and Rocks under Pressure. 251 



and shall assume here the results of the analysis, which 

 will be given in detail in the following paper. Let us 

 consider the ideal case of an infinitely long hollow cylin- 

 der subjected to hydrostatic pressure over its external 

 surface. If the material is isotropic the system of stresses 

 and strains is well known, and is very simple. Every 

 plane cross section of the cylinder remains plane, and the 

 distortion consists merely of a shortening of every radius 

 without any change in the angle between any two radii. 

 The most intense stress and strain are both at the inner 

 surface. The stress at the interior is a compression on 

 planes including the axis and the radius, amounting to 

 approximately twice the external hydrostatic pressure. 

 The amount of strain depends of course on the elastic 

 constants ; its nature is an elongation of the fibers along 

 the radius at the inner surface (a paradoxical result) and 

 a numerically much greater shortening of the circum- 

 ferential fibers. 



The elastic deformation in a crystal of quartz is much 

 more complicated. The most important difference com- 

 pared with the isotropic case is that plane cross sections 

 do not remain plane, but become warped, the warping of 

 course satisfying the conditions of symmetry and repeat- 

 ing itself every 120°. The warping with cylinders of the 

 dimensions above, the inside diameter of which was 3-6 

 mm. and the outside diameter 2-0 cm., is a maximum at 

 about 2-7 mm. from the axis. The shearing strain due to 

 the warping is a maximum at the inner surface, however, 

 and may amount to 35% of the maximum circumferential 

 compression. In addition to the warping there are fur- 

 ther distortions in the plane perpendicular to the axis. 

 The radial displacement is not independent of the orienta- 

 tion in the crystal, but fluctuates with a period of 60°. 

 The strain resulting from this fluctuation is only 4% of 

 the maximum. Furthermore, there is a displacement 

 along the circumference with a period of 60°, the resulting 

 strain being only about 1% of the maximum. This com- 

 plicated set of displacements results in a much more com- 

 plicated system of stresses than in an isotropic solid. 

 The most important of these additional stresses is a 

 shearing stress along the axis in planes containing the 

 axis and radius, rising at the inner surface to a maximum 

 of 47 % of the external pressure. 



Numerical computation shows that with quartz of the 

 dimensions above (inside diameter equal 1, outside diam- 



