[lang] 



HIGH FREQUENCY VIBRATIONS, ETC. 



169 



w 



1 



1- 



Te'' M 



J Kl 



where AP denotes the dynamical and Af the static value of Young's 

 modulus, 7" the absolute temperature,'/ Joule's equivalent, e the 

 strain produced by an elevation of temperature by 1° while the 

 body is under constant stress, K the specific heat under constant 



stress, and p the density. The value of the ratio — for iron on this 



basis works out as 1.0026. 



Wertheim^ as long ago as 1848, by the methods then prevailing 

 measured the static and dynamic moduli of metal wires, the former 

 by the method of direct elongation, and the latter by transverse 

 and longitudinal vibrations. Examples of his results are the following: 



Copper wire — drawn — Young's modulus, by 



'direct elongation, 1.245 x 10' gms. 



sq. cm. 

 trans, vibration, 1.251 gms. sq. cm. 

 Jongit. M 1.254 gms. sq. cm. 



Copper wire — annealed 



Silver — drawn 



Steel — drawn 



II 



f Direct elongation, 1.052 gms. sq. cm. 



" ■{ trans, vibration, 1.183 gms. sq. cm. 



[ longit. " 1.254 gms. sq. cm. 



f direct elongation, 0.736 gms. sq. cm. 



" \ trans, vibration, 0.782 gms. sq. cm. 



[ longit. " 0.758 gms. sq. cm. 



direct elongation, 1.881 gms. sq. cm. 

 trans, vibration, 2.071 gms. sq. cm. 

 longit. " 1.994 gms. sq. cm. 



In the propagation of elastic waves through a metal, a quite low 

 frequency of vibration should be sufficient to ensure that this process 

 is entirely adiabatic, so that on this score no change should be ex- 

 pected in the modulus of elasticity and therefore in the velocity of 

 propagation as the frequency increased up to very high values. 

 By the method described in this paper this point was investigated 

 up to a frequency of 50,000 vibrations per second by using steel 

 and brass rods to a shortness of 5 cms. Following are two tables 

 of values, I. and II., the first derived from steel bars ranging in 

 length from 200 to 5 cms., and the second for brass bars of length 

 30 to 5 cms. It can be seen from both these tables that the velocity 



'Wertheim. Ann. de Chimie, 1848. 



