[ 212 ] 



XXVII. On the Transformation of the Vibroscope into a Tono- 

 meter, and its employment for the Determination of the Absolute 

 Number of Vibrations. By A. Terqtjem*. 



BY the optical study of vibrations and the construction of the 

 vibroscope, M. Lissajous has endowed acoustics with means 

 of investigation much more accurate than those based upon 

 hearing only; nevertheless this optical method does not appear 

 hitherto to have been conveniently applied to the determination 

 of the absolute number of vibrations. I have thought that it 

 could be utilized for this purpose, and that a tonometer might 

 be more easily constructed with its aid than by the operation 

 devised by Scheibler. The new tonometer, at least as accurate, 

 would be much less [costly ; and it could be employed to give, 

 by simple reading, the number of vibrations of any sonorous 

 body whatever, and that through a very great extent of the 

 musical scale. 



I have had made by M. Konig four diapasons furnished with 

 cursors, and each carrying at the extremity of one of its branches, 

 like the diapason of the vibroscope, a small biconvex lens to 

 serve as an objective. These diapasons can be successively fixed 

 upon the same support, on which an ocular is placed. By shift- 

 ing the cursors, we can obtain all the sounds comprised between 

 ut 2 (128 double vibrations) anduT 3 ; moreover some sounds are 

 common to two diapasons which immediately follow one another. 

 The diapasons were divided by M. Konig after his tonometer, 

 in such sort that, by shifting the cursors the space which sepa- 

 rates two strokes, the sound is changed two double vibrations ; 

 but I consider this only a completely arbitrary division which 

 might be replaced by any other made by means of a dividing 

 machine. I shall give to these diapasons the name of standards. 



I have, besides, other diapasons, not graduated, but likewise 

 furnished with cursors and extending from ut 2 to ut 3 . Two are 

 sufficient, because spare cursors can be adapted to them. I 

 shall give to these the name of auxiliary diapasons. 



The first standard diapason and the first auxiliary are fixed 

 the one in front of the other, on suitable supports, in one and 

 the same horizontal plane, and at a right angle ; moreover the 

 vibrations of the standard diapason (which serves as a vibro- 

 scope) being made as usual, in a vertical plane, those of the 

 auxiliary take place in a horizontal plane. 



That the curves resulting from the coexistence of the two 

 vibratory movements at a right angle might be readily perceived, 

 particles of finely powered antimony have been fixed with gum 



* Translated from a separate impression, communicated by the Author, 

 from the Comptes Rendus de VAcademie des Sciences, January 12, 1874. 



