Decembee 27, 1901.] 



SCIENCE. 



993 



note does not preserve its timbre, being 

 resolved into simple components. 



Regnault's experiments have recently 

 been repeated by M. Violle in the large 

 sewers near Grenoble and Argenteuil, some 

 of Regnault's apparatus being employed 

 for the purpose. The results of these ex- 

 periments have not, however, been yet 

 published. 



PITCH. 



Before the last century, as already men- 

 tioned, Mersenne had attempted to deter- 

 mine the vibrations of a cord by deducing 

 them from very slow vibrations of the same 

 cord when lengthened. Cheadni's tonom- 

 eter, which consisted of a vibrating metal 

 rod of variable length, was based on the 

 same principle. In 1819 Cagniard de la 

 Tour invented the siren, a much superior 

 instrument, but incapable of giving very 

 exact results, notwithstanding the simplicity 

 of its mechanism. The same remark may 

 be made of the toothed wheel invented 

 by Savart in 1830. 



A most important step in advance was 

 made in 1834 by Henri Scheibler, of Crefeld, 

 who in that year invented his tonometer, 

 consisting of a series of 56 forks going 

 from A (440) to its octave (880), the vibra- 

 tions increasing regularly by differences of 

 eight, any two adjacent forks thus giving 

 four beats per second. Curiously enough, 

 although Scheibler went to Paris and ex- 

 hibited his tonometer there, he was unable 

 to interest savants in his discovery ; and 

 it was not until the London exhibition of 

 1862 that the attention of physicists and 

 musicians was directed to the value of the 

 instrument by Koenig. The apparatus in 

 its new form contained 65 forks going from 

 C3 (512) toC, (1024). 



Notwithstanding the great utility of this 

 tonometer to the acoustician, it still left 

 undetermined the absolute pitch of the fun- 

 damental note, and hence of the whole 

 series. This problem of realizing a stand- 



ard of pitch remained practically unsolved, 

 even after the French Government in 1859 

 decreed that the standard should be A = 870 

 V. 8., at 15° C. The standard then con- 

 structed by Lissajous^was found, in 1880, 

 to be too high by -^-^ of a vibration. The 

 standard employed since 1880 by Koenig 

 is C = 512 V. s. at 20°. The acoustical 

 standard before that date was in reality 

 512.35 at 20°. The problem of realizing a 

 standard fork, which had given rise to much 

 controversy among physicists, was finally 

 solved in 1880 by Koenig, who in that year 

 published his paper ' Recherches sur les vi- 

 brations d'un diapason normal.' In this 

 paper Koenig describes how by means of a 

 clock-fork (horloge a diapason compara- 

 teur) he established a standard fork, the 

 error of which did not exceed ^o'li^ of a 

 vibration. The clock- fork method enables 

 us at the same time to determine readily 

 the variations in the number of vibrations 

 due to a rise or fall of temperature. Hav- 

 ing established in this way an absolute 

 standard of C3 =„512 v. s. at 20° C, Koenig 

 commenced the construction of a universal 

 tonometer based thereon, a colossal under- 

 taking which he finished in 1897, after 

 working a score of years. This tonometer, 

 which has a range from 32 to 180,000 v. s., 

 consists of the following : 



1. 4 forks giving vibrations from 32 to 

 128, with diflerences at first of ^ v. s. and 

 afterwards of 1 v. s. 



2. 132 large forks, tuned to give (with- 

 out the sliders) the 127 harmonics of Cj, 

 C^, C3, C„ C5, Cg, being in duplicate. 



Each fork can be lowered, by means of 

 sliders, to unison with the fork next be- 

 low. 



The differences immediately obtainable 

 by sliders are : 



1 V. d. between C, and C3 ; 2 v. d. between 

 C3 and C5 ; 4 v. d. between C5 and C^. 



3. 40 resonators to reinforce forks 

 of 2. 



