130 KENNELLY-TAYLOR— EXPLORATIONS OVER [April 22. 



lagging 90° behind OP. As the frequency varies between 923 and 

 1,074---', the displacement amplitude almost covers the entire graph 

 of the approximate circle OM'P' , commencing at about i //,, nearly 

 in phase with the vibro-motive force, and ending at about i /* in 

 nearly opposite phase. These amplitudes correspond to the ordi- 

 nates of the resonance curve in Fig. 9. 



It follows from (4) that if the vibro-motive force / is kept 

 constant, and the angular velocity adjusted until the central vibra- 

 tion velocity is a maximum, this will occur when the mechanical 

 reactance is zero, or when 



5 dynes . . 



mwQ - — = o 'I • , (7) 



coo cm. /sec. ^ 



that is 



Is radians , ^ 



coo = V- • (8) 



^w sec. • 



So that 



dynes 



5 = mw(f . (9) 



cm. ^ 



When the vibro-motive force / is made to vanish in (3) with the 

 diaphragm in motion, the solution of the equation is 



w = We ^"^ sin (cot -f- e) cm., (10) 



where W is the initial displacement (cm), and e a suitable phase 

 (radians). If we obtain two successive values of iv, (w^^ and z^o), 

 corresponding to two successive elongations in the same direction, 

 we have 



Wi 



= e'/2m« = gA/« numeric, (ii) 



Wo 



whence 



■■2mn\og€ (zv^/zu^), dynes/ (cm./sec), (12) 



where A is the damping constant (i/sec). 



The quantity loge (zt'i/Ws) is well known as the logarithmic 

 decrement of the decay curve. 



