﻿54 On Torsional Oscillations of Wires. 



Period of Oscillation. 



The potential energy of the system is 



Y = ikO 2 -p0 m . 



The kinetic energy of the system oscillating as a whole is 



1T0 2 

 2- L(7 > 



where I is the moment of inertia; and the second term in 

 the expression for V represents kinetic energy of molecular 

 motion. So the total kinetic energy at the angle is 



T = iI6 2 +pd m . 

 Hence we have 



I6 2 + k6 2 = constant, 



which sKows that the motion outwards is simple harmonic 

 motion as reckoned from the origin; but it is only so in 

 virtue of the condition that the defect of the potential energy 

 from the value that it would have in accordance with Hooke's 

 Law is due to its transformation into a kinetic form. The 

 periods of the outward swing from zero and of the inward 

 swing to the position of set, on the assumption that k does 

 not change, are each equal to 



7T n 

 Wt 



Wiedemann's statical experiments show that after the few 

 preliminary applications of the maximum twisting couple 

 necessary to fix the set, 6— a varies almost in accordance 

 with Hooke's Law, and that the slight difference is in the 

 direction of too great magnitude as the torsion increases : 

 and Tomlinson has shown that great permanent torsion de- 

 creases the torsional elasticity. These facts may indicate 

 that Tc is slightly decreased at the greater torsions, in which 

 case the period of oscillation will slightly increase as the 

 range is increased. 



Concluding Remarks. 



The experiment A was not the first made with the given 

 wire, though it was the first made with it under the stated 

 conditions of length &c. Thus, in A the wire was in a fatigued 

 condition relatively to its condition in the experiments R 

 and S. 



It has been found by Kelvin and Tomlinson that, in the 

 case of small ranges, the rate of decrease of range per oscil- 

 lation is practically constant for all periods of oscillation in 



