particle 

 retarded with a force proportional to the velocity, it is necessary 



Fig. 16. Vector Diagram of Reinforced Vibration. 



to supply energy continuously to the particle and to act upon it with 

 a force equal but opposite to the velocity-resisting force. The orbit 

 will then be restored from an inmoving spiral to a simple circle. 

 The displacement, velocity and acceleration of the particle, Fig. 16, 

 will then be severally expressed by equations (i), (2) and (3) ap- 

 plied to Fig. 14. 



Let OR, Fig. 16, be an outwardly directed force from the center 

 0, the magnitude of OR being some function mx(r) of the radius 

 of displacement, and 6 the phase retardation behind the displace- 



