RIGIDITY OF ROCKS AM» HYSTERE8I8 FUNCTION. 5 



ARRANGEMENT AND TWISTING APPARATUS. 



The arrangement for the experiment was, on the whole, one and 

 the same as that used bv Professor H. Nagaoka, (1) but with such 

 adaptations as were necessary to make the stress cyclical. Pre- 

 liminary experiments, as the professor noted in his publication above 

 cited, showed a great defect of Hooke's law and the existence of 

 remarkable hysteresis. Fig. 1, PJ. I., shows the general features of 

 the relation of stress to strain in a piece of sandstone. Thus, it will 

 be obvious that, in the ordinary sense of the term, it is nonsense to 

 speak of the modulus of rigidity of rocks. The value suggested by 

 the mathematical theory as the limiting one is to take the tangent of 

 the angle which the tangent at the origin to the stress-strain curve 

 makes with the strain axis. But, it is extremely difficult to 

 determine this angle, because the experimental error due to the non- 

 delicacy of the apparatus is greatest where the stress is vanishingly 

 small. Possibly sound-experiments might be the best method of 

 ascertaining this limiting value. The result deduced from such 

 infinitely small strains as occur in sound vibrations is no doubt of 

 great value as regards the elastic property of matter ; but it must be 

 far from what we have to consider in the study of the geological 

 phenomena and seismic waves. 



The chief features of my improvements of the arrangement 

 were ; — firstly, to twist the specimen cyclically with increasing and 

 decreasing couple passing through zero continuously ; secondly, 

 to get rid of the influence of the friction between the parts of the 

 instrument ; and thirdly, to eliminate any external disturbance such 

 as the yielding of the scale-support or minute displacements of the 

 telescope. 



(1) H. Xagaoka. The Pub. of the Earthquake Invest. Committee in Foreign Languages. 

 No. 4. 1900. 



