RIGIDITY OF ROCKS AND HYSTERESIS FUNCTION. pi 



yielding appears necessarily to be elastic] or recovery is complete 



if the stress be removed for an infinite time. Tims, absolute sei 



is disregarded here. It may have, no doubt, more or less magnitude; 

 — in magnetic hysteresis, indeed, we recognize its existence as very 

 common. I doubt, however, whether it is really as great as it is 

 repeatedly reported to be in the writings of experimentalists. What 

 many experimentalists have called set appears to have been 

 in greater part not absolute set but elastic yielding. For 

 instance, when E. Chevandier and G. \Yertheim (1) considered the 

 strain to consist of two parts, i.e. an elastic part and permanent part, 

 or when G. "\Yiedeman (2) speaks of the temporary torsion and the 

 torsional sets, the elastic yielding obviously comes within the latter 

 category. To cite the best example, Ignace Giulio (3) whose experi- 

 mental discussion of set is very interesting, says himself : " On voit 



encore que ce que j'ai nommé jusqu'ici Allongement Permanent 



disparait en grande partie après un temps suffisamment long " 



The following pages contain some mathematical investigations 

 concerning the Hysteresis Function due to the elastic yielding. As- 

 sume that the strain consists of two parts of which the first follows 

 Hooke's law, being independent of time, and the second, though it is 

 also proportional to the stress, depends on a time-element in a manner 

 given by the relation established in the former experiments. Then 

 an interesting formula for the hysteresis function may be deduced, 

 from which the expressions for the amount of yielding as well as for 

 the amount of residual after any number of reversals of twisting and 

 untwisting, and all other properties of the torsional hysteresis follow 

 at once. 



(1) E. Chevandier and G. Wertheini. Mémoire sur les propriétés mécaniques du bois. 1848. 



(2) G. Wiedemann. Pogg. Annalen. Bd. CVI. 1859. 



(3) I. Giulio. Memorie délia reale Accademia délie Scienze di Torino. Serie II, Tom. 

 IV. 1842. 



