270 BECKER 



mantle of the cylinder expanding to the shape of a barrel. The 

 reason for this is that intense friction is produced by the effort 

 of the end surfaces to expand in contact with the rigid planes 

 exerting the vertical pressure. I have experimented somewhat 

 elaborately on the character of this strain and have determined 

 the position of the strain ellipsoid at 64 points on a vertical cross- 

 section. The greatest axis of the ellipsoid lies in the plane 

 passing vertically through the center of the cylinder, but it is 

 not horizontal ; it is inclined to the horizontal at an angle which 

 varies with the distance from the central vertical axis of the 

 barrel-shaped mass. The least axes of the ellipsoid also lie in 

 the vertical central cross-section of the mass and the surfaces ^ 

 of " maximum tangential strain " are conoidal with their apices 

 in the axis of figure. It is along these latter surfaces that rup- 

 ture due to pressure must occur if at all, as I showed long ago. 

 At any one point of such a cylinder the strain is homogeneous 

 and exactly comparable to that in a uniformly strained cube. 

 The peculiarity of experimental results on cylinders lies in the 

 radial symmetry of the stress system. 



If it were possible to crush cylinders between frictionless sur- 

 faces, so that the deformed blocks would retain a uniform diam- 

 eter, the strain ellipsoids would have 2 equal horizontal axes, 

 and, if the mass were ideally homogeneous, it is difficult to see 

 what would determine the position of the ruptures. But this is 

 not an important question. In real matter the resistance could 

 not be exactly the same in all directions and 2 S3"stems of joints 

 would form as in the cube. In a cubical mass, or in one of 

 square cross-section, the cracks will be perpendicular to the 

 sides of the cube as explained above, because this is the posi- 

 tion of least resistance, or because a unit area of rupture in this 

 orientation goes farthest towards relieving the strain in the 

 yielding mass. 



In the lithosphere, when crushing or jointing takes place, the 

 masses exerting the pressure are almost invariably little more 

 resistant than the rock which is ruptured. It is very seldom, 



' U. S. Geol.[Suiv. Bull., 241, 1904. The surfaces of rupture are such as would 

 be obtained by rotating Fig. 14 of that bulletin about its smallest diameter, but if 

 the deformation were small these surfaces would be indistinguishable from right 

 cones. 



