524 THE THEORY OF SCREWS. 



latter a rotation or force. The pitch is S . The equation to the central axis is 



p = V xtr. The work done in a small motion is S-m^ S-ar^ . The existence 



&amp;lt;r 



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). Sulleforze in equilibrio. Darmstadt, 1875. 



This is an interesting geometrical memoir in which the beautiful methods of 

 Mobius 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. 



&quot;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.&quot; 



&quot; 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.&quot; 



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.) Geometric und Geomechanik. Vierteljahrschrift der naturforschenden 



Gesellschaft in Zurich (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, Hire Beweglichkeit und Zwanglaufig 



keit. Der Civilingenieur, Vol. xxn. (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 

 &quot;Kinematische Kette&quot; is a conception quite distinct from that of the Screw-chain 

 discussed in the present volume (Chap. xxiv.). In a further paper (lac. cit. xxiv. 

 1878) the author develops cases in which the conditions are of increased generality. 



