Geological Society. 51 



section L — L y/ = 0, L -f L /y = 0, L y + L, y = 0, L, — L,, = 0. 

 First, all six planes of intersection pass through the intersec- 

 tion of the three planes of contact, for their equations are all 

 satisfied by L = 0, L, = 0, L /; = 0. And as before they pass 

 three by three through the same lines. 



Suppose the enveloping surfaces to be cones, and we have 

 a theorem corresponding to Brianchon's. 



Form the reciprocal theorem and we get the following: — 



" Take any three plane sections of a surface of the second 

 degree ; through any two of them a pair of cones can be drawn. 

 The six vertices of these cones are in the same plane, and each 

 set of three on the same right line." They form in fact the 

 angles of a complete quadrilateral. 



How analogous this theorem is to Pascal's, the reader will 

 perceive more plainly if he form a figure. Mark the six sides 

 of a hexagon inscribed in a conic ABCDEF, and the three 

 intersections of opposite sides GHK. Now irmigine the conic 

 to represent a surface of the second degree, A D, B E, C F, 

 three plane sections of it, ABGDE, BCHEF, CDKFA, 

 three cones containing these sections. This theorem asserts 

 that the three vertices GHK are still on a right line. 



M. Poncelet has given this property in his treatise on pro- 

 jective properties, but I do not think it has been perceived 

 how analogous it is to the theorem of Pascal. M. Chasles, 

 for example, has assigned a different theorem as the one cor- 

 responding to Pascal's. As his theorem however only asserts 

 that certain lines are generatrices of the same hyperboloid of 

 one sheet, the analogy can hardly be considered so perfect as 

 in the present instance. 

 Trinity College, Dublin, GEORGE SALMON. 



October 5, 1843. 



XI. Proceedings of Learned Societies. 



GEOLOGICAL SOCIETY. 



Feb. 22, \ PAPER was read "On some new species of Fossil 

 1843*. ■**- Chimaeroid Fishes, with remarks on their general affi- 

 nities," by Sir Philip Grey Egerton, M.P., F.G.S. 



The number of described species of Chim3era— soft-boned fishes 

 of singular forms — is very small, whether existing or extinct. They 

 were first recognised in a fossil state by Dr. Buckland in 1835. 

 The original memoir comprised descriptions of four species ; two 

 others were added by Professor Agassiz. The list was soon after- 

 wards augmented by two species from the Stonesfield slate, con- 

 structed by Dr. Buckland from some enigmatical specimens forwarded 

 by the author under the impression that they had some resemblance 

 to the subjects he was engaged upon. A ninth species came from 



* The President's Annivesary Address, delivered Feb. 17, will be found 

 in Phil. Mag. S. 3. vol. xxii. p. 51 1. 



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