168 THE ROYAL SOCIETY OF CANADA 



the tube is diminished and the wave velocity is therefore lowered. 

 Lamb* gives the following data. If the theoretical velocity of the 

 waves in the fluid is Q and the actual velocity C these velocities 

 are related in a tube of thickness ]i as follows: 



^2_ ° Where a is the internal radius; K the volume 



2 K a elasticity of the fluid, and E Young's modulus 



hE for the material of the tube. 



Since K for air has the value 10^ and E for glass is 6.03 x 10^\ 

 we see that for a glass wall 1mm. thick and 1.4 cms. diameter, the 

 squares of the velocities have the ratio 1:1.0000232. Therefore this 

 effect also need not be considered as affecting results. 



A Test for Hardness 



An investigation was made to see if this method might be used 

 as a means for testing the hardness of steel. Another set of readings 

 was taken with the identical bar used for the first table but this time 

 the bar was hardened by slowly heating and quenching in cold water. 

 The bar was used in this dead hard state without drawing the temper. 



It was found that thjC distance between successive loops had 

 increased from 59.5 cms. for 30 loops before tempering the bar to 

 60.2 cms. for 30 loops after tempering; i.e. from 1.98 cms. to 2.01 cms. 

 This gives a change in the value of Young's modulus due to tempering 

 from 2.15 x lO^^ dynes per square cm. to 2.09 x 10^- dynes per square 

 cm., or about 3%. 



Static and Dynamic Moduli 



It was suggested by Rayleigh^ that it was probable that the 

 value of Young's modulus for a metal as found by a static method 

 would be somewhat different from that which corresponded to a 

 dynamical condition such as prevails in the propagation of sound. 

 The variation would depend on the difference, if any, between the 

 isothermal and adiabatic elasticities of the metal. In solids this differ- 

 ence is inappreciable. Kelvin^ has calculated the value of the ratio 

 of the dynamic to the static moduli of elasticity, and finds it to be 



*Lamb, Dynamical Theory of Sound, p. 173. 

 *Rayleigh, Theory of Sound, Vol. 1, p. 246. 



* Kelvin, Encyclopedia Britannica, New Werner Edition, Vol. VII, Article on 

 "Elasticity." 



