132 LOUIS VESSOT KING 
rock powder. We are therefore able to assert that for a state of 
stress at ordinary temperature and lasting for 75 days, S lies between 
the limits of 160,000 and 200,000 pounds per sq. in., i.e., 
160,000<.S< 200,000 pounds per sq. in. (24) 
Even at a temperature of 550 C. experiment 381 (p. 115) shows 
that S is greater than 96,000 pounds per sq. in. 
We cannot, however, safely assert that flow or rupture would 
not take place for a stress-difference less than S if the boundary 
conditions were very different from these already described at the 
surface of a cylindrical cavity. In order to settle this point experi- 
ments of the type described in § 4 would be required. The value 
given in (24) for S is very much greater than the limiting stress- 
difference of 27,000 pounds per sq. in. obtained by means of the 
usual crushing test. Since this granite is typical of the great mass 
of igneous rocks which make up the earth’s crust, it follows that 
in geophysical problems which involve a knowledge of limiting 
stress-difference in the earth’s crust, a value considerably higher 
than that usually employed must be taken. 
§ 7. ON THE EXISTENCE OF CAVITIES IN MEDIA UNDER STRESS 
(7) State of Stress in the Neighborhood of Cavities in Elastic Media 
under Shear 
It can be shown that in the neighborhood of both a spherical 
and a cylindrical cavity, the shear can be nearly equal to twice 
the shear at a distance.t We see therefore that the medium near 
a cavity will collapse if the stress-difference at a distance exceeds 
half the limiting stress-difference of the rock material. If the 
cavity be small this limiting stress-difference may be taken to be 
the value of S given in equation (24). 
(ii) State of Stress in the Neighborhood of a Spherical Cavity im a 
Medium under Pressure 
If p be the hydrostatic pressure in the medium it can easily be 
shown from the solution given by Love? for a spherical shell under 
t Love, Elasticity, 2d ed., 245. See also a paper by Larmor, Phil. Mag. (Ser. 5), 
XXXIII, 1892, p. 77. 
2 Love, op. cit., 139. 
