16 



or, in other words, the body will at last be brought back to 

 the position from which it set out. 



Finally, it may be mentioned that the author is in posses- 

 sion of a general method for expressing by quaternions the 

 tangent planes and normals to curved surfaces ; and that in 

 applying this method to find the cone of tangents enveloping 

 a given sphere, and drawn from a given point, the geometrical 

 impossibility of the problem, when the point is an internal 

 one, is expressed by the square of a vector becoming in this 

 case positive. 



The special thanks of the Academy were voted to Doctor 

 Simpson of Christiania, for his donation of a^c simile of an 

 Irish MS. in the Library of Copenhagen. 



DONATIONS. 



Statutes of Trinity College (1844), Dublin. 



Catalogue of the Egyptian Manuscripts in the Library of 

 Trinity College, Dublin, By Edward Hincks, D. D. 



A Catalogue of Roman Silver Coins in the Library of 

 Trinity College. Presented by the Provost and Senior 

 Fellows. 



Recueil des Actes de la Seance Publique de VAcademie 

 Imperiale des Sciences de St. Petersbourg, tenue le 29 De- 

 cembre, 1840, et 12 Janvier, 1843. 



Memoires de VAcademie Lnperiale des Sciences de St. 

 Petersbourg ; sixth series. Sciences Mathematiques, torn. 3, 

 livraisons4, 5, 6; torn. 4, livraison 1. Sciences Politiques, 

 torn. 6, livraisons 4, 5, 6 ; torn. 7, livraisons 1, 2, 3. 



