FRICTION AND LIMITING STRENGTH OF ROCKS 639 



None of these simple problems corresponded, however, to any 

 detailed observations available. The position with regard to the 

 final mathematical interpretation of Tresca's observations was 

 summed up by Saint- Venant in a communication to the French 

 Academy. 1 It was stated that, before much progress could be 

 made in formulating a mathematical theory of plastic flow, it would 

 be necessary to plan experiments more easily capable of mathe- 

 matical specifications; in particular he recommended that means 

 be taken to trace out in the interior of the solid the extent of the 

 plastic deformations. The difficulty of doing this without at the 

 same time interfering with the continuity of the solid under test has 

 apparently not been overcome up to the present, so that data on 

 plastic deformation available for mathematical treatment are still 

 very meager. 



It is interesting to notice, however, that we have available at 

 the present day a method of exploring the internal structure of 

 solids which seems to fulfil the need expressed by Saint- Venant. 

 By the use of extremely powerful X-rays it has been found possible 

 to detect internal cavities in steel castings not visible on the sur- 

 face. The subject has recently been extensively studied by Davey, 2 

 who states that it is possible to detect an air-inclusion 0.021 inch 

 thick in i\ inches of steel and an air-inclusion 0.007 mcn thick in 

 f inch of steel. More recently Pilon, 3 making use of the Coolidge 

 tube, has successfully penetrated 5 . 5 centimeters of steel. This 

 method appears to the writer to offer the means of studying in 

 successive stages the plastic deformation of specimens of various 

 materials under conditions of intense stress. In these circumstances 

 it would be necessary only to drill extremely fine holes in the 

 specimen in various directions and to study the deformation of 

 these as the solid is made to flow. 



Tresca's hypothesis that flow in a solid commences and continues 

 as long as the shearing stress exceeds a definite limit has been found 



1 Saint-Venant, "De la suite qu'il serait necessaire de donner aux recherches 

 experimentales de plasticodynamique," Comptes Rendus, LXXXI (juillet, 1875), 

 115-21. 



2 W. P. Davey, Trans. Am. Electrochem. Soc, XXVIII (1915), 407-18. 



3 H. Pilon, Rev. de Met., XII (Nov., 1915), 1017-23. 



