1 88 APPENDIX I. 



BATTAGLINI (G.) Sul movimento geometrico infinitesimo di un 

 sistemo rigido. 



Estratto dal Rendiconto della JR. Accademia delle Seienze fisiche 

 e Matematiche. (Fascicolo, May 5, 1870). 



This paper and the last belong to a series by the same 

 author, in which the tetrahedron co-ordinates are employed in 

 the analytical development of the statics of a rigid body, as 

 well as the theory of small displacements. 



MANNHEIM (A.) Etude sur h deplacement dune figure de forme in- 

 variable. Recueil des Memoires des Savants etrangers ; t. xx. 

 Journal de l'6cole Polytechnique, cah. 43, pp. 57-122 

 (1870). 



This paper discusses the trajectories of the different points of 

 a body when its movement takes place under prescribed condi- 

 tions. Had I been sooner acquainted with this paper, I should 

 have attributed to M. Mannheim the theorem about the screws 

 of zero pitch on a cylindroid given in 95. Another theorem of 

 the same class is also given by M. Mannheim. When a rigid 

 body has freedom of the third order, then for any point on the 

 surface of a certain quadric* the possible displacements are 

 limited to a plane. 



BALL (R. S.) On the small oscillations of a Rigid Body about a 

 fixed point under the action of any forces, and, more particu- 

 larly, when gravity is the only force acting. Transactions 

 of the Royal Irish Academy, Vol. xxiv., pp. 593-627 

 (January 24, 1870.) 



The principal theorems contained in this paper are demon- 

 strated in 130 of the present volume. 



* The reader \rill easily see that this is the pitch quadric. 



