APPENDIX I. 179 



along four lines i, 2, 3, 4 equilibrate, the intensities of these 

 forces are proportional to 



^23.24.14, ^13.14.34, A/12. 14. 24, A/12. 13.23 



It is also shown that the product of the forces on i and 2, 

 multiplied by 12, equals the product of the forces on 3 and 4 

 multiplied by 34. He hence deduces Chasles' theorem (Liou- 

 ville's Journal, t. xii., p. 222), that the volume of the tetrahe- 

 dron formed by two of the forces is equal to that formed by the 

 remaining two. 



i 



MoBlUS (A. F.) Ueber die Zusammensetzung unendlich kleiner 

 Drehungen. Crelle's Journal ; t. 18, pp. 189-212 (Berlin, 

 1838). 



This memoir contains many very interesting theorems, of 

 which the following are the principal : Any given displace- 

 ment of a rigid body can be effected by two rotations. Two equal 

 parallel and opposite rotations compound into a translation. 

 Rotations about intersecting axes are compounded like forces, 

 If a number of forces acting upon a free body make equilibrium, 

 then the final effect of a number of rotations (proportional to 

 the forces) on the same axes will be zero. If a body can be 

 rotated about six independent axes, it can have any movement 

 whatever. 



RODRIGUES (O.) Des lots geometriques quirtgissent les deplacements 

 d'unsysteme solide dans Fespace et de la variation des co-ordon- 

 nees, provenant de ces deplacements considers independamment 

 des causes qui peuvent les produire. Liouville's'Journal ; t. 5, 

 pp. 380-440 (5th Dec., 1840). 



This paper consists mainly of elaborate formulae relating to 

 displacements of finite magnitude. It has been already cited 

 for an important remark ( 12). 



