A Treatise on the Theory of Screws

PREFACE. j^BOUT thirty years ago I commenced to develop the consequences of certain important geometrical and dynamical discoveries properly associated with the illustrious names of Poinsot and Chasles, Hamilton and Klein. The result of my labours I have ventured to designate as “ The Theory of Screws.” As the theory became unfolded I communicated the results in a long series of memoirs read chiefly before the Royal Irish Academy. To this learned body I tender my grateful thanks for the continual kind- ness with which they have encouraged this work. I published in 1876 a small volume entitled The Theory of Screws: A Study in the Dynamics of a Rigid Body. This contained an account of the subject so far as it was then known. But in a few years great advances were made, the geometrical theories were much extended, and the Theory of Screw-chains opened up a wide field of exploration. The volume just referred to became quite out of date. A comprehensive account of the subject as it stood in 1886 was given in the German work Theoretische Mechanik starrer Systeme: Auf Grund der Methoden und Arbeiten und mit einem Vorworte von Sir Robert S. Ball, herausgegeben von Harry Gravelius, Berlin, 1889. This work was largely a translation of the volume of 1876 supplemented by the sub- sequent memoirs, and Dr Gravelius made some further additions. The theory was still advancing, so that in a few years this considerable volume ceased to present an adequate view of the subject. For example, the Theory of Permanent Screws which forms perhaps one of the most