364 



KENNELLY AND UPSON— HUMMING TELEPHONE. 



[July 20, 



an inductance ratio 5":= 0.0575 between primary and secondary 

 windings. Proceeding in this way, the following table has been 

 arrived at, giving the conductances which when multiplied by the 

 equivalent transmitter e.m.f. yield the current strength in the sec- 

 ondary circuit of Fig. 21. 



Table III. 



Frequency Cycles per 

 Second, n. 



637 



796 

 956 



637 

 796 



Angular Velocity 

 Radians per Second 



Capacity in Secondary j Conductance of Secon- 

 Circuit. fif. dary. Mhos. 



0.009 /23° 



0.0087 /i7° 



0.0093 /l2° 



0.0054 \ i40° 



0.0095 \ I23° 



o. 1 1 \ 115° 



Although the assumptions employed do not anticipate a high 

 degree of accuracy in the conclusions above tabulated, yet we may 

 safely infer that when no condenser is used in the secondary circuit 

 (^f . = (X )^ the secondary current will lead the impressed primary 

 e.m.f. by a small angle, and this current will have substantially the 

 same strength and phase for all frequencies between 600 r-^ and 

 1,000 '—'. When, however, a condenser of 0.2 /xf. is inserted in the 

 secondary circuit, the current in the receiver will be advanced in 

 phase about 110° or nearly a third of a cycle; while the strength of 

 this current will be considerably greater at the higher frequencies 

 than at the lower frequencies. 



Since the total lag in phase of the restoring electromagnetic force 

 behind the displacement of the receiver diaphragm includes (i) the 

 electric current lag; (2) any hysteretic electromagnetic lag in the 

 receiver cores; (3) any mechanical inertia lag of the transmitter 

 diaphragm ; (4) the acoustic lag in the air column of the tube ; it 

 follows that the total lag with a condenser of 0.2 \xi. should be about 

 1 10° less than with short-circuited condenser ; while the higher fre- 

 quency notes should be favored, and the lower frequency notes dis- 

 favored. Fig. 9 shows that both these effects took place, the acous- 

 tic lag had to be increased by about 12 cm., or about 110°, in order 

 to produce mean frequency, and compensate for the current lead. 



