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XVI. Vibration Curves simultaneously obtained from a Mono- 

 chord Sound-Box and String. By E. H. Barton, JD.Sc, 

 F.R.S.E., and C. A. B. Garrett, B.Sc* 



[Plate I.] 



ri^HE vibrations o£ a bowed string have been treated both 

 -L experimentally and mathematically by Helmholtz. It 

 was thus shown that the displacement-time curve at any 

 point of a well-bowed string is a zigzag line, the up and down 

 slopes of which are both straight but in general at different 

 angles. Hence the Fourier components of the string's 

 motion have frequencies in the relation 1, 2, 3, 4, &c, and 



respective amplitudes 1, ^ , ^ , j- 2 , &c, each to infinity. 



Thus the main features of the motion of a well-bowed string- 

 are known. It is, however, a matter of common knowledge 

 that the sound received by the ear from a string does not 

 come chiefly from the string direct. Indeed, if a string is 

 mounted on very rigid and massive supports scarcely any 

 sound can be obtained from it, although the amplitude of its 

 vibrations may be considerable. Under the usual conditions 

 the string moves the bridges over which it is stretched, they 

 in turn move the belly, sides, and back of the sound-box, and 

 the air within the box pulsates in response. Probably, there- 

 fore, the chief part of the sound received by the ear comes 

 from the belly and other parts of the sound-box, as it has a 

 larger surface and is therefore better able to set the external 

 air in vibratory motion. 



Now the question naturally arises, are these vibrations of 

 the same quality as those executed by the string itself ? 

 That is, may they be compounded of the same Fourier terms ? 

 Probably not ; for the worth of a violin does not lie in the 

 strings but in the sound-box. 



It appears, therefore, to be a matter of some importance to 

 attempt to trace the changes in the character of the vibrations 

 which occur as we pass through the series string, bridges, 

 sound-box, air within the sound-box, air outside the sound- 

 box. As this, so far as we know, has not hitherto been done, 

 we attacked the problem, commencing with a monochord, 

 and hoping afterwards to pass on to a violin. 



Preliminary trials were made with a Nernst lamp, optical 

 levers, and a rotating mirror. These showed that the motions 

 of the bridge, belly, and air (in and out of the holes of the 

 sound-box) were all detectable. The corresponding vibration 



* Communicated by the Authors. 



