352 KENNELLY AND UPSON— HUMMING TELEPHONE. [July 20, 



the working range of the tube. The constants f and I may be 

 modified by the presence of condensers, and other circumstances. 



3. The range of pitch variation, and the breaking positions, are 

 determined by the transmitter, and by the reinforcing capability of 

 the system. For systems that are weak, either electrically or acous- 

 tically, the range of pitch, above or below the mean, will be small. 



4. The primary current, as measured by a d.c. instrument, is 

 ordinarily a minimum at the mean frequency, and a maximum at 

 a break. 



5. Transmitters may be tested for effectiveness, by measuring 

 their hum-extinguishing resistances in the primary or secondary 

 circuit. The tube-length should be such as to produce mean fre- 

 quency if one connection of receiver only is used, but should favor 

 both connections equally, if both connections of receiver are used. 



Outline of Theory of the Humming Telephone. 

 Preliminary Considerations. Simple Orbital Motion and Simple 

 Unretarded Vibration. — Let a particle of mass m grammes de- 

 scribe a simple plane circular orbit cab, Fig. 14, about the center 



b 

 Fig. 14. Vector Diagram of Free Undamped Vibration. 



O. Let the radius Oz=^r cm., and let OX be the initial line of 

 reference. At time t = o seconds, let the particle occupy the posi- 

 tion s; so that its initial radius vector is Os. Let w be the uniform 

 angular velocity of the particle about the center O, in radians per 

 second. Then, after the lapse of / seconds, the particle will occupy 

 a point in the plane defined by the vector displacement 



