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



When the phase retardation 6 of the restoring force (Fig. 16) 

 is less than 270°, we should expect, according to the theory, that the 

 pitch should rise ; because the elastic resilience of the diaphragm is 

 virtually increased by the OS component of the new force, and when 

 6 > 270°, on the contrary, the pitch should fall. This was always the 

 case in the observations. We have to bear in mind, however, that 

 with any given tube-length, an alteration of pitch involves a change 

 of wave-length, and therefore a change of phase in transmission 

 through the air-column, besides any electrical change in phase due 

 to change in current frequency. In Figs. 3, 4 and 6, the sloping 

 dotted lines are drawn to indicate constant acoustic phase retardation 

 of 270° for all of the frequencies within the range considered. 

 Taking, for instance, Fig. 6, the break at P occurred 103° in phase 

 from the dotted line of 270°, and the return at 6^ occurred 'jy° in 

 phase from the dotted line. According to the theory, assuming no 

 electric change of phase, each of these angles should be something 

 less than 90°, since the phase retardation must be something more 

 than 180° on the side of increasing pitch. The discrepancy here is 

 not serious; for the mean of the two angles is 90°. At T and W, 

 however, the corresponding angles are 153° and 119°, with a mean 

 of 136°, which should be something less than 90°, a greater diver- 

 gence from the theory than observation errors can explain. While, 

 therefore, the theory accounts for all of the experimental results in 

 a general way, it can only be regarded as a first approximation. For 

 example, it is possible that superposed harmonic currents might have 

 to be considered ; or that in estimating the damping forces, the in- 

 clusion of higher powers of the velocity than the first might be 

 necessary. 



Setting aside unexplained deviations, as the tube-length is short- 

 ened from a point of 6 = 2yo°, the phase retardation of the electro- 

 magnetic reinforcement on the receiver diaphragm is diminished. 

 This causes the pitch to rise, and incidentally readjusts the phase 

 change to a lower value than if the pitch were kept steady. The 

 amplitude of vibration diminishes until the diaphragm suddenly 

 selects a lower pitch for the same tube-length, to which the ampli- 

 tude will be greater. In other words, the receiver diaphragm auto- 

 matically seeks to maintain the greatest amplitude that the condi- 



