Coefficient of Normal Viscosity of Metals. 

 Hence, by observing X and T, f can be determined. 



4tt 2 M 



117 



Since 



E = 

 E 



ST 2 ' 



2 



77 



In the case of metals, we cannot apply the above method 

 for determining the coefficient of normal viscosity ; because 

 in this system, the period and the amplitude of longitudinal 

 oscillations are very small and difficult to determine accurately. 



4. For the actual determination of the coefficient f, the 

 following vibrating system will meet -our purpose. Let a 

 metallic band be vertically fixed at its upper end, and a lead 

 sphere fixed at its lower end. If this suspended system be 

 made to oscillate laterally, then the equation of motion can 

 be found in the following way : — 



Let us take the axes of coordinates as shown in fig. 1. 

 Suppose the lead sphere be slightly displaced toward the 



Fig. 1. 



-G--^ 



right ; then denoting the thickness and the breadth of the 

 band by a. and b respectively, we have for the moment 

 of elastic restoring force of the band 



i 



dh 



1 



dh, 



1 dx 2 12 dx 2 



where dh is an elementary layer at a distance h from the 

 neutral layer. If the system be in a way of oscillation, then 

 the moment of the normal viscous force is given by 



-Consider next the equilibrium of the lower part of tho 



