BIBLIOGRAPHICAL NOTES. 519 



BATTAGI.INI (G.) Sulle dinami in involuzione. Napoli Atti Accad. Sci., iv., 1869 

 (No. 14). Napoli Rendiconto, viii., 1869, pp. 166-167. 



The co-ordinates of a dyname are the six forces which acting along the edges of 

 a tetrahedron are equivalent to the dyname. This memoir investigates the 

 properties of dynames of which the co-ordinates satisfy one or more linear equa 

 tions. The author shows analytically the existence of two associated systems of 

 dynames such that all the dynames of the first order are correlated to all the 

 dynames of the second. These correspond to what we call two reciprocal screw 

 complexes. 



BALL (R. S.) A Problem in Mechanics. To determine the small oscillations of a 

 particle on any surface acted upon by any forces [1869], Quart. Journ. 

 Math., 1870, pp. 220-228. 



With reference to this paper I may mention the following facts connected 

 with the history of the present volume. 



In the spring of 1869 I happened to attend a lecture at the Royal Dublin 

 Society, given by my friend Dr G. Johnstone Stoney, F.R.S. 



For one illustration he used a conical pendulum : he exhibited and explained 

 the progression of the apse in the ellipse described by a heavy ball suspended from 

 a long wire. 



I was much interested by his exposition, and immediately began to work at the 

 mathematical theory of the subject I was thus led to investigate some general 

 problems relating to the small oscillations of a particle on a surface. Certain 

 results, at which I arrived, seemed to me interesting and novel. They appeared 

 in the paper now referred to. This paper was soon followed by another of a more 

 general character and the subject presently began to develop into what was soon 

 after called the &quot;Theory of Screws.&quot; 



BATTAGLINI (G.) Sul movimento geometrico infinitesimo di un sistema rigido. 

 Napoli Rendiconto, ix., 1870, pp. 89-100. Giornale di Matemat., x., 1872, 

 pp. 207-216. 



In this paper tetrahedral co-ordinates are employed in the analytical develop 

 ment of the statics of a rigid body, as well as the theory of small displacements. 

 Besides the papers by this author to which I have specially referred there are 

 several others (generally short) in Napoli Rendiconto, v.-x., both inclusive, which 

 are of interest in connection with the fundamental notions involved in the theory 

 of screws. 



MANNHEIM (A.) Etude sur le deplacement d une figure de forme invariable. 

 Nouvelle methode des normales ; applications diverses. Paris, Acad. Sci. 

 Compt. Rend., Ixvi., 1868, pp. 591-598. Paris, Ecole Polytechn. Journ., 

 cap. 43 (1870), pp. 57-121 ; Paris, Mem. Savants Etrang., xx., 1872, 

 pp. 1-74. 



This paper discusses the trajectories of the different points of a body when its 

 movement takes place under prescribed conditions. It has been already cited 

 ( 121) for a theorem about the screws of zero pitch on a cylindroid. Another 

 theorem of the same class is 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. 



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



