The Stresses in Masonry Dams

Abstract

I DO not think that Prof. Pearson proves his point. Is it not an axiom of practical mathematics that nearly identical functions (within certain limits) may have widely different second differentials? Between o and, for example, a parabola can be found differing but little from sin x. To show that the stresses and are widely different in a plate dam and in a complete dam, it would therefore seem essential to integrate the two equations given by Prof. Pearson in his last letter, and to compare these integrals, or else to decide the matter on other considerations. The integration is, I understand, impracticable, and this being so, the argument in my letter of January 2 would seem to apply. It was to the effect that if in the case of a plate it is permissible to write throughout, then to the same order of approximation the stresses and are the same in the plate dam and in the actual structure. If the stresses and are zero in the case of the plate, then the stresses which are developed when the lamina forms part of the complete structure cannot, themselves, give rise to any such shears as or and as the dam is not constrained at top or flanks, it is difficult to see how, in the absence of these shears, the stresses and can be affected. Certainly not by the 30 per cent, which Prof. Pearson gives as the order of the error.