994 



SCIENCE. 



[N. S, Vol. XIV. No. 365. 



4. One large resonator of diameter 0.48 

 m. and of length varying from 0.30 m. to 

 2.30 m. 



5. 18 forks for notes from C, to Fg. 



6. 15 forks for notes from Sol^ to 180,000 

 V. s. 



Under the head of pitch come two very 

 difficult questions relating to the audibility 

 of very low or very high sounds. With re- 

 gard to the former Helmholtz has shown 

 that if the vibrations are very slow and do 

 not follow the pendular law (the funda- 

 mental being thus accompanied by a series 

 of harmonics), the fundamental may be 

 quite inaudible, whilst the harmonic is 

 heard distinctly. In such a case the har- 

 monic is often mistaken for the funda- 

 mental. On the other hand, if we employ 

 large tuning forks, vibrating rods, or the 

 wave siren, for the purpose of obtaining 

 pendular vibrations, we are still met with 

 the difficulty of determining accurately the 

 limits of audibility, owing to the fact that 

 it not only depends on the intensity of the 

 vibrations, but varies from one observer to 

 another. In general it may be stated that 

 it requires from 60 to 80 v. s. to produce a 

 sound perfectly continuous and possessing 

 a musical character. In usiog very power- 

 ful high forks to produce beats, which were 

 gradually diminished in number, Koenig 

 found that the sensation of a continuous low 

 sound ceased when their number did not 

 exceed 26. 



As to the high notes above C, = 8,192, the 

 amplitudes of the vibrations are generally 

 so small that the ordinary methods no 

 longer serve to determine the pitch. For 

 this reason it was at first the practice to 

 tune forks above C- by means of the ear. 

 The high forks constructed by Marloye and 

 presented to the Academy of Sciences at 

 Paris, in 1848, by Depretz, were constructed 

 in this way. In 1858, however, Koenig 

 showed that even in the upper half of the 

 octave Cg — C,, the best musicians ceased 



to judge the intervals accurately, a fact 

 which seemed to show that it was ex- 

 tremely unlikely that forks giving notes two 

 octaves higher could be tuned accurately by 

 the ear. For this reason Koenig effected 

 the tuning of very high forks by means of 

 the sounds resulting from their beats. The 

 first series of forks tuned in this way were 

 made by Koenig in 1876. A set of similar 

 forks constructed about the same time by 

 Preyer, and going, as he alleged, as high as 

 EjQ were shown by Melde, in 1894, to be 

 greatly out of tune, the intervals being 

 wrong by as much as a third, and even an 

 octave. In 1897, Melde's results were con- 

 firmed by Stumpf and Meyer. 



In 1899 Koenig published his researches 

 on very high notes. In this memoir, after 

 showing the exactness of the tuning at- 

 tained by the sounds of beats in forks be- 

 tween Cj and Fg, he proceeds to state that, 

 by means of Kundt's method of using light 

 powders, he had constructed a series of 

 high forks accurately tuned and proceed- 

 ing according to the intervals of the perfect 

 (major) scale, from C„ to the enormous 

 pitch of 180,000 V. s., and that without 

 reaching a limit to the number of such 

 vibrations. 



As to the audibility of these high forks, 

 it has been remarked by Koenig that those 

 between C, and Cj are generally audible, 

 whilst C,o and those above are entirely in- 

 audible. He further remarks that the 

 limit of audibility, which thus lies between 

 Cj and Cjo, largely depends, as in the case 

 of low sounds, on the intensity, and varies 

 with the individual. 



INTENSITY. 



With regard to the question of intensity 

 of sound, it is only necessary to say that 

 there exists here a great lacuna in our 

 acoustical knowledge, as we do not yet pos- 

 sess a means of measuring the physiolog- 

 ical intensity of sound. 



