RIGIDITY OF ROCK'S AND in M'KKESIS FUNCTION. -J'.) 



released, and it is much more easily twisted in one direction than in 

 the other. This is shown by the fact that ^ and . % have dif- 

 ferent values at this stage. Moreover, in this case, though both p or 

 n and f] are zero, -^v- is not generally zero ; so that we have 



Proposition X. A lately twisted specimen, which is actually in the 

 non-twisted state, becomes gradually twisted with the lapse of time without 

 any application of external couple. 



After all, a specimen which has been, twisted at least once can 

 not be really neutral one like a virgin piece. The neutral state is 

 the state of no internal stress which is the same as that which 

 Saint- Venant used as a means of deducing the uniqueness of the 

 solution of the elastic equations under the name " L etat dit naturel 

 ou primitif." An interesting explanation for the internal state of 

 molecular equiliblium by Sir W. Thomson (1) may be cited here ; 



" the outer particles will be strained in the direction opposite 



to that in which it was twisted, and the inner ones in the same 

 direction as that of the twisting, the two sets of opposite couples thus 

 produced among the particles of the bar balancing one another." 



The further nature of the Hysteresis function is to be most 

 clearly comprehended by tracing the curve representing it. The 

 result of a laborious calculation is graphically shown in the figure in 

 PL XIV. It represents the Hysteresis function for a particular 

 case ; — 21=10 ; X=0, 1, 2 ; and -105i(p or «)Sj + 10, as well as for two 

 other cases where the amplitude for the one and the centre for the 

 other was changed for different cycles. 



As to the Hysteresis curve, it may be necessary to remark that, 



(1) Sir W. Thomson. Mathematical and Physical papers. Vol. III. 



