XI.—On the Practical Application of Reciprocal Figures to the Calculation of Strains on Framework

Abstract

The theory of reciprocal figures used as diagrams of forces was first completely stated by Professor T. Clerk Maxwell, in a paper published in the “Philosophical Magazine,” April 1864. The following definition of reciprocal plane figures, and their application to statics, are there given as follows:—“Two plane figures are reciprocal when they consist of an equal number of lines, so that corresponding lines in the two figures are parallel, and corresponding lines which converge to a point in one figure form a closed polygon in the other.”“If forces represented in magnitude by two lines of a figure be made to act between the extremities of the corresponding lines of the reciprocal figure, then the points of the reciprocal figure will all be in equilibrium under the action of these forces.”The demonstration of this statement is given. The conditions under which stresses are determinate, and some examples of reciprocal figures, are also given in the paper, which leaves nothing to be desired by the mathematician.