BEHAVIOUR OF OVER-STRAINED MATERIALS 475 



question, but also on all the previous stresses to which it has 

 been subjected, and that in a way which is very difficult to 

 understand. The fundamental principles upon which the de- 

 velopment of a theory may be based become, under the circum- 

 stances, insufficient, and the theorist is usually reduced to the 

 necessity of determining experimentally the form of some function 

 or other, in order to make progress. The result is that the theory, 

 although perhaps to some extent useful, is not a true physical 

 explanation of the observed phenomena. It has been usual among 

 experimentalists on this subject of elastic after-effect to attempt 

 to fit empirical equations to the curves obtained, both in the case 

 of the increase in strain in a body subjected to a constant stress 

 and in that of the recovery from strain after release ; and, further, 

 to those curves representing the value of the stress necessary to 

 maintain the strain constant as time goes on. The early work 

 of Weber and Kohlrausch was mainly upon the slow recovery 

 after over-strain. They found that the equation 



log x = A - at m 



was capable of representing the after-effect in all the bodies inves- 

 tigated (which included silk, indiarubber, and several metal wires), 

 where x denotes that deformation which persists in a wire or fibre 

 after the torsional forces have ceased to act, and / is the time that 

 has elapsed since release. In many cases the simple formula 



C 



X = — , 



or, better — 



X = 



(b + ty 



sufficed. In these formulae, everything except x and / is constant. 

 In Weber's very first results he used the value a = i, but later 

 found a value less than unity to be more suitable. O. E. Meyer, 1 

 in 1874, made the first attempt to develop a theory of " Elastische 

 Nachwirkung," and was successful in obtaining for the after- 

 effect a formula of the same form as that made use of by Weber 

 and Kohlrausch for representing their observations, but did not 

 extend the theory to the case of the variation of stress with time 

 necessary to keep the strain in the body in question constant. 

 This latter case would be expected to be more simple than that 

 of actual recovery from strain, for, since no change in outward 



1 O. E. Meyer, Pogg. Ann. 151 (1874) ; 154 (1875) ; Wied. Ann 4(1878). 



