﻿Torsional Oscillations of Wires, 47 



tion to the left. If the wire now receives an impulse in the 

 positive direction, which again elongates it up to + a, accord- 

 ing to the laws of perfect elasticity it will swing back again to 

 the position + b. If it now swings beyond this position farther 

 to the right, and if the molecules in their rotation had no 

 friction on one another at all to overcome, it would arrive at 

 the elongation —a, since the same force that twists it from 

 + 6 to + a twists it in the contrary direction from + b to —a, 

 while the axes of the molecules would be rotated just as far 

 (—a) to the right as previously to the left. Again, with 

 perfect elasticity the wire would go back to the position — b, 

 in which the molecules would be rotated — /3, and so forth. 

 The to-and-fro motions of the wire, between ±a and ±b, 

 are perfectly elastic ; therefore the performances of work in 

 the swingings outwards and the swingings back again must, 

 within these limits, completely compensate one another. In 

 fact, however, there results a diminution of the amplitudes of 

 oscillation ; hence the loss of vis viva therein can only corre- 

 spond to the work which is expended for the alteration of the 

 positions of equilibrium, or the rotation of the molecules 

 from -f /3 to — /3, which determine it. 



Theory of the Present Results. 



The kinetic theory of the viscosity of gases, as developed 

 by Maxwell, asserts that viscosity is due to interchange of 

 momentum between relatively-moving portions of the sub- 

 stances — this interchange being effected by the passage of 

 molecules from one portion to the other. In the same way 

 the viscosity of liquids is explained. There is essentially 

 a passage of molecules from one group to another. Such 

 passage does not take place in a perfectly elastic solid ; but 

 there may still be interchange of momentum in the relative 

 motion of the constituents of a group, and therefore true 

 viscosity in a solid. Yet, if the potential energy of deforma- 

 tion of a group is large in comparison with the kinetic energy 

 of average relative motion of the constituent molecules of the 

 group — a condition which holds in the case of the torsional 

 vibrations of a tine metallic wire to the free end of which is 

 attached a mass of great moment of inertia — it seems certain 

 that the energy dissipated by true viscosity will be small in 

 comparison with the energy dissipated in the breaking down 

 of molecular groups (as in Maxwell's theory of a molecularly 

 constituted solid) , should such rupture take place to, possibly, 

 a small extent only. 



Wiedemann seems to regard the loss of energy as due to 

 the work done in rotating the molecules from one position of 



