r t = k logz 



RIGIDITY OF ROCKS AND II YSTKKESls KUMTIoN. 27 



(22). 



/Ï»-jp}[/Ï3>-*-«»}J [/ T {(4A.+i)a+i-i»+i}J"[r{a+j-jp+i}J 



Hence the difference between the amounts of yielding at two con- 

 secutive stages is 

 A$ _ kI {3-p}[{S>-j>-3313J' [MK+Da+j-p+if [a+j-P+if 



Ai? " [»-p-«J , (a>-j»-5aj' [30+i-p+iJ 



Putting herein p=j, we have the increase of yielding at the stage 

 corresponding to the centre of the smaller cycle in its increasing stage. 

 The result is 



JAU = k {S-i}(5>-J-3^ fru+pa + ij [g + i )V o 



I Ap ip-j [2)-j-3(J J [^-i-52(J [3o+i] 2 > 



whose sign wholly depends on the relative values of 2t, a and j. This 

 is a more general case of the fourth proposition. 



Taking its differential with respect to /, we have 



(25). 



A f Ay ] = k j { ^-J-HC^-J- acJCsp-j-i-sstj 8 {n + MK + i)a-j-iJ 



A/'lApi-, ' { 2) -i } [2) - j - 1 - 21 J[2) - j - 33( J [31+4(^+1)0-^ < 



which is always negative since we have 



Proposition VII. ÏTiê hysteresis curve, whose amplitude is given, 

 tends to become more and more horizontal when its centre becomes more and 

 more remote from the neutral state of the specimen. 



In the equation (8) put t = and i>=0, then the value of >;, 

 which corresponds to the residual after the first cycle, is 



r ' x - klog um+m — 



while, putting ^. = 1 and.p=0, the residual after the second cycle is 



