360 



KENNELLY AND UPSON— HUMMING TELEPHONE. 



[July 20, 



ing vectors, it follows that if any automatically reinforced vibrating 

 system, such as an electromagnetic bell, electromagnetic tuning fork, 

 or humming telephone, is propelled by an elastic force proportional 

 to the displacement, reinforced by a cyclic force some function of the 

 displacement, and damped by a force proportional to the velocity, it 

 is subject to equations (17), (18) and (19) which appear to be new. 

 In the series of measurements on the humming telephone above 



g s $ s. § ^ § 



9 D&qrees of L,a,q. 



Fig. 17. Reinforced Frequency in Relation to the Phase of the Reinforcement. 



outlined, the force function R^mx{r) was not measured. The 

 restoring electromagnetic force on the receiver diaphragm, due to the 

 action of the transmitter, will manifestly diminish when the tube- 

 length is increased. For a fixed tube-length, moreover, it cannot 

 increase indefinitely in simple proportion to the displacement of the 

 diaphragm, or to its amplitude of vibration. If we assume pro- 

 visionally that R increases as the square root of the amplitude of 



