1880.] 



Notes of Observations on Musical Beats. 



523 



given temperature is known, and both forks may be assumed to be 

 altered in the same ratio by heat, then the temperature need not be 

 observed ; but the unknown fork may be presumed to be as many 

 vibrations sharper (or natter) than the measured fork at the tempera- 

 ture at which the latter was measured, as beats in a second, were 

 observed to take place. This is because the alteration is very small, 

 and would be quite inappreciable for the few vibrations between them. 

 But for tonometrical purposes an allowance must be made. 



The coefficient of temperature has not been satisfactorily determined. 

 It varies from '00004 to '00006 for each vibration and each degree 

 Fahrenheit. Possibly the mean '00005 is the best number to take, 

 but I have used 1-^21000 = '0000476. The flattening seems to be 

 chiefly due " to the effect of temperature on elasticity. A large fork 

 of about 435*44 vibrations at 59° F., grew sharper and beat more and 

 more brightly as the temperature descended to 10° or 15° F., being 

 easily counted for 20 seconds and more. At 104° F. it could scarcely 

 be counted for 20 seconds, at 112° F. scarcely for 10 seconds, and at 

 164° F. I could not count it at all, the sound not lasting- more than 

 2 or 3 seconds, and the beats varying during that time. The effect 

 also seems to vary with the metal and make of the fork and its size, 

 and the coefficient to be greater for high than for low temperatures. 

 For a fork of about 256 vibrations at 59° F., the coefficient from 14° 

 to 59° F. was about '0000305 or 1-^32,760, but from 59° F. to 175° F. 

 about '0000548 or 1-4-18,280. These experiments, which I made by 

 dipping the forks in freezing mixtures and hot water, and beating them 

 with a fork at mean temperature, are unsatisfactory. In the same 

 way M. Aristide Cavaille-Coll, the well-known organ-builder of Paris 

 (private letter), experimenting on two forks of about 435 vibrations, 

 one of Scheibler's and one a large-sized diapason normal, found — 



Coeff. for 1° F. and 1 rib. 

 1st fork, from 59° F. to 194° F. . . '0000567 = 1-4-17,650 

 2nd „ „ 60°-8F. to 194° F. .. '0000589 = 1-4-16,970 



Scheibler (" Tonmesser," p. 50) himself found for a rise of 45° F. — 



Coeff. for 1° F. and 1 yib. 

 1st fork, about 440 vibrations . . '00006=1-4-16,670 

 2nd ,, „ 220 „ .. -00005 = 1-4-20,000 



Kayser, for two large forks, furnished with mirrors, &c. (" Wied. 

 Ann.," 1879, p. 444) — 



Coeff. for 1° F. and 1 vib. 

 1st fork, about 72 vibrations . . '0000494=1-4-20,250 

 2nd „ „ 85 „ .. -0000566 = 1-4-18,000 



Koenig's recent careful experiments (" Wied. Ann.," 1880, p. 413), 

 not made by freezing mixtures and hot water, give two different co- 



