450 KENNELLY, TAYLOR— PROPERTIES OF 



angles on opposite sides of the resonant diameter, have the resonant 

 frequency as their geometric mean. The acoustic criterion c is, 

 however, in general, less satisfactory than the resonant sharpness 

 \ ; because the greater the resonant sharpness the greater becomes 

 ^ but the smaller becomes c. 



From an examination of Fig. 19, it is evident that, at resonance, 

 the phase of the deflection or angular displacement of the mirror is 

 just 90° behind the phase of the angular velocity, and of the current 

 in the instrument. If OR represents the current phase; then, at 

 resonance, Or is the phase of the mirror's maximum elongation. At 

 impressed frequencies below 980^ — \ the phase of displacement in 

 the deflection graph is almost exactly coincident with that of the 

 current. On the other hand, at impressed frequencies above 

 1,020'—', the phase of displacement is almost exactly opposite to, or 

 180° removed from, that of the current. 



An attempt was made to ascertain how the constants A, m, r and 

 .y of the Duddell instrument varied with difl:"erent tuning and lengths 

 of free suspension. It was found, however, that owing to some 

 friction in the suspension pulley, the tension of the two wires did not 

 equalize sufficiently to prevent the appearance of partial unifilar 

 characteristics, which vitiated the results. Such departures from 

 pure bifilarity would not, however, aflfect the above mentioned phase 

 relations between displacement and current. 



A similar set of measurements may be applied to an oscillograph. 

 The normal alternating-current strength required to operate the 

 oscillograph may, however, be greater than can conveniently be sup- 

 plied through a Rayleigh bridge, as used for testing telephones or 

 vibration galvanometers. In that case, a convenient technique is to 

 supply a measured R.M.S. current from a Vreeland oscillator to 

 the oscillograph vibrator, and observe the amplitude of the mirror's 

 deflection thereby produced, on each side of the zero, reducing the 

 same to radian measure from the geometry of the optical system. 

 The angular velocity ojq radians per second, necessary for maximum 

 resonance, has to be carefully observed, and at the same time the 

 maximum resonant mirror deflection 6m radians. This gives equa- 

 tions (8) and (12). The freciuency is then gradually changed until 

 the deflection is reduced in the ratio i/\/2, the change being made 



