BIBLIOGRAPHICAL NOTES. 533 



CAYLEY (A.} Non-Euclidian Geometry. Transactions of the Cambridge Philo 

 sophical Society, Vol. xv., pp. 37-61 (1894). Read Jan. 27, 1890. See 

 also Collected Papers, Vol. xiii., p. 480. 



This is perhaps the best paper in the English language from which to obtain a 

 general view of the Non-Euclidian Geometry. The development is here conducted 

 mainly along geometrical lines. On this account a study of this paper is specially 

 recommended in connection with Chap. xxvi. of the present volume. 



BUDDE (E.) Allgemeine Mechanik der Punkte und starren Systeme. 2 vols. 8vo. 

 Berlin, 1891. 



This comprehensive work may be cited in illustration of progress made in the 

 use of the Theory of Screws in advanced text-books of Dynamics in Germany. 

 There is an excellent account of the theory of the cylindroid in Vol. n., pp. 

 596-603. The only exception, and it is a very small one, which I feel inclined to 

 take to this part of Professor Budde s work is that he speaks of the composition of 

 Screws. It seems to me better to preserve the notion of a screw as simply a 

 geometrical entity and to speak of the composition rather of twists or of wrenches 

 on the screws than of composition of the screws themselves. Vol. n. pp. 639-644 

 gives an account of the fundamental parts of the theory of reciprocal screw 

 systems. The geometrical construction for the cone of screws which can be drawn 

 through any point reciprocal to a cylindroid ( 22), and which was originally given 

 in the Theory of Screws, 1876, p, 23, has been here reproduced. A good account 

 is also given, Vol. n., pp. 905-908, of the geometrical theory of the restraints of 

 the most general type. This subject is developed both by the elegant methods of 

 Mannheim and also by those of the Theory of Screws. 



ROUTH (E. J.) Treatise on Analytical Statics, Vol. i., 2nd Edition, 1896. 



In this standard work several of the fundamental Theorems of the Theory of 

 Screws will be found. See pp. 202-208. 



KLEIN (.}Nicht-Euclidische Geometric : Vorlesuny. 188990. Ausgearbeitet von 

 Fr. Schilling. Gottingen, 1893. 



This is a lithographed record of Klein s lectures. It is invaluable to any one 

 who desires to become acquainted with the further developments of that remark 

 able Theory which is of such great importance in the subject of this volume as in 

 so many other departments of Mathematics. The bearing of the Theory of Screws 

 in its relation to the Non-Euclidian geometry is discussed by the author. 



BURNSIDE (W.) On the Kinematics of Non-Euclidian Space, London Math. Soc. 

 Proceedings, xxvi. 33-56, Nov. 1894. 



The paper consists of a number of applications of a construction for the 

 resultant of two displacements (or motions), the construction being formally 

 independent of the nature of the space, Euclidian, elliptic or hyperbolic, in which 

 the motions are regarded as taking place. 



II. of the paper gives the application to elliptic space. The main point 

 in this case is to deduce synthetically, from the construction, the existence of finite 

 motions which correspond to the velocity-systems that Clifford has called ri&amp;lt; r ht- 

 and left-vectors (the same words are here applied to the Unite displacements 

 themselves). This deduction is materially aided by considering the system of 

 equidistant surfaces of a given pair of conjugate lines, the two sets of generators 

 on which constitute respectively the right-parallels and the left-parallels of the 



