A Treatise on the Theory of Screws

BIBLIOGRAPHICAL NOTES. I here briefly refer to the principal works known to me which bear on the subject of the present volume. Poixsot (L.)—Sur la composition des moments et la composition des aires (1804). Journal de 1’Ecole Polytechnique; vol. vi. (13 cah.), pp. 182-205 (1806). In this paper the author of the conception of the couple, and of the laws of composition of couples, has demonstrated the important theorem that any system of forces applied to a rigid body can be reduced to a single force, and a couple in a plane perpendicular to the force. Chasles (M.)—Note sur les propriétés generales du Systeme de deux, corps semblables entr’eux et places d’une maniére quelconque dans Vespace ; et sur le déplace- ment fini ou infiniment petit d’un corps solide libre. Férussac, Bulletin des Sciences Mathérnatiques, Vol. xiv., pp. 321-326 (1830). The author shows that there always exists one straight line, about which it is only necessary to rotate one of the bodies to place it similarly to the other. Whence (p. 324) he is led to the following fundamental theorem :— L'on peut toujowrs transporter un corps solide libre d’une position dans une autre position quelconque, determines par le mouvement continu d’une vis ä laquelle ce corps serait fixe invariablement. Three or four years later than the paper we have cited, Poinsot published his celebrated Theorie Nouvelle de la Rotation des Corps (Paris, 1834). In this he enunciates the same theorem without reference to Chasles, but that it is really due to Chasles there can be little doubt. He explicitly claims it in note 34 to the Aperqu Historique. Bruxelles Mém. Couronn. xi., 1837. Hamilton (W. R.)—First supplement to an essay on the Theory of Systems of Rays. Transactions of the Royal Irish Academy, Vol. xvi., pp. 4—62 (1830). That conoidal cubic surface named the cylindroid which plays so fundamental a part in the Theory of Screws was first discovered by Sir William Rowan Hamilton. In his celebrated memoir on the Theory of Systems of Rays he demonstrates the remarkable proposition which may be thus enunciated :— The lines of shortest distance between any ray of the system and the other contiguous rays of the system have a surface for their locus, and that surface is a cylindroid. We can illustrate this as follows by the methods of the present volume. The Hamiltonian system of rays here considered form a congruency. If we