Temperature on Modulus of Rigidity of Solid Metals. 417 



second term be negligibly small compared with the third 

 term, the viscosity is negligible and the oscillation undamped. 

 If a damping exists, the second term cannot be negligible. 

 As we have seen, the coefficients of b and a in the second and 

 third terms have the same form — that is, 



7D7R 4 , 7niR 4 



b=— ^— and a= 0/ ' 



Hence, in order that the damping may be appreciable in a 

 continuation of oscillations, r\ must have a value greater than 

 about joo^o or Toooo or * ^ ue vaiue o£ rigidity n — that is, a 

 value of an order of magnitude amounting to 10 9 to 10 8 . 

 Hence we conclude tliat the above values of rj are of the right 

 order of magnitude. 



From the logarithmic decrement-temperature curves we 

 notice that, unless metals have high melting points, logarithmic 

 decrement increases at first slowly and then rapidly ; hence 

 the coefficient of viscosity must also undergo a similar 

 change. Now, it is highly conceivable that, as in the case of 

 a liquid, the viscosity of a metal will decrease with a rise of 

 temperature, because it is intimately related to the magnitude 

 of molecular force, which diminishes with the rise of 

 temperature. But in an actual case the viscosity rapidly 

 increases with the temperature. This seemingly abnormal 

 phenomenon may be understood in the following way : — 



It is highly probable that in a single crystal having a 

 regular distribution of molecules in a space-lattice, damping 

 of oscillation does not exist. What contributes to damping- 

 is irregularly distributed molecules existing in the boundaries 

 of elementary crystals constituting the whole mass. As the 

 temperature rises, thermal motion causes an increase of 

 molecules, which are irregularly distributed in the boundaries, 

 and hence the damping of oscillation. It is easy to see that 

 as the temperature becomes higher, the number of irregularly 

 distributed molecules rapidly increases and causes a rapid 

 increase of viscosity. Since fine crystals constituting the 

 specimen become larger by a prolonged heating, it is to be 

 expected from the above view that annealing causes a 

 diminution of logarithmic decrement, as is actually the 

 case. 



As in the case of a liquid, the specific property of viscosity 

 may be considered to diminish with the rise of temperature. 

 Thus the initial decrease of n with the rise of temperature 

 may be explained as the temperature effect of viscosity at low 



Phil Mag. 8. 6. Vol 42. No. 240. Sept. 1921. 2 V 



