RIGIDITY OP HOCKS AND BFSTERESIS FUNCTION. 15 



is drawn in the figure. Then, the equation of the corresponding 

 hyperbola ls 



A* 10 



which is also traced in the corresponding figure. (Eight of such 

 straight lines and hyperbolas should be drawn in the figures to 

 correspond to all the points dotted there.} 



Assuming that the relation between the rate of yielding and the 

 time-element is given by the above equation, we may write. 



which when integrated becomes 



-■= Ji Jog t + constant. 

 Let the value of r at the time £=1 be represented by " , and we have 



-r t — - — r —k log t 

 as the value of the twist due to the yielding, provided the yielding is 

 counted after the lapse of a unit time. In Fig. 18, PI. IX., the 

 curves are traced for two different values of k. Here it must be 

 observed that the constant Jc must depend on the amount of the 

 constant couple as well as on the nature of the rocks. As C. F. 

 Dietzel (U found in his experiments on vulcanized caoutchouc the 

 yielding is, most probably, proportional to the stress, so that we may 

 put 



&=v. (S 

 or jy=v. 6. log t. 



where y is a constant depending on the nature of the rock. 



Now it may be doubted whether the yielding can actually 

 proceed without limit in time. To ascertain this point, a specimen 

 was subjected under a constant couple for a long time, and then the 

 time variation of its twist was observed. The result is shown in 



(1) C. F. Dietzel. Polytechnisches Centralblatt : Jahrgang 1857. Leipzig. 



