BIBLIOGRAPHICAL NOTES. 527 



Cox (Homersham) On the application of Quaternions and Grassmann s Aus- 

 dehnungslehre to different kinds of Uniform Space. Cambridge Philosophical 

 Transactions, Vol. xiii., Part n., pp. 69-143 (1882). 



So far as the Theory of Screws is concerned the chief result in this paper is 

 the demonstration that the homologue of the cylindroid in non-Euclidian space 

 which Lindemann had already shown to be of the fourth degree may be represented 

 by the equation 



The function known as the sexiant ( 230) is here generalized into the corre 

 sponding function of six screws in non-Euclidian space. It is of course a 

 fundamental theorem that a ray crossing two screws of equal pitch meets the 

 cylindroid again in a third screw which it cuts perpendicularly ( 22). This is here 

 generalized into the theorem that a transversal across two screws of equal pitch on 

 the cylindroid in elliptic space intersects that surface also in two other generators 

 which are conjugate polars with respect to the absolute. 



I may take this opportunity to observe that the function 4 which enters 



1-po.p? 

 into the above equation of the surface has an instructive property. If pa. and pp 



be transformed into ~ - an d -s-^- - respectively, where m is different from 



mp a 



unity, then the above function is unaltered. Hence it follows that if the pitch p 

 of every screw on a screw-system of the nth order in non-Euclidian space receive 



/v\ .1 n-y* 



the transformation into ~ - then the screws so altered will still constitute an 

 1 + mp 



w-system. Thus we generalize that well-known feature of an ?^-system of screws 

 in ordinary space which asserts that if the pitches of the screws in an n-system be 

 augmented by a constant the screws so altered will remain an w-system. (See 

 Proceedings of the Royal Irish Academy, 2nd Series, Vol. iv., p. 256 (1884).) 



PADELETTI (Dino) Sulla piu semplice forma dell equazioni di equilibrio di un 

 sistema rigido vincolato. Rendiconto della R. Accaclemia Scienze Fis. e 

 Mat. di Napoli, Fascicolo 1, 1883. 



In this short paper the author discusses separately two different cases of 

 freedom and by the aid of the reciprocal screw-system gives in each case the 

 equations of equilibrium. 



HEATH (R. S.) On the Dynamics of a Rigid Body in Elliptic Space. Phil. Trans. 

 Part n., 1884, pp. 281-324. 



&quot;The special features of the method employed are the extensive use of the 

 symmetrical and homogeneous system of coordinates given by a quadrantal tetra 

 hedron, and the use of Professor Cay ley s co-ordinates in preference to the Rotors 

 of Professor Clifford to represent the position of a line in space.&quot; The Theory of 

 Screws is considered and the nature of the cylindroid in Elliptic Space discussed. 

 The general equations of motion referred to any moving axes are then found, and 

 in a particular case they reduce to a form corresponding to Euler s equations. 

 When there are no acting forces these equations are solved in terms of the theta- 

 functions. This paper has been already cited in 412, 420. 



