180 APPENDIX I. 



CHASLES (M.) Proprietes geometriques relatives au mouvement in- 

 finiment petit cTun corps solide libre dans. Vespace. Comptes 

 Rendus; t. xvi., pp. 1420-1432 (1843). 



A pair of " droites conjugue"es" are two lines by rotations 

 about which a given displacement can be communicated to a 

 rigid body. Two pairs of " droites conjugue"es" are always 

 generators of the same hyperboloid. 



POINSOT (L.) Th&orie nouvelle de la rotation des corps. Liouville's 

 Journal ; t. xvi., pp. 9-129, 289-336 (March, 1851). 



This is Poinsot's classical memoir, which contains his beau- 

 tiful geometrical theory of the rotation of a rigid body about a 

 fixed point. In a less developed form the Theory had been pre- 

 viously published in Paris in 1834, as already mentioned. 



CAYLEY (A.) On a new analytical representation of curves in space 

 Quarterly Mathematical Journal; Vol. iii., pp. 225-236 

 (1860). Vol. v., pp. 81-86. 



In this paper the conception of the six co-ordinates of a line is 

 introduced for the first time. 



SYLVESTER (J. J.) Sur T involution des lignei droites dans Tespace* 

 considerees comme des axes de rotation. Comptes Rendus ; 

 t. Hi., pp. 741-746 (April, 1861). 



Any small displacement of a rigid body can generally be 

 represented by rotations about six axes (Mobius). But this is 

 not the case if forces can be found which equilibrate when 

 acting along the six axes on a rigid body. The six axes in 

 this case are in involution. The paper discusses the geometrical 

 features of such a system, and shows, when five axes are given, 

 how the locus of the sixth is to be found. Mobius had shown 

 that through any point a plane of lines can be drawn in involu- 

 tion with five given lines. The present paper shows how the plane 

 can be constructed. All the transversals intersecting a pair of 

 conjugate axes are in involution with five given lines. Any 

 two pairs of conjugate axes lie on the same hyperboloid. 



