LIMITING STRENGTH OF ROCKS UNDER STRESS 1209 
The results given in Table I are shown graphically in Fig. 2, 
where the radial strains are plotted on a load base. Equation (16) 
shows that if the rock specimen had behaved throughout as a 
perfectly elastic solid, U’/c should be proportional to the load, and 
the curve connecting load and strain should be a straight line. 
Even taking into account the equatorial bulge of the nickel-steel 
jacket the proportionality of strain to stress should be exact on the 
elastic solid theory... We may interpret the results just obtained to 
a gradual change in the value of the elastic constants which may be 
regarded as continuous functions of the stress-differences; in fact, 
if the departure of Curve I of Fig. 2 from a straight line be 
attributed to a change in the modulus of rigidity, the variation of 
the latter with stress-difference might be deduced from an analysis 
of the curve. The theoretical curve for the radial strain over the 
center of the specimen agrees well with that observed until a load 
of 80,c00 pounds per sq. in. is reached. A curve for the displace- 
ment that would be given if the specimen possessed zero rigidity 
and a Poisson’s ratio of 3 is also shown in the diagram. The depar- 
ture of the observed curve from that obtained on the hypothesis of 
perfect elasticity shows that the rigidity modulus diminishes under 
load and that Poisson’s ratio increases toward the limit $. The 
observations also indicate that when the load is removed the speci- 
men has received a permanent set with a tendency to recovery 
with time, showing an indication of elastico-viscous properties.’ 
The elastic moduli are also permanently changed; a curious fact 
explained by this means is that the specimen after having been 
tested shows a smaller diameter across the center than across the 
ends, whereas the radial displacement was greatest at that point. 
Since the displacements were greatest in the central part of the 
specimen it is reasonable to suppose that the rigidity is permanently 
altered to a lesser value thanin the ends. The result is that when 
the load is removed the lateral pressure exerted by the nickel-steel 
jacket is able to produce a greater displacement at the center of the 
specimen than at the ends, so that a slight waist is produced in 
the rock cylinder. 
«Cf. Filon, loc. cit. 
2G. H. Darwin, “On the Bodily Tides of Viscous and Semi-elastic Spheroids,” 
Phil. Trans. Roy. Soc., CLXX, 17. 
