444 KENNELLY, TAYLOR— PROPERTIES OF 



components, especially in the elastic constant ^. 

 From 3, we have 



1^ / 



jco I r + j ( WO) - - j I 



radians Z (4) 



The instantaneous E.M.F. overcoming the counter E.M.F. of vibra- 

 tion is 



Af AH 

 e^ = Ae = — = — = JZ, abvolts Z , (5) 



z z 



where Z is the motional-impedance of the instrument. 

 Hence, at resonance, 



A6m = ImZm, abvolts, (6) 



and 



_ ImZm _ ImZm dyne perp. cm. 

 Bm <^oGm ' absampere 



where /,« is the maximum cyclic value of the current in absamperes, 

 Zm is the maximum motional-impedance — which is reactanceless, or 

 a simple resistance — and 6m the observed maximum cyclic resonant 

 angular displacement, in radians. The resonant impressed angular 

 velocity at which this occurs is denoted by wq radians per second. 

 Atoj = ojo (4) becomes 



Aim 



coor 

 whence 



radians, (8) 



Aim dyne perp. cm. 



dmO^o ' radian per second 



From the motional-impedance circle of the instrument, as plotted 

 from observations of impedance at dififerent impressed frequencies, 

 the decrement per second A, or the hyperbolic angular velocity of 

 decay in amplitude, may be obtained, by taking half the difference 

 between impressed angular velocities cu^, w, at the quadrantal points 

 in the circle ; or 



f 0)2 — '•'i 

 A = — = = 7r(«2 — Wi), hyps, per sec, (10) 



