ON THE LIMITING STRENGTH OF ROCKS UNDER CON- 
DITIONS OF STRESS EXISTING IN THE 
EARTH’S INTERIOR 
LOUIS VESSOT KING, B.A. (Cantab.) 
Lecturer in Physics, McGill University, Montreal 
§ 1. INTRODUCTION 
One of the most important problems in geophysics is to obtain 
a knowledge of the limiting strength of the material forming the 
solid core of the earth as well as that of the principal rocks forming 
its crust. According to the modern theory of elasticity the tend- 
ency of a solid to rupture is measured by the maximum difference 
of the greatest and least principal stresses. This criterion first 
due to Tresca and followed by Sir G. H. Darwin" has been found by 
J. J. Guest? to give the best agreement with observed results from 
experiments on metal tubes subjected to various systems of com- 
bined stress. Coulomb’s suggestion that the greatest shear pro- 
duced in a material is a measure of its tendency to rupture leads 
to a result substantially the same as that given by the hypothesis 
of maximum stress-difference. This follows from the theorem; 
that the shearing stress at any point Is greatest on a plane whose 
normal lies in the plane of the axes of the algebraically greatest 
and algebraically least stress and bisects the angle between them, 
its value being half the algebraic difference between these stress- 
intensities. The family of surfaces whose tangent planes satisfy 
the above condition determines the surfaces along which flaws will 
develop or the material commence to rupture. These surfaces are 
are called surfaces of maximum shear. 
The difficulty in the way of the practical application of these 
criteria lies especially in the determination of the numerical values 
of the limiting stress-difference for different materials. For the 
t Darwin, “On the Stresses Produced in the Interior of the Earth by the Weight 
of Continents and Mountains,” Phil. Trans. Roy. Soc., CLX XIII (1882). 
2 Guest, Phil. Mag. (Ser. 5), XLVIII (1900). 
3 Minchin, Staizcs, 4th ed., 1889, II, 425. 
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