A Treatise on the Theory of Screws

BIBLIOGRAI^HICAL NOTES. 519 Battagi.ini (G.)—Sulle dinami in involuzione. Napoli Atti Accad. Sei., iv., 1869 (No. 14). Napoli Rendiconto, viii., 1869, pp. 166-167. The co-ordinates of a dyname are the six forces which acting along the edges of a tetrahedron are equivalent to the dyuaine. This memoir investigates the properties of dynames of which the co-ordinates satisfy one or more linear equa- tions. The author shows analytically the existence of two associated systems of dynames such that all the dynames of the first order are correlated to all the dynames of the second. These correspond to what we call two reciprocal screw complexes. Ball (R. S.)—A Problem in Mechanics. To determine the small oscillations of a particle on any surface acted upon by any forces [1869], Quart. Journ. Math., 1870, pp. 220-228. With reference to this paper I may mention the following facts connected with the history of the present volume. In the spring of 1869 I happened to attend a lecture at the Royal Dublin Society, given by my friend Dr G. Johnstone Stoney, F.R.S. For one illustration he used a conical pendulum: he exhibited and explained the progression of the apse in the ellipse described by a heavy ball suspended from a long wire. __ , I was much interested by his exposition, and immediately began, to work at the mathematical theory of the subject I was thus led to investigate some general problems relating to the small oscillations of a particle on a surface. Certain results, at which I arrived, seemed to me interesting and novel. They appeared in the paper now referred to. This paper was soon followed by another of a more general character and the subject presently began to develop into what was soon after called the “Theory of Screws.” Battaglini (G )__Sul movimento geometrico infinitesimo di un sistema rigido. Napoli Rendiconto, IX., 1870, pp. 89-100. Giornale di Matemat., x., 1872, pp. 207-216. In this paper tetrahedral co-ordinates are employed in the analytical develop- ment of the statics of a rigid body, as well as the theory of small displacements. Besides the papers by this author to which I have specially referred there are several others (generally short) in Napoli Rendiconto, y.-x., both inclusive, which are of interest in connection with the fundamental notions involved in the theory of screws. Mannheim (A.)—Etude sur le deplacement d’une figure de forme invariable. Nouvelle methode des normales-, applications diverses. Paris, Acad. Sei. Compt. Rend., Ixvi., 1868, pp. 591 598. Paris, Ecole Polytechn. Journ., cap. 43 (1870), pp. 57-121 ; Paris, Mém. Savants Etrang., xx., 1872, pp 1-74. This paper discusses the trajectories of the different points of a body when its movement takes place under prescribed conditions. It has been already cited (R 121) for a theorem about the screws of zero pitch on a cylindroid Another theorem of the same class is given by M. Mannheim. When a rigid body has freedom of the third order, then for any point on the surface of a certain quadric the possible displacements are limited to a plane. The reader will easily see that this is the pitch quadric. _____________________________________________ ______