526 THE THEORY OF SCREWS. 



Constraint of the most general nature cannot, however, be so produced. It is 

 sufficient to mention that in the case of freedom of the fifth order the screw 

 reciprocal to the system must have zero pitch, if the constraint is of the nature 

 supposed by Schell, while in the general case the pitch may have any value. 



BALL (R. S.) On Homographic Screw Systems. Proceedings of the Royal Irish 

 Academy, Ser. 2, Vol. iii. p. 435 (1881). 



The theory of Homographic Screws shows the connection between certain 

 geometrical theories of an abstract nature and Dynamics. The intimate alliance 

 between geometry and the higher branches of Rigid Dynamics is illustrated in this 

 paper. Invariant functions of eight screws are studied, and a generalized type of 

 homographic ratio involving eight screws is considered. (See Chap, xix.) 



BALL (R. S.) On the Elucidation of a question in Kinematics by the aid of Non- 

 Eiiclidian Space. Report of British Association, York, 1881, p. 535. 



Certain peculiarities which presented themselves in the geometrical representa 

 tion of the screws of a three-system by points in a plane are here shown to be due 

 to the conventions of Euclidian space. The screws of a three-system in non- 

 Euclidian space can be arranged in equal pitch hyperboloids, which have eight 

 common points and eight common tangent planes. In Euclidian space the cor 

 responding quadrics are inscribed in a common tetrahedron and pass through 

 four common points as explained in Chap. xv. 



BALL (R. S.) Certain Problems in the Dynamics of a Rigid System moving in 

 Elliptic Space. (Fifth Memoir.) Transactions of the Royal Irish Academy, 

 Vol. xxviii., pp. 159-184 (1881). 



The chief theorem proved in this paper is, that though the virtual moment of 

 two homonymous vectors is zero only when the two vectors are &quot;rectangular,&quot; yet 

 the virtual moment of two heteroriymous vectors is always zero. 



I may here mention another memoir which bears on the same subject. The 

 title is, On the Theory of the Content. Transactions of the Royal Irish Academy, 

 Vol. xxix., pp. 123-181 (1887). 



In this it is shown that the order in which two heteronymous vectors in 

 elliptic space are applied to a rigid system may be inverted without affecting 

 the result, which is, however, not a vector at all. On the other hand, when two 

 homonymous vectors in elliptic space are applied to a rigid system, the result is, 

 in every case, a homonymous vector ; but then the order of application could not 

 be inverted without changing the result. 



These papers have contributed to Chap. xxvi. of the present volume. 



PADELETTI (Dino) Osservazioni sulla teoria delle dinami (Theory of Screws). 

 Rendiconto della R. Accademia di Scienze Fis. e Nat. di Napoli, Fascicolo 

 2 Feb. 1882. 



The author here gives a general account of the Theory of Screws so far as it 

 had been developed up to 1876. The method he has employed for deducing the 

 equations of the cylindroid is novel and instructive. The same author in the same 

 journal for May 1882 has a paper entitled, Su un Calcolo nella teoria delle 

 dinami analogo a quello dei quaternioni. 



