THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 

 AUGUST 1887. 



XVII. On the Maintenance of Vibrations by Forces of Double 

 Frequency, and on the Propagation of Waves through a 

 Medium endowed with a Periodic Structure. By Lord 

 Rayleigh, Sec. R. S., Professor of Natural Philosophy in 

 the Royal Institution*. 



THE nature of the question to be first considered may be 

 best explained by a paragraph from a former paper f , 

 in which the subject was briefly treated. " There is also 

 another kind of maintained vibration which, from one point of 

 view, may be regarded as forced, inasmuch as the period is 

 imposed from without, but which differs from the kind just 

 referred to (ordinary forced vibrations) in that the imposed 

 periodic variations do not tend directly to displace the body 

 from its configuration of equilibrium. Probably the best- 

 known example of this kind of action is that form of Melde's 

 experiment in which a fine string is maintained in transverse 

 vibration by connecting one of its extremities with the vibra- 

 ting prong of a massive tuning-fork, the direction of motion of 

 the point of ' attachment being parallel to the length of the string^. 

 The effect of the motion is to render the tension of the string- 

 periodically variable ; and at first sight there is nothing to 

 cause the string to depart from its equilibrium condition of 

 straightness. It is known, however, that under these circum- 

 stances the equilibrium position may become unstable, and 

 that the string may settle down into a state of permanent and 



* Communicated by the Author. 



t " On Maintained Vibrations." Phil. Mag. April 1883, p. 229. 

 | " When the direction of motion is transverse, the case falls under the 

 head of ordinary forced vibrations." 



Phil. Mag. S. 5. Vol. 24. No. 147. August 1887. L 



