234 Lord Kayleigh on Maintained Vibrations. 



while if e be negative, 



pS=n 2 +j\u 2 - K y\. 



If a be very much greater than fcp, e= + 577-, which indicates 

 that when the system passes through its position of equili- 

 brium the spring is at its maximum or at its minimum. 



The inference from the equations that the adjustment of 

 pitch must be absolutely rigorous for steady vibration will be 

 subject to some modification in practice ; otherwise the expe- 

 riment could not succeed. In most cases n 2 is to a certain 

 extent a function of amplitude; so that if n? have very nearly 

 the required value, complete coincidence is attainable, without 

 other alteration in the conditions of the system, by the assump- 

 tion of an amplitude of large and determinate amount. 



When a particular solution of (5) has been found, it may be 

 generalized by a known method. Thus, if d = A6 l7 we have as 

 the complete solution 



0=A0 1 + BoS t $- 2 e- Kt dt- 



which may be put into the form 



e^ve-veS e~\-^dt. . . . (12) 



When t is great, the second term diminishes rapidly, and the 

 solution tends to assume the original form = TO lm 



The number of cases falling under the present head which 

 have been discovered and examined hitherto is not great. 

 The mysterious son rauque of Savart, which sometimes accom- 

 panies the longitudinal vibrations of bars, and is attributed by 

 Terquem to an associated transverse vibration, is doubtless of 

 this character. Just as in Melde's experiment already spoken 

 of, the periodic variations of tension accompanying the longi- 

 tudinal vibrations will throw the bar into lateral vibration, if 

 there happen to be a mode of such vibration whose pitch is 

 nearly enough coincident with the suboctave of the principal 

 note. 



For a lecture illustration we may take a pendulum formed 

 of a bar of soft iron and vibrating on knife-edges. Under- 

 neath the pendulum is placed symmetrically a vertical bar 

 electromagnet, through which is caused to pass an electric 

 current rendered intermittent by an interrupter whose fre- 

 quency is twice that of the pendulum. The magnetic force 

 does not tend to displace the pendulum from its equilibrium 

 position, but produces the same sort of effect as if gravity 

 were subject to a periodic variation. 



