82 A. M. Mayer — Researches in Acoustics. 



their frequencies of vibration ascertained by the standard forks 

 of Dr. R. Kcenig'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 center with a rubber hammer, and their frequencies of 

 vibration determined by the forks of the tonometer. 



The mean departure of the observed from the computed 

 numbers of transverse vibrations (see Table I) is ¥ -J-g- ; the 

 computed frequency being always in excess of the observed, 

 except in the case of glass, where the computed is -^\ T below the 

 observed frequency. 



In Table I, I — length and t = thickness of bar in centime- 

 ters at 20°. Y = velocity of sound in centimeters in bar at 

 20°. N = number of vibrations per second at 20°. 



The close agreement of the computed and observed values 

 shows that, by vibrating a bar at various temperatures, the varia- 

 tion of its modulus of elasticity with change in its temperature 

 can be obtained. We observe, N, at various temperatures of the 



N V 3 ^ 



bar; then V = — — — is computed, and the modulus M = — -. 



l-02'79— 9 



c 



As t, Z, and d (the density of the bar), vary with the tempera- 

 ture, the coefficient of expansion of each bar and its density at 

 4° were determined, so that the dimensions and density of the 

 bar could be computed for each of the temperatures at which 

 it was vibrated. 



Experiments were made on five bars of different steels, on 

 two of aluminum, on one of St. G-obain glass, one of brass, one 

 of bell-metal, one of zinc and one of silver. The results of 

 these experiments may be summed up as follows : 



The modulus of elasticity of St. Gobain glass is 1*16 per ct. less at 100° than at 0°. 



five steels 



" 2-24to3-09 



» 



brass 



" 3-73 



(< 



bell-metal 



4-3 



" 



aluminum 



5-5 



<( 



silver 



2-47 



" 60 



zinc 



41 6-04 



" 62 



The decrease of the modulus of elasticity of glass, aluminum 

 and brass is proportional to the increase of temperature ; 

 straight lines referred to coordinates giving the results of 

 experiments on these substances. The five steels, silver and 

 zinc give curves, convex upwards, showing that the modulus 

 decreases more rapidly than the increment of temperature; 

 while bell-metal alone gives a curve which is concave upwards ; 

 its modulus decreasing less than the increment of temperature. 

 (See fig. 5, p. 95.) 



