Temperature on Modulus of Rigidity of Solid Metals. 415 



b has the same form as the coefficient a of the third term in 

 the equation of motion, the only difference being that the 

 rigidity n is replaced by ?;. Since 



_bT _ 8XU _ nXT 



X_ Tl ; .-. V-^trp or _ ^ . 



Thus, by observing the period of oscillation T and loga- 

 rithmic decrement X, ?? can be calculated. It must be stated 

 here that, although the viscosity rj contains the rigidity n as 

 well as the logarithmic decrement \, the rate of increase of \ 

 with the rise of temperature predominates the decreasing 

 effect of the rigidity by different order, so that the curve 

 of rj takes approximately the same course as that of the 

 logarithmic decrement. 



From the expression given by W. Voigt, we obtain for 

 the expression of r) ( = a 2 in his notation) 



n\T E 



V = 



7T 2 4(E-n)' 



where E is Young's modulus of elasticity. This expression 



E 



differs from ours bv a factor -7-^ , . From our method 



4(E — n) 



of calculation it seems to us untenable that the expression 

 for the coefficient of viscosity contains Young's modulus of 

 elasticity. 



In the measurement of the coefficient of viscosity at 

 ordinary temperature we used the second apparatus sketched 

 in fig. B. The effect of the surrounding air in the logarith- 

 mic decrement was deduced from two experiments made in 

 the atmosphere and in a vacuum by taking the difference of 

 the two logarithmic decrements. The logarithmic decrement 

 due to the surrounding air alone was 0*00023 in the mean, 

 the amplitude of oscillation of the inertia ring being 

 2°-86. 



The logarithmic decrement in a vacuum increases linearly 

 with the amplitude. This increase \\ as proved to be caused 

 partly by the amplitude of oscillation being not sufficiently 

 small, and partly by the energy loss through the suspension 

 outward : hence we found the values of logarithmic dee re- 

 m en t corresponding to zero amplitude by extrapolation, 

 and used them in the calculation of the values of ?;. The 

 following table contains the results of our experiments : — 



