DEFORMATION OF ROCKS 197 
are saturated with superheated water. We also need a satisfac- 
tory theory of the flow of viscous liquids or plastic solids. 
In the absence of these data a first approximate solution of 
the problem has been made by Professor L. M. Hoskins, of Stan- 
ford University, based upon the elastic limit and the ultimate 
strength of rocks. The most carefully conducted experiments 
agree with theory and seem to show that rock masses of the 
same form have the same crushing strength per unit of area 
whether in large or small masses. In experiments on cubes 
running from I to 12 inches in diameter,! in each set there 
are irregular variations per unit area on each side of the average, 
but these are probably explained by the unavoidable variations 
in the strength of the different pieces tested and the impossi- 
bility of obtaining exactly similar conditions. 
Professor Hoskins, after a comprehensive discussion, reaches 
the following general conclusions upon the closing of cavities in 
rocks: 
(I.) In any region if the three principal stresses of a rock mass are equal, 
a spherical cavity cannot exist permanently if the normal stress in the rock 
exceeds the pressure within the cavity by as much as two-thirds the elastic 
limit or the ultimate strength. 
(II.) If two of the three principal stresses are equal, a cylindrical cavity of 
considerable length whose axis is parallel to the third direction cannot exist 
permanently if either of the equal principal stresses exceeds the interior pres- 
sure by as much as half the elastic limit or the ultimate strength, or if the 
third principal stress exceeds the interior pressure by as much as half the 
elastic limit or ultimate strength. 
Although the discussion has been confined to these special cases, it seems 
safe to state the following general proposition as at least probably tue: 
(III.) No cavity can exist permanently in a rock throughout a considerable 
portion of which the normal stress in any direction exceeds the pressure within 
the cavity by as much as the elastic limit or ultimate strength of the rock. 
Professor Hoskins further says that: 
The intensity of stress upon a horizontal plane at any depth is equal to 
the weight of a column of rock of unit cross-section extending to the surface. 
‘Tests of metals and other materials for industrial purposes, made with the United 
States testing machine at Watertown Arsenal, Mass., by S. V. Benét, Chief of Ord- 
nance. Rept. of Chief of Ordnance for year ending June 30, 1884, pp. 126, 166, 167 
188-199, 212, Washington, 1886. 
