﻿On Torsional Oscillations of Wires. 37 



practically proportional to the stress so long as the original 

 value of the couple is not exceeded. Another is that the 

 reversed couple produces a greater strain, measured from the 

 last set, than does the equal direct couple ; the difference in 

 this case corresponds to the change of zero produced by the 

 reversal of the couple — that is, to the set. Again, by repeated 

 reversals of twist under a given couple, the total torsion and 

 the set diminish to fixed minimum values. Also, in the case 

 of torsion in one direction, the values of the total torsion and 

 of the set increase at increasing rates as the couple increases, 

 and the latter relatively at a greater rate than the former : 

 these values for a given couple increase to maxima by repeated 

 applications of the couple, and this increase is also relatively 

 greater in the set than in the total torsion. Wiedemann 

 remarks that the approach of the position of final set to that 

 of final total torsion in this case is a phenomenon of the same 

 kind as the narrowing of the limits of total torsion and of set 

 by repeated reversals of a given couple ; the only difference 

 is that the negative couple is zero. He calls the process by 

 which the wire is brought into the steady state as regards 

 total torsion and set the process of accommodation. 



In 1865 (Proc. Roy. Soc. Lond.) Lord Kelvin described 

 results obtained from the observation of torsional oscillations 

 of wires. He discovered the phenomenon of " elastic fatigue," 

 and found that the diminution of the range of oscillation, per 

 equal number of oscillations, followed the law of compound 

 interest when the range was very much smaller than the 

 palpable limits of elasticity. Tomlinson's observations (Phil. 

 Trans. 1886) support this conclusion. 



Present Observations and Results. 



So far as 1 am aware, no attempt has been made to find the 

 law of decrease of the range of oscillation when it is so large 



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that it is accompanied by marked set — set which may amount 



to a large fraction of the total range. Lord Kelvin's obser- 

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vations were purposely made upon small oscillations in order 

 to avoid the disturbances which are introduced when the oscil- 

 lations are large. Because of the known intimate dependence 

 of the instantaneous state of strain of a body under given 

 stresses upon all the previous strains to which it has been 

 subjected, it might be supposed that it would be absolutely 

 impossible to deduce with certainty any general law of decay 

 of large oscillations. In other words, any systematic arrange- 

 ment of conditions might seem to be unattainable because of 

 the possible intrusion of arbitrary and uncontrollable, perhaps 

 even untraceable, conditions. As a matter of fact, I have 



