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XXII. Researches in Acoustics, — No. X. 

 By Alfred M. Mayer*. 



[Contents. — The Variation of the Modulus of Elasticity with Change 

 of Temperature, as determined by the Transverse Vibration of Bars at 

 Various Temperatures. The Acoustical Properties of Aluminium.] 



Summary of the Research, 



POISSON, in his Traite de Mecanique (Paris, 1833, t. ii. 

 pp. 368-392) t discusses the laws of the transverse 

 vibrations of a bar free at its ends and supported under its two 

 nodes. He shows that the frequency of the vibrations of the 

 bar is given by an equation, which, reduced to its simplest ex- 

 pression, is N=Vx r0279jj; in which N is the number of 



vibrations per second of the bar, t its thickness, I its length, 

 and Y the velocity of sound in the direction of the length of 

 the bar. 



To ascertain how nearly the frequency of the transverse 

 vibrations of a bar, computed by Poisson's formula, agrees 

 with the result obtained by experiment, the following method 

 of experimenting was used, 



Rods of steel, aluminium, brass, glass, and of American 

 white-pine (Pinus Strobus) — substances differing greatly in 

 their moduli of elasticity, densities, and physical structures — 

 were carefully wrought so as to have the length of 1*5 + metre, 

 the thickness of 0*5 cm., the width of 2 cms., and a uniform 

 section throughout their lengths. The velocity of sound in 

 these rods was determined by vibrating them longitudinally 

 at a temperature of 20°, while held between the thumb and 

 forefinger, and their frequencies of vibration ascertained by 

 the standard forks of Dr. R. Koenig's tonometer. 



Out of each of these long rods were cut three bars of the 

 length of 20 cms., and these bars, also at 20°, were supported 

 on threads at their nodes, vibrated transversely by striking 

 them at their centre with a rubber hammer, and their 

 frequencies of vibration determined by the forks of the tono- 

 meter. 



The mean departure of the observed from the computed 

 numbers of transverse vibrations (see Table I.) is -g^-g ; the 

 computed frequency being always in excess of the observed, 



* From an advance proof from the American Journal of Science for 

 February 1896 communicated by the Author, having been read before 

 the British Association at Oxford, August 1894. 



t See also < The Theory of Sound/ by Lord Rayleigh, 1894, vol. i. 

 chap. 8. 



