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 fac 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 Séance Publique de l Académie 
Imperiale des Sciences de St. Petersboury, tenue le 29 De- 
cembre, 1840, et 12 Janvier, 1843. 
Memoires de I! Académie Imperiale des Sciences de St. 
Petersbourg ; sixth series. Sciences Mathématiques, tom. 3, 
livraisons 4, 5, 6; tom. 4, livraison 1. Sciences Politiques, 
tom. 6, livraisons 4, 5, 6; tom. 7, livraisons 1, 2, 3. 
