II. On the mathematical theory of the stability of earth-work and masonry

Abstract

In the preparation of my course of lectures, I have found it necessary to re-investigate much of the above-named branch of mechanics, and I have now a paper in preparation on the subject, which I propose to offer to the Royal Society when it is ready. In the meanwhile, it appears to me that the two fundamental principles on which my researches are based are of such a nature, that they may very properly be communicated to the Royal Society at once. They are as follows:― I. Principle o f the Stability of Earth . At each point in a mass of earth the directions of greatest and least compressive stress are at right angles to each other; and the condition of stability is, that at each point the ratio of the difference of those stresses to their sum shall not exceed the sine of the angle of natural slope of the earth.