12 ART. 9. S. KUSAKABE. 



cases ^Ylle^e the specimen is bent convex rightliand or lefthand 

 side respectively, while the lower branches correspond to the 

 increasing stress and the upj^er to the decreasing one, would all 

 shrink to a single horizontal straight line. In the case wdiere 

 no hysteresis exists, both the upper and the lower branches 

 would coincide mth each other to make a line not necessarily 

 straight. 



For all cases of rocks here experimented upon, the upper 

 branch is concave towards the positive axis of the ordinate. As 

 to its character, however, the variety is very abundant : circular, 

 hyperbolic, oval and other curves of higher order of complexity. 

 The curvature of the lower branches is turned sometimes upwards 

 and at other times downwards. Although it is not easy to de- 

 termine any law according to which the modulus varies with the 

 phase of the cycle, we may find, as a first approximation, an 

 empirical expression for each specimen. For instance, in the 

 case of sandstone, we have. 



for the upper branch, yi =0*243 + 0'92x" 



for the lower branch, y2 = 0*243 +0'043x" 



where y and x represent Ex 10"^^ and the phase respectively. 

 As a matter of fact, the constant term of yi is equal to that of 

 y2, representing the modulus of elasticity at the state where no 

 external force is acting. 



In the following table, the constant term of the expression 

 for every specimen is given as the modulus of elasticity of several 

 rocks. It corresponds therefore to the value of the modulus of 

 elasticity in the state when the bending force became zero, during 

 which the specimen, whose section was about one centimeter 

 square and the distance between the fulcrums was 10 centimeters, 

 was bent cyclically on both sides by a force varying between 



