The principles set forth in this paper, though now (with the exception of the first theorem) published for the first time, were communicated to the French Academy of Sciences fifteen years ago, in a memoir entitled “de I Equilibre intérieur d'un Corps solide, élastiqne, et homogène,” and marked with the motto, “Obvia conspicimus, nubem pellente Mathesi,” the receipt of which is acknowledged in the Comptes Rendus of the 6th April 1857 (vol. xliv. p. 706.)

The author quotes a theorem discovered by him, and previously published in the Philosophical Magazine for December 1855, called “the Principle of Isorrhopic Axes,” viz., “Every self-balanced system of forces applied to a connected system of points, is capable of resolution into three rectangular systems of parallel self-balanced forces applied to the same points.”