RIGIDITY OF KOCKS AND HYSTERESIS FUNCTION. -J 1 



'-^ïr+n+lî/ïn+l} ' (4) " 



Lastly, if the couple remains constant after this moment, then 

 the yielding at the instant T=p+r+n+t is given by 



'/{r + ^ + ^+lj^n + ^+l} V 



Proceeding in this way, we may find the value of r t after any 

 number of torsional cycles. I give here its general form. Suppose 

 we start from the origin, at the instant r==o, which corresponds to 

 the neutral state of the specimen, and for the sake of simplicity also 

 suppose that the change of couple takes place by unit amount per 

 unit of time. 



1. Increasing the couple step by step we reach a couple =1 at the 

 instant r=*i, so that I=i x ; 



2. for the next r x minutes, the couple remains constant to the 

 instant T=i i + r 1 ; 



3. then it decreases step by step and ultimately, going even to the 

 negative direction, becomes equal to II at the instant T=i l + r l + i 2 , so 

 that II=ii— ii ; 



4. here the couple remains constant and equal to II. during the 

 next r.y minutes ; 



5. again, the couple increases once more till it becomes equal to III 

 at the instant T=i l + r l + L, + r*+i^ so that III. =h—h+h ; 



etc. etc. etc. 



where /, II, III, N represent certain definite amounts of 



couple, positive or negative as the case may be. Let p and n denote 

 any given stage in the cycle on the increasing or decreasing pro- 

 cedures respectively, and t the time during which the couple remains 

 constant at the last stage jp or n • also let f be the number of reversals 

 of the couple from increasing to decreasing or from decreasing to 



