VIBRATING TELEPHONE DIAPHRAGMS. 441 



P^^S^. The decay of amplitude is so slow, that these conditions re- 

 peat themselves very closely for several oscillations above and below 

 the standard amplitude of K^ ; so that the observations can be re- 

 peated at several successive oscillations for an average. 



The oscillation frequency of Kq is then increased in small suc- 

 cessive steps, by shortening up the suspension L^,, and the above men- 

 tioned observations are repeated at each step. The amphtude of 

 oscillation of /v^ increases rapidly as resonance is approached. In 

 the model used, the resonant sharpness A is 252, but this can be 

 controlled at will, by applying any motional resistance to Kj^ which 

 is substantially proportional to the velocity. Fig. 18 gives the an- 

 gular-amplitude and angular-velocity circles for the model. It is 

 seen that the semicircular range of resonant frequency, as computed 

 from the circle diagram, is between 0.3692 ^ at o)^ and 0.3707 -—^ 

 at ojo. For impressed frequencies below this range, the oscillation 

 of i^i comes nearly into cophase with /Vy. On the other hand, at 

 impressed frequencies above this range, the amplitude of K^ comes 

 nearly into opposite phase with K(,. At resonance, the oscillation of 

 /v\ is in quadrature with the amplitude of iv ; or the angular veloc- 

 ity of iv'i will be in cophase OA with the vector torsional force or 

 vibromotive force (V.M.F.) exerted by the wire on /v^. This 

 V.M.F. is proportional to the angular displacement between the ends 

 of Lj, and the observations obtained must be corrected to constant 

 maximum cyclic V.M.F. 



A student working with the model in the above described man- 

 ner, can acquire a concrete conception of a motional-velocity circle, 

 based upon direct observations of oscillations executed so leisurely 

 that they are easily observed directly by the eye, without the use of 

 reflecting mirrors or of electrical apparatus. Moreover the oscil- 

 lations are sufficiently large to be perceived directly by a large class. 

 When A'^ oscillates in air, the motional resistance r seems to increase 

 somewhat with the amplitude. When K^ was allowed to oscillate 

 in water, the motional resistance was found to be more nearly 

 constant. 



When it is desired to study the phenomena of absorption, a sec- 

 ondary torsion pendulum LJ-Cn is attached to K^. It is then con- 

 venient to adjust the natural frequency of the secondary pendulum 



