134- Royal Society. 



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

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

 An example of these 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 semidi- 

 urnal 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- 

 terised 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 

 undulations above, and two below the equator. The right section 

 of this cone presents two opposite hyperbolas between asymptotes 

 which cross one another at right angles. This cone varies in its 

 breadth in different positions of the sphere : diminishing as the la- 

 titude of the place increases. 



The cones to which the other ancient hour lines belong, are of the 

 same description, having undulations alternately above and below 

 the equator; but they differ from one another in the number of the 

 undulations: and some of these require more than one revolution 

 to complete their surface. The properties of the cones and lines 

 thus generated, may be rendered evident by drawing the sections 

 of the cones on the sphere, in perspective, either on a cylindrical 

 or on a plane surface : several examples of which are given in the 

 paper. ___ 



GEOLOGICAL SOCIETY. 



Dec. 15. A paper was first read, entitled, An Explanatory Sketch 



of a Geological Map of Transylvania, by Dr. Ami Boue", For. Mem. G.S. 



The author premises that this sketch, having been written before his 



specimens 



