LIMITING STRENGTH OF ROCKS UNDER STRESS 2 
in heavy nickel-steel jackets lend themselves especially well to a 
determination of stress-differences according to the elastic solid 
theory. An indeterminate condition which might vitiate the 
application of analysis to the problem is the state of initial stress 
brought about by shrinking the nickel-steel jacket over the rock 
specimen. Since the ends of the specimen are free during this 
process it is probable that the rock will adapt itself to a state of 
small initial stress by slight displacements in the direction of the 
axis. This will especially be the case if some time is allowed to 
elapse before the test is carried out. Care was taken to make this 
stress as small as possible under the circumstances; see p. 105. 
One of the most serious objections to the application of the 
theory of elasticity to the determination of conditions of rupture 
lies in the fact that in most tests the conditions of small strains 
upon which the theory is based are violated long before rupture 
takes place. Under the conditions just described the strains remain 
small in consequence of the very slight yielding of the nickel-steel 
jacket. It is well known that the elastic constants are only deter- 
minate so long as the strains are small and that when the material 
is stressed beyond a certain limit the rigidity and compressibility 
take quite different values, so that in most cases the values of the 
stresses just before rupture cannot be calculated from the conditions 
of the test. In the present instance, however, by measuring the 
lateral dilatation of the nickel-steel jacket during a test in the 
manner described in §4, it is possible to determine how the elastic 
constants of the rock change in value with stress. In this way it 
is legitimate to make use of the equations of the elastic solid theory, 
provided we employ imstantaneous values of the constants for the 
specimen and as long as the stresses in the nickel steel do not exceed 
the limiting stress for that material. 
§ 3. DETERMINATION OF STRESSES IN ROCK CYLINDER UNDER TEST 
If we consider the state of stress in the rock specimen and in 
the nickel-steel jacket as one of plane stress, the problem may be 
solved without an undue degree of complication. The measure- 
ments given in the next section of the lateral dilatation of the 
nickel-steel jacket when the rock specimen is under pressure show 
