BIBLIOGRAPHICAL NOTES. 523 



LINDEMANN (F.) Ueber unendliclt, kleine Bewegungen und iiber Kraftsysteme bei 

 cdlgemeiner projectivischer Massbestimmung. Math. Ann., Vol. vii., pp. 

 56-143 (July, 1873). 



This is a memoir upon the statics and kinematics of a rigid body in elliptic or 

 hyperbolic space. Among several results closely related to the Theory of Screws, 

 we find that the cylindroid is only the degraded form in parabolic or common space 

 of a surface of the fourth order, with two double lines. Lindemann both by this 

 memoir and by that entitled &quot; Projectivische Behandlung der Mechanik starrer 

 Korper&quot; in the same volume has become the pioneer of an immense and most 

 attractive field of exploration. He has laid down the principles of Dynamics in 

 Non-Euclidian space. One small part of this subject I have endeavoured to 

 develop in Chap. xxvi. 



WEILEK (A.) Ueber die verschiedenen Gattungen der Complexe zweiten Grades. 

 Math. Ann., Vol. vii., pp. 145-207 (July, 1873). 



In this elaborate memoir the author enumerates fifty-eight different species of 

 linear complexes of the second order. The classification is based upon Kummer s 

 surface, which defines the singularities of the complex. These investigations are of 

 importance in the present subject because, to take a single instance, the screws 

 of a system of the fourth order form a linear complex of the second order. This 

 complex is of a special type included among the 58 species. 



BALL (R. S.) Screw Co-ordinates and their applications to problems in the 

 Dynamics of a Rigid Body. Third memoir. Transactions of the Royal 

 Irish Academy, Vol. xxv., pp. 259-327 (January 12, 1874). 



The progress of the present theory was much facilitated by the introduction of 

 screw co-ordinates. The origin and the use of such co-ordinates are here explained. 

 It is, however, to be understood that screw co-ordinates, though no doubt arrived 

 at independently, ought properly to be regarded as an adaptation for dynamical 

 purposes of Klein s co-ordinates of a linear complex referred to six fundamental 

 complexes, of which each pair are in involution or reciprocal, as we say in the 

 terminology of this volume. 



The pitch of a screw a as expressed in terms of its six co-ordinates a,, ... a 6 

 is Sjt^a, 2 where p l ... p 6 , &c. are the pitches of the co-reciprocal screws of reference. 

 The virtual coefficient of two screws a and (3 is 2/^/3,. In the dynamical part 

 of the subject the chief result of this paper is the fundamental theorem that, 

 when the six screws of reference are the six principal screws of inertia, then 

 Pi a D P 2 a 2} P6 a e are the co-ordinates of the impulsive wrench which will make 

 the body commence to move by twisting about the screw a } ... a 6 . 



This was, perhaps, all that could be desired in the way of a simple connexion 

 between an impulsive screw and the corresponding instantaneous screw, so far as 

 their co-ordinates were concerned. Long before this paper was published I had 

 been trying to find a geometrical connexion between two such screws which would 

 exhibit their relation in a graphic manner. But the search was not to be successful 

 until the results in the Twelfth Memoir were arrived at. 



EVERETT (J. D.) On a new met/tod in Statics and Kinematics. (Part I.) 

 Messenger of Mathematics. New Series. No. 39 (1874), 45, 53 (1875). 



The papers contain applications of quaternions. The operator ta + Va- ( ) is a 

 &quot; motor,&quot; -or and a- being vectors, the former denoting a translation or couple, the 



