lb 



Rapport sur le Prix de Statistique (decerne a l'ouvrage de M. Falret, 

 sur les alienes, les suicides, et lesmorts subites). 4to. — The Aca- 

 demy. 



Eloge Historique de L. F. E. Baron Ramond. Par M. le baron 



Cuvier. 4to. — The Academy. 

 Eloge Historique de M. Bosc. Par M. le baron Cuvier. 4to. — The 



Academy. 



Discours de M. Feletz, Chancelier, prononce aux Funerailles de 

 M. le baron Fourier. 4to. — The Academy. 



Discours de M. Girard, President de l'Academie des Sciences, pro- 

 nonce aux Funerailles de M, le baron Fourier. 4to. — The Aca- 

 demy. 



Memoire Physiologique sur le Cerveau. Par M. Magendie. 4to. — 



The Academy. 



A Paper was read, " On the Hour Lines of the Ancients." By W. 

 A. Cadell, Esq. F.R.S. 



The hour lines on the sundials of the ancient Greeks and Romans 

 correspond to the division of the time between sun-rise and sun-set 

 into twelve equal parts, which was their mode of computing time. 

 An example of the.se hour lines occurs in an ancient Greek sundial, 

 forming part of the Elgin collection of marbles at the British Mu- 

 seum, and which there is reason to believe had been constructed 

 during the reign of the Antonines. This dial contains the twelve 

 hour lines drawn on two vertical planes, which are inclined to each 

 other at an angle of 106° ; the line bisecting that angle having 

 been in the meridian. The hour lines actually traced on the dial 

 consist of such portions only as were requisite for the purpose the 

 dial was intended to serve: and these portions are sensibly straight 

 lines. But the author has shown, in a paper published in the Trans- 

 actions of the Royal Society of Edinburgh, that if these lines are 

 continued through the whole zone of the rising and setting semi- 

 diurnal arcs, they will be found to be curves of double curvature on 

 the sphere. In the present paper the author enters into an inves- 

 tigation of the course of these curves; first selecting as an example 

 the lines indicating the 3rd and the 9th hours of the ancients. 

 These lines are formed by the points of bisection of all the rising 

 and setting semidiurnal arcs ; commencing from the southern point 

 where the meridian cuts the horizon, and proceeding till the line 

 reaches to the first of the always apparent parallels, which, being a 

 complete circle, it meets at the end of its first quadrant. At this 

 point the branch of another and similar curve is continuous with it : 

 namely, a curve which in its course bisects another set of semi- 

 diurnal arcs, belonging to a place situated on the same parallel of 

 latitude as the first, but distant from it 180° in longitude. Conti- 

 nuing to trace the course of this curve, along its different branches, 

 we find it at last returning into itself, the whole curve being charac- 

 terized by four points of flexure. If the describing point be consi- 

 dered as the extremity of a radius, it will be found that this radius 

 has described, in its revolution, a conical surface with two opposite 



