RIGIDITY OF ROCKS AND HYSTERESIS FUNCTION. 25 



equation is (1). For:! particular case, p= 10 and r=0, the curve of 

 recovery is traced in Fi" - . 27, PI. VIII. 



Again, from the equation (8), the difference between the yield- 

 ing« at the two consecutive stages £> and.p+1 is 



J4(Ä+l)3l+J)+lM/0 [4(A,+l)3l-(4p+3)2l+J»+l | (17). 



tSTi MIL J 



--J-=Jclog— j °— _ -=Jcloge say. 



LI [~4( a, +l)3ï- (4/9+1)21 +P+l"\ 



o 



Putting jp= — 31, the expression for s may be written in a form, if 

 we write 8 for 4(^+l)3t, 



e= - { "g + i-9C }{ ^ + i-*2(j { s 3 + i-43j}{$ + i-32t} {i +43(} 1 <1 



{33+i-z2l} 2 {93 + 1-Ö31} 3 {i+22t}- 



which is less than unity since each group of the component fractions 

 is less than unity ; whence for this value of p, 



l^L) <0. (18). 



I Ap Jj> = -31 



Putting p=2t, it may also be written in a form 



c __ {33+i + 31} {S + i-231} 2 {t+62(} 2 {i+23t} 3 j 



{ s -ö + i} ~ {95+i}{aj+i-42l} [1+821] {1+431} {1 + 431} i 



which is greater than unity, so that for this value of p we have 



|-^2_1 >0 (180. 



From what has been proved just above, (18) and (18'), we may infer 

 Proposition IV. When a specimen is twisted cyclically, the Hoist 



may increase notwithstanding the decrease of the applied couple, and vice 



versa. 



The equation (17) may be written in a form, if we put 



9? = 4(/+])21+;j + 1 for the sake of brevity, 



A? = k , M{9l-33Q' fc + 1+g} * 



&p J {di-$iy{di-5%Y {p+i+-d%y 



whose differential with respect to the amplitude 21 is 



