268 



CATALOGUE. — ACUS TICS, SOURCES OF SOUND. 



Eulcr on the equilibrium and motion of flex- 

 ible and elastic bodies. N. C. Petr. XV. 

 381.XX.28G. 



Euier on unequal vibrating chords. N. C. 

 Petr. XVII. 381. A. Petr. 1780. IV. ii. 

 99. 



EuIer finds, that a chSrd composed of two parts, of which 

 the length is reciprocally as the thickness, will sound like a 

 single one. A chord composed of two parts equal in length, 

 one four times as heavy as the other will produce sounds 

 related as .30)08 .69501, 1.30408, 1.60501,2.30408, and 

 will therefore be very discordant. 



Euler on the vibrations and revolutions of 

 extended musical chords. N. C. Petr. 

 XIX. 340. XX. 304. A.Petr. Ill.ii. 116. 

 1782. VI. ii. 148. 



Observes, that the revolutions may be reduced to com- 

 pound vibrations. 



Euler on the perturbation of the motion of a 

 chord from its weight. A. Petr. 1781.V. i. 

 178. 



When the chord is horizontal the perturbation vanishes. 



Dalembert on the curve of a vibrating chord. 



A. Berl. 1747.214, 220. 1750.355. 

 Dalembert's remarks on vibrating chords. A. 



Berl. 1763. 235. M. Taur. III. ii. 389. 

 Kiccati on elastic force. C. Bon. I. 523. 

 M.Young on sounds and musical strings. 

 J. Bernoulli on the problem of vibrating 



chords. Hind. Arch. III. 266. 

 Montucla and Lalande. III. 659. 

 Voigt on the nodes of chords. Ph. M. IV. 



347. 



Surfaces. 



Euler on the vibrations of drums. N. C. Petr. 



X. 243. 

 Riccati on the vibrations of drums. Ac. Pad. 



1.419. 

 Biot on the vibrations of surfaces. M. Inst. 



IV. 21. 



Extr. B. Soc. Phil. n. 43. 

 Says, that the time of vibration depends on the initial fi- 



gure. This doe« not however appear to agree with expe- 

 riment. 



Vibrations from Elasticity. 



Lateral Vibrations. 

 Birch. II. 475. 



Hooke explained the vibrations of a glass bell by putting 

 fiouron it, which moved differently, according to the differ- 

 ence of the sounds. 



Blondel on the sound of a glass full of wa- 

 ter. A. P. I. 209. 



Carre on the sounds of cj'linders. A. P. 1709. 

 47. H. 93. 



-j-Lahire on the extinction of sounds at the 

 ends of a cylinder. A. P. 1709. H. 96 



Bernoulli on the curvature of an elastic rod. 

 C. Petr. III. 62. 



Bernoulli on the vibrations of plates. C.Petr. 

 XIII. 105, 167. 



The sounds are related as 1, 6.32. 17.63, 34.54, 57. 1, 

 86.3. The length of a pendulum vibrating with equal fre- 

 quency is to the linear deflection by a given weight at the 

 end of a rod fixed at the extremity, as 12 times the weight 

 of the rod to 49 times the deflecting weight ; thus a knitting 

 needle weighing 15.5 grains was deflected by a weight of 

 1000 grains -^^L. of the length of the second pendulum : 

 hence the length of the synchronous pendulum is .1025, 

 and it makes 175 or 178 vibrations in a second, the note 

 being G, as it was found. The length was -j^'i ; half the 

 length gave the double octave, the time of vibration be- 

 ing always as the square of the length. At the standard 

 concert pitch the note would be nearly F. 

 Bernoulli. N. C. Petr. XV. 361. 

 Euler on the vibrations of rigid bodies. C. 



Petr. VH. 99. 

 Euler on bells. N. C. Petr. X. 26. 



Makes the sounds as l , ^/o, v'20, \/50; considering 

 the bell as composed of rjpgs. 



Euler on the vibrations of plates. N. C. Petr. 

 XVII. 449. ' 



The progression of sounds as 1.192, 6.9977» I9.638a. 



Euler on the vibrations of plates. A. Petr. 

 III. i. 103. 



The sounds of rings are as the squares of the natural 

 numbers. 



