178 APPENDIX I. 



That this theorem is really due to Chasles there can be little 

 doubt. He explicitly claims it in note 34 to the Aperqu Histo- 

 rique. Three or four years later'than the paper we have cited, 

 Poinsot published his celebrated " Theorie Nouvelle de la Rota- 

 tion des Corps" (Paris, 1834). In this he enunciates the same 

 theorem. As Poinsot does not refer to Chasles, I had been led, 

 in ignorance of Chasles' previous paper, to attribute the theorem 

 to Poinsot (Transactions of Royal Irish Academy, Vol. xxv., 

 p. 1 60); but I corrected the mistake in Phil. Trans., 1874, 

 p. 16. 



MOBIUS (A. F.) Lehrbuch der Statik (Leipzig, 1837). 



This book is, we learn from the preface, one of the numerous 

 productions to which the labours of Poinsot has given rise. 

 The first part, pp. 1-355, discusses the laws of equilibrium 

 of forces, which act upon a single rigid body. The second 

 part, pp. 1-313, discusses the equilibrium of forces acting 

 upon several rigid bodies connected together. The charac- 

 teristic feature of the book is its great generality. I here 

 enunciate some of the principal theorems. 



If a number of forces acting upon a free rigid body be 

 in equilibrium, and if a straight line of arbitrary length and 

 position be assumed, then the algebraic sum of the tetrahedra, 

 of which the straight line and each of the forces in succession 

 are pairs of opposite edges, is equal to zero (p. 94). 



If four forces are in equilibrium they must be generators of 

 the same hyperboloid (p. 177). 



If five forces be in equilibrium they must intersect two 

 common straight lines (p. 179). 



If the lines of action of five forces be given, then a certain 

 plane S through any point P is determined. If the five forces 

 can be equilibrated by one force through P, then this one force 

 must lie in S (p. 180). 



To adopt the notation of Professor Cayley, we denote by 

 12 the perpendicular distance between two lines i, 2, multiplied 

 into the sine of the angle between them (Comptes Rendus, 

 t. Ixi., pp. 829-830). Mobius shows (p. 189) that if forces 



