136 LOUIS VESSOT KING 
No account is here taken of stress-difference brought about by 
the folding of the earth’s crust or that due to residual effects of 
a state of very intense stress which may have been brought into 
existence at a very remote period of the earth’s history. 
(iz) Collapse Due to Pressure in the Earth’s Crust 
We have noticed in $8 that the pressure at any point of the 
earth’s crust may be roughly represented by the weight of a column 
of rock of that depth. If w represent the average weight of rock 
at the earth’s surface per cubic cm. and / the depth in cms., a small 
spherical cavity can exist provided 
wh<2S (26) 
where S is the limiting stress-difference of § 6 expressed in grammes 
per sq. cm. Making use of the numerical values corresponding to 
a limiting stress-difference between 160,000 and 200,000 pounds 
per sq. in. (.13X10® and 1.41X10° grammes per sq. cm.) for 
Westerly granite and taking 2.7 as the mean density of sur- 
face rocks, we can assert that small cavities in the earth’s crust will 
not collapse provided the depth does not exceed a quantity / whose 
value lies between 27.7 and 33.7 kilometers (i between 17.2 and 
20.9 miles). This estimate is several times greater than that 
deduced by Hoskins," the reason being that it is necessary to make 
use of a very much higher value of limiting stress-difference than 
that employed in the investigation referred to. Even at a tem- 
perature of 550° C. which is supposed to exist at a point 11 miles 
below the earth’s surface, Adams has shown that S is greater than 
95,000 pounds per sq. in. which corresponds to a depth of 15 miles. 
Any internal pressure in the cavity (due to water-pressure, steam, 
etc.) would increase the above estimate for the depths at which 
cavities can exist. 
The size of a cavity which can exist at a given depth depends 
on considerations of stability and would demand a separate inves- 
tigation. 
1 Hoskins, op. cit., 859. Hoskins expresses the result of his investigation in the 
form ‘‘cavities must certainly close up if wk>S.” The value for S is taken to be 25,000 
pounds per sq. in. The much higher value between 160,000 and 200,000 pounds per 
sq. in. indicated by experiments on Westerly granite shows that Hoskins’ estimate for 
the depth at which cavities must close, must be increased between 7 and 8 times. 
