physics. 585 



must be very small. The first experiments were made with coal gas. A 

 whistle whose bore was 0.04 inch in diameter was attached to a gas-jet by 

 a rubber tube, and the piston adjusted. When its length was 0.13 inch 

 no sound could be perceived. On suddenly squeezing the tube filled with 

 air at 0.14, a faint musical note could be heard, which became purely 

 musical at 0.25 inch. When the gas was allowed to fill the tube, and 

 it was again squeezed, it gave the same barely perceptible sound as 

 with air at 0.14. By the use of hydrogen this little whistle would give 

 at 0.14 about 83,000 vibrations per second. (Nature, March, 1883, 

 xxvn, 491.) 



Pauchon has experimented to determine whether the upper limit of 

 the perceptibility of sounds varies for the same ear with the intensity 

 of the sound. A powerful Caignard-Latour siren, driven by steam, 

 was used to produce the sound. He finds that when the pressure varies 

 from 0.5 to 1.5 atmospheres the limit of perceptibility varies from 48.000 

 to 60,000 simple vibrations. With a pressure of 2.5 atmospheres the 

 disk rotates 600 times a second, giving 72,000 vibrations, the maximum 

 limit reached. These experiments were repeated, using metal rods 

 made to vibrate longitudinally by friction with a resined cloth ; but the 

 minute variations of length could not be measured with sufficient accu- 

 racy. When the sound ceases to the ear it still acts on a sensitive flame. 

 [C. P.. April, 1883, xcvi, 1041 ; Phil. Mag., May, 1883, V, xv, 371.) 



Krebs has studied the laws of the reciprocal excitation of elastic 

 bodies tuned to nearly the same pitch. When the pitch of two forks 

 or of two wires is exactly the same, one of these, as is well known, can 

 excite the other. The author finds that if the pitch is not exactly the 

 same in the two cases, the one having the lower tone can excite the 

 other, but not the reverse, provided the difference is at least two or three 

 vibrations, at most three or four. This result is well shown on a sonom- 

 eter. In the case of tuning-forks the deeper-toned one can excite the 

 other only if the difference in the number of vibrations does not exceed 

 one. The experiment, however, is easily repeated. ( Wied. Ann., xix, 

 935 ; Phil. Mag., October, 1883, V, xvi, 318.) 



Clarke has replied to the assertion of Chappell that those who propose 

 to divide the octave into twelve equal semitones instead of equally 

 tempered semitones, are deficient in musical ear, by showing that the 

 term equally tempered semitone is inaccurate, since no one of the equal 

 semitones on a piano thus tuned can be altered without making them 

 unequal ; that the moving of the note E ever so little from the value 2& 

 introduces a greater error somewhere else; that unequal tempering is 

 in use because all keys are not used equally often, the keys C, G, A, 

 aud F being fair, E, B flat, E flat tolerable, and the others very much 

 worse than on an equal semitone piano. He concludes that the best 

 plan of tuning a piano for vulgar music and vulgar players is that now 

 in ordinary use by timers and recommended by Chappell, but if the 

 piano is to be used equally in all keys (or even frequently in four or 



