﻿Transverse Vibrations of a String. 931 



as well as the fact that if the displacement and Stefan- 

 Boltzmann laws are to be satisfied, the complete equation 

 must have the general form 



The only novelties in the above deduction, if there are any 

 at all, occur in sections 4 to 7 ; but it seems to me that greater 

 clearness has been attained without any real sacrifice of 

 rigour, and by only the most elementary means. 



Bureau of Standards, 



Washington, Feb. 28th, 1912. 



XOIL On Transverse Vibrations of a String Maintained, by 

 Forces of Double Frequency. By Joseph H. T, Roberts, 

 31. Sc, University of Liverpool *. 



THERE is a type of maintained vibration, which has the 

 peculiarities that the frequency of the imposed varia- 

 tions is twice that of the maintained variations, and that the 

 imposed periodic variations do not tend directly to displace 

 the body from its equilibrium configuration, The most 

 familiar example of such motion is that form of Melde's 

 experiment in which the prongs of the fork vibrate in the 

 direction of the length of the string ; the motion of the fork 

 causes the tension of the string to be periodically variable, 

 and there does not appear, at first sight, to be anything to 

 cause the string to depart from its equilibrium condition of 

 straightness ; as is well known, however, the equilibrium 

 may become unstable under these circumstances, and the 

 string may be maintained in permanent vibration whose 

 frequency is half that of the fork. 



Melde's experiment was one of the methods used by 

 students in this laboratory to determine the frequency of a 

 tuning-fork from the equation 



__1 fmg 



but it was found that there was a very considerable range of 

 tension for which a given string would vibrate with a given 

 fork. In this experiment the string was attached to the 

 upper extremity of the prong, and the fork was caused to 

 vibrate by bowing. It was thought that the discrepancy 

 might be due simply to the large motion of the point oi 



# Communicated by the Author, 



3 P 2 



