456 Prof. Barton and Mr. Ebblewhite on 



function of fa and fa, see (17), a solution, correct to tbe 

 third order of small quantities, is readily developed ; it is 

 hardly necessary to give the details. 



In 'Theory of Sound ' (loc. cit.) I remarked upon the 

 failure of the simple theory to deal with the apparently 

 simple problem of the vibrations in one dimension of a 

 column of gas, obeying Boyle's law, and contained in a 

 cylindrical tube with stopped ends. So far as I am able to 

 see, the present extension does not help the matter. In this 

 case there are an infinite number of coincidences between 

 natural frequencies of infinitesimal vibration and harmonics 

 of the fundamental vibration. From what we know of the 

 behaviour of progressive waves of finite amplitude, it is 

 perhaps not surprising if no solutions exist of tbe character 

 contemplated. Probably after the lapse of a finite time 

 discontinuity will ensue. 



Terling Place, Witham, Aug. 8. 



XLY. Vibration Curves of Violin Bridge and Strings. By 

 Edwin H. Barton, D.Sc, F.R.S.E., Professor of Experi- 

 mental Physics, and Thos. F. Ebblewhite, B.Sc, Heymann 



Exhibitioner, University College, Nottingham *. 



[Plates VII.-IX.J 



FOLLOWING the work of one of us and others f, the 

 present paper deals with the simultaneous motions 

 of a violin bridge and the strings. The violin being mounted 

 horizontally in the usual position of playing, the vertical 

 motions of each upper corner of the bridge are recorded, 

 also the motions of the same corners lengthwise of the 

 strings. Each string is dealt with separately and its 

 vibration simultaneously with that of the bridge recorded 

 photographically. Further, the strings were excited at 

 various places by bowing, plucking, striking, &c, seventy- 

 two photographic records being now presented. 



Comparing this work with that on the violin belly (August 

 1909), the following points may be noted here : — 



1. The vibrations of the bridge show more variety of form 

 than those of the belly. 



* Communicated by the Authors. 



t Phil. Mag. July 1905, pp. 149-157; Dec. 1906, pp. 576-578; 

 April 1907, pp. 446-452 ; Aug. 1909, pp. 233-240. 



