﻿50 Dr.W. Peddieo/i 



right than it resists equal displacements to the. left. These 

 facts illustrate Wiedemann's experimental results with regard 

 to the torsion of wires. 



Consider the wire in its initial undisturbed condition, or in 

 any condition of equilibrium with set provided that the next 

 torsion is to be oppositely directed to that which was last 

 performed and which produced the set. If the wire be now 

 twisted through an angle 0, and if, during that twist, no 

 configurations break down, the potential energy will be re- 

 presented, in accordance with Hooke's Law, by the expression 



where k is a constant. If there is rupture of molecular 

 groups, the potential energy will fall short of the above 

 amount by a quantity which we shall assume to be propor- 

 tional to a power of the angle. Thus we get 



v=p0 2 -p<r. ' (3) 



In those cases in which the loss of energy, per outward 

 swing, is small in comparison with the total energy, so that 

 the set is negligible in comparison with the total range, the 

 loss is practically equal to k6 d0. Hence (3) takes the form 



-kdde= P G m dt, (4) 



where dt is the time of an outward swing. The integral is 



0"(« + g=i, (5) 



where b and t are constants, and n = m + 2. 



This is exactly our empirical equation (1) ; which we thus 

 derive as an approximate consequence of the theory that the 

 loss of energy is due to the rupture of molecular configura- 

 tions, and is proportional to a power of the'angle of torsion. 



A glance at the curves in fig. 1 will show that, in the 

 steeper portions, the drop of angle per single swing is not 

 really negligible in comparison with the range, though, even 

 in the steepest portions, it does not exceed one tenth part of 

 the range and rapidly diminishes as the range decreases. 

 Hence we cannot expect the values of n which hold through- 

 out those portions of the curves which are dealt with in 

 Table II. to hold at still smaller angles of distortion. The 

 value of n which holds approximately over a considerable 

 stretch of a curve where the angle is large will, quite apart 

 from after-action, be greater than the value which holds over 

 a considerable stretch where the an pie is small. 



Deduction of the Compound-Interest Laic. 

 In experiment C the value of n decreased, as time went 

 on, from a value greater than unity to a value less than unity. 



