296 THE ROYAL SOCIETY OF CANADA 



not be independent of the frequency; but here, in order merely to get 

 an idea of the order of its effect, we shall assume that C is a constant 

 of the material, the frictional dissipating force being strictly pro- 

 portional to the rate of deformation. Also, theoretically, C may be 



taken as equal to -r- , where ^ is the actual coefficient of viscosity in 



6p 



C.G.S. units, without departing from the correct order in our cal- 

 culations.^ 



Unfortunately we have no value of the coefficient of viscosity, n, 

 that can be quoted to evaluate this damping constant, though experi- 

 ments now in progress may be able to disclose its value at least 

 approximately. Recently Ronda and Konno^ have experimented on 

 the determination of the coefficient of normal viscosity of metals, and 

 find the normal and the tangential viscosity to be of the same order. 

 The normal and tangential viscosities correspond, respectively, in 

 elasticity' to the modulus of elasticity and the modulus of rigidity; 

 and hence it is the normal viscosity which is acting when a solid bar 

 or rod vibrates longitudinally. But such vibrations in the case of 

 metals are too rapid and too small in amplitude for experiments by a 

 method such as was used by Honda and Konno. Accordingly the 

 measurements to find the normal viscosity were made indirectly on 

 larger and less rapid, flexural, vibrations, with period about 0.7 per 

 second, and amplitude 5 to 25 mms. of maximum flexure on a length 

 of 26 cms. The results show that the logarithmic decrement of these 

 flexural vibrations, and therefore presumably also that of the accom- 

 panying longitudinal vibrations, decreases linearly with decreasing 

 amplitude of oscillation, and for metals are of the order . 7 to 27 X 10^ 

 in C.G.S. units. In the case of steel the coefficient of viscosity in- 

 creases with the content of carbon and has an average value of 4 X 10^ 

 (about). 



Although these values of normal viscosity correspond to the 

 longitudinal vibrations of a rod — produced by flexure — the order is 

 altogether too high to apply to plane longitudinal waves through the 

 body of a bar without flexure, as in the case of a metal bar struck 

 with a hammer. 



A calculation from the theoretical formula for the velocity of 

 longitudinal waves in the struck bar, viz. : 



p Vs p/ 4 



will make this clear. 



^Rayleigh, loc. cit. 



^Phil. Mag., Vol. 42, July, 1921. 



