Car/ tie* in Rocks exposed to High Pressures. 6" 91 



cavities appear on the polished surface. The Solenhofen 

 rock is too well known to require description. 



li is hoped to continue the experiments at the earliest 

 opportunity. 



The elastic theory is readily applied to these experiments, 

 the requisite equations having already been developed by 

 Love and Williamson. 



Taking the case of a sphere of homogeneous material with 

 a small concentric spherical cavity, it is shown that if the 

 sphere i« externally submitted to a hydrostatic pressure p 9 

 then any diametral plane is a plane of principal stress ; so 

 that if the sphere were composed of two hemispheres merely 

 laid together, the ease is theoretically the same as that of 

 the undivided sphere. The radial stress diminishes, of course, 

 from p on the exterior to zero at the interior surface. The 

 perpendicular stress {e.g. on the plane surface of each hemi- 

 sphere) is slightly greater than p near the outer surface, and 

 near the inner surface (L e. the cavity) it increases to 

 nearly |jt?. Rupture will tend to begin at the surface of 

 the cavity and the planes of greatest shearing stress are at 

 45 to the radius. 



The actual conditions of experiment differed from this 

 ideal case in that the interior cavity was hemispherical 

 instead of spherical. In such a case we should expect 

 rupture to begin in the plane surface of the cavity where 

 this first loses support from the opposed flat surface, i. e. at 

 the corners where the cavity meets the overlying plane. 



The elastic theory shows that for a spherical cavity, if P 

 and Q are the stresses (measured as pressures) respectively 

 radial and at right angles to the radius at a distance r from 

 the centre, where ?\ and r 2 are the radii of cavity and sphere : 



P - J^W ( X - l \ 



_nW /I 1\ 



^ r 2 3 -n 3 W ^2rV P ' 



I desire to express my thanks to Mr. J. li. Cotter for 

 a helpful discussion of the theoretical aspect of these 

 experiments. 



Iveagh (ieological Laboratory, T. C. 1). 

 Sept 25th, 1020. 



