May 15, 1919] 



NATURE 



20: 



THEORY OF BOWED INSTRUMENTS.' 



DIFFICULT as the violin may be to play, there 

 are many who play to one who experiments 

 ujX)n it scientifically ; and, scarce as the experi- 

 mentalrst may be, the successful theorist is yet 

 scarcer. But we have now before us the first part 

 of an elaborate investig-ation in which mathe- 

 matical theory and confirmatory experiments hap- 

 pily alternate. Important and interesting results 

 have already been reached, and others equallv so 

 are likely to follow, thus clearing up a number 

 of points which have hitherto been obscure. 



Helmholtz was able to show, by his vibration 



D-Stn„ 



w,iK load of I : 



ftrainnir* (ixr<l 



Fir.. I. — Simultaneous vibration-curves illustrating effect of loading the j 

 violin bridge on its horizontal motion transverse to the strings (observed j 

 at the G-string corner). 



microscope, that the bowed point of a violin string 

 might execute a motion the graph of which is a | 

 two-step zigf-zag^. He also surmised that the for- 

 ward speed of the bowed place of the string 

 equalled that of the bow when a good tone was | 

 obtained. From this experimental two-step zig- j 

 zag Helmholtz proceeded to his theory of the well- 

 bowed string". 



F. Krigar-Menzel and A. Raps photographed 



' "On the Mechanical Thooryof the Vibrations of Bowed Strings «nd of | 

 Mmsical Instruments of the Violin Family, with Experimental Verification 

 of the Results." Parti. By C. V. Raman. (Bulletin No. 15.) Pp. iii + 

 158.. (Calcutta: The Indian Association for the Cultivation of Science, 

 1918.) Price 3J. ^li. 



(upon a film on a revolving drum) various points 

 of bowed strings, and so obtained much informa- 

 tion on the subject of the vibrations possible to 

 the strings themselves. 



Prof. E. H. Barton and his students took simul- 

 taneous photographs of the behaviour of the. 

 strings arid of the bridge, belly, or air of a mono- 

 chord and of a violin. But in none of the fore- 

 going cases was a direct mechanical theory of the: 

 string, bridge, etc., attempted. This has now 

 been accomplished by Prof. C. X. Raman. 



The equations of motion of the string are 

 written and solved for the case of a periodic trans- 

 verse force applied by the bow at a given position. 

 The equations of motion of the bridge are next 

 written and dealt with. Then follow photographs 

 of simultaneous vibration-curves of belly and G- 

 string of a violoncello at the "wolf-note " pitch, 

 showing cyclical changes of amplitude. The 

 modus operandi of the bow is next examined, and 

 a simplified kinematical theory of the bowed 

 string based upon it. This leads to a number, 

 of types of vibration: two-step, three-step, etc, 

 zig-zag motions appearing in the corresponding 

 graphs. 



Another very interesting subject is that of the 

 effect of the mute, which, by loading the bridge, 

 enfeebles and veils the tone of the instrument. 

 To investigate this effect, loads were placed in 

 different positions on the bridge of a violin, andi 

 simultaneous vibration-curves of string and : 

 bridge taken. The results for the G-string and 

 D-string are here reproduced (Fig. i), the dark 

 zig-zag line on light ground giving the displace- 

 ment-time graph of the string, the light wavy line 

 on black ground being the graph of the bridge's 

 horizontal motion transverse to the string. 

 Similar results were obtained for the other two- 

 strings. 



Other points dealt with in the present instal- 

 ment of the investigation are the effects of the 

 variation of pressure and velocity of bowing, the 

 relation between pressure and speed, and the. 

 vibrations obtained from a 'cello when played 

 pizzicato. 



The paper contains twenty-eight text figures 

 and twenty-six full-page photographic reproduc-- 

 tions, many of them of distinct beauty and in- 

 structiveness. All these should be consulted in 

 the original by those interested. Indeed, the 

 entire work well deserves careful study, present- 

 ing, as it does, a valuable contribution on the; 

 subject of bowed instruments. 



STATISTICS OF SYNTHETIC DYES. 



IT was pointed out, in an article in Nature for 

 November 21, 1918, that one of the first 

 things which ought to be done in efforts to re- 

 suscitate the dye industry in Great Britain is to 

 survey the whole field of dyes and intermediate 

 compounds, so as to determine the source of 

 supply, to ascertain more precisely the needs of 

 the community, both for home purposes and for 

 export trade, to concentrate attention on the 



NO. 2585, VOL. 103] 



