RIGIDITY OP ROCKS AND HYSTERESIS FUNCTION. 



:;:, 



would be, al least, one oj the principal causes of the diminution of 

 velocity. In the equation (17) put p=0 and ^=1, then 

 ( A/ ' \-hloa [Sg+lKfig+im + iP _- sav 



Ins vnlue < 



>f 



Ai> 



expressed as a function of the amplitude ^re- 



presents the amount of the increase of twist due to i\\v yielding, per 

 unit increase of couple in the stage of zero couple after one cycle of 

 twisting tl in >ugh an amplitude 31. Now, the actual amount of twist 

 is the sum of two terms ; i.e. 



where ~i is the term which fulfils Hooke's law. Let y and c be the 

 velocity and factor of proportionality respectively, then we have 



If the yielding be disregarded, then neglecting - we have 



V = V„ 



so that .all waves with different amplitudes propagate with a common 

 velocity if, and only if, the stratum of roclcs through which they propagate 

 does not yield. 



When the yielding is enormous, which is the case for a loose stratum 

 such as the earth's crust, the velocity decreases very rapidly when the 

 amplitude of the ware increases. The quantitative relation between 

 these two elements is given in the following table. 



