MATtU 



STAT. 



UBRARY 



PEE FACE. 



A 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 rny labours I have ventured to designate as 

 &quot; The Theory of Screws.&quot; 



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 quite out of date.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 

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