A Treatise on the Theory of Screws

524 THE THEORY OF SCREWS. latter a rotation or force. The pitch is <S’ ?. The equation to the central axis is P = F -- - æ<r. 1 he work done in a small motion is - - Sts^. The existence of k equations of the first degree between n motors is the condition of their belonging to a screw system of the first degree, and of order n-k. Several of the leading theorems in screws are directly deduced from motor equations by the methods of determinants. Sturm (Rudolf).—Sulle furze in equilibria. Darmstadt, 1875. This is an interesting geometrical memoir in which the beautiful methods of Möbius in his Lehrbuch der Statik have been followed up. Ball (R. S.)—The Theory of Screws. A study in the Dynamics of a rigid body. Dublin, 8vo., 1876, pp. (1-194). The substance of this volume (now out of print) has been incorporated in the present one. The necessity for a new work on the subject will be apparent from these bibliographical notes, from which it will be seen how much the subject has grown since 1876. It will be here sufficient to give an extract from the preface. “The Theory presented in the following pages was first sketched by the author in a Paper communicated to the Royal Irish Academy on the 13th of November 1871. This Paper was followed by others, in which the subject was more fully developed. The entire Theory has been re-written, and systematically arranged, in the present volume.” “ References are made in the foot-notes, and more fully in the Appendix, to various authors whose writings are connected with the subject discussed in this book. I must, however, mention specially the name of my friend Professor Felix Klein, of Munich, whose private letters have afforded me much valuable informa- tion, in addition to that derived from his instructive memoirs in the pages of the Mathematische Annalen.” An abstract dated Nov. 1875 of the chief theorems in this book has been given in Math. Annalen, Vol. ix., pp. 541-553. Fiedler (W.)—Geometrie und Geomechanik. Vierteljahr Schrift der natur for sehenden Gesellschaft in Zürich (1876), xxi. 186, 228. This valuable paper should be studied by any one desirous of becoming acquainted with the history of the subject. Dr Fiedler has presented a critical account of the manner in which the Theory of Screws has grown out of the works of the earlier mathematicians who had applied the higher geometry to Dynamics, especially Chasles, Poinsot, Mobius and Pliicker. The paper contains an account of the chief results in the Theory so far as they were known in 1876. Many of the investigations are treated with much elegance, as might indeed have been expected from a mathematician so accomplished as the German translator of Dr Salmon’s great works. Rittershaus (T.)—Die Kinematische Kette, ihre Beweglichkeit und Zwangläufig keit. Der Civilingenieur, Vol. xxii. (1877). This is the study of the kinematics of three rigid bodies whereof the first and second are hinged together, as are also the second and third. The cylindroid is employed to obtain many theorems. Of course it will be understood that the “Kinematische Kette” is a conception quite distinct from that of the Screw-chain discussed in the present volume (Chap. xxiv.). In a further paper (Zoc. cit. xxiv. 1878) the author develops cases in which the conditions are of increased generality.