BEHAVIOUR OF OVER-STRAINED MATERIALS 477 

 D', then the value of the torsion after an elapse of time / is given 



a, b, and p, as before, being constants. 



When the wire has been for a long time under the action 

 of this couple, and is suddenly released, then if 6 is the angle 

 reckoned from the position occupied by the wire at the moment 

 of release, its value at any subsequent time is given by the same 

 formula, i.e. the recovery corresponds in every respect to the 

 strain originally produced. Here again, however, the restriction 

 must be imposed that the formula is inadequate for very small 

 values of /. It will be seen that if t is put equal to zero, then 

 the corresponding value of 6 is infinity in the negative sense, 

 which is, of course, inadmissible. 



Considerable experimental evidence is forthcoming in support 

 of these results of Boltzmann's. Had all subsequent workers 

 attempted to apply his theory to their results, it would probably 

 have been even greater. In making this application to the case 

 of variation of stress at constant strain, Kohlrausch found that 

 the couple D necessary to keep the torsion constant in a suddenly 

 twisted glass fibre could be represented with great accuracy 

 (except for very small values of t) by the formula 



D — a — b log t, 



which will be seen to be of precisely the same form as that 

 given by Boltzmann's result for that case. The formula proved 

 also to be valid for very large values of f, and Kohlrausch 

 considered the small variations which did occur as being 

 sufficiently accounted for by possible changes in temperature, 

 which, as before pointed out, have considerable effect on the 

 phenomenon. Recently, Prof. Trouton and the writer found 

 that the stress-time curve at constant strain for lead wires, 

 both for stretching and torsion, could be represented with 

 considerable accuracy by the equation 



S =a- Klog(pt+ 1). 



The introduction of the third constant in this empirical 

 formula was an attempt to make it valid for t = o, but for values 

 of t not too small a formula precisely of the Boltzmann type 

 sufficed. The formula made use of by Mr. Phillips for stretched 

 indiarubber also supports that of Boltzmann, and the writer has 



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