Geological Society. 225 



comparison with one another of the empirical laws resulting from 

 their separate investigation. Very valuable materials for this purpose, 

 he expects, will hereafter be furnished by the observations now making, 

 on a judicious system, at the St. Katharines' docks. 



Jan. 16, 1834. — "On a new property of the Arcs of the Equi- 

 lateral Hyperbola." By Henry Fox Talbot, Esq., M.P., F.R.S. 



By an analytical process, the author arrives at the following theorem, 

 namely, if three abscissa; of an equilateral hyperbola are materially 

 dependent by reason of two assumed equations, which are symmetrical 

 with respect to these three abscissae, the sum of the arcs subtended 

 by them is equal to three quarters of the product of the same ab- 

 scissae, or only differs therefrom by a constant quantity. In order to 

 satisfy himself of the correctness of this theorem, the author calculated 

 various numerical examples, which entirely confirmed it. This simple 

 result is essentially a relation between three arcs of the equilateral 

 hyperbola, and is by no means reducible to a relation between two ; 

 and therefore is not reducible to the celebrated theorem of Fagnani, 

 concerning the difference of two arcs of an ellipse or hyperbola, nor 

 to any other known property of the curve. 



Appendix to a Memoir, lately read to the Society, on the Quality 

 and Quantity of the Gases disengaged from the Hot Spring of the 

 King's Bath, in the City of Bath. By G. B. Charles Daubeny, M.D., 

 F.R.S. 



The author has lately examined two tepid springs, which, since the 

 setting in of the wet weather, have broken out at the foot of St. 

 Vincent's rocks, Clifton, immediately below the Cliff, against which 

 the suspension bridge over the Avon is designed to abut. The tem- 

 peratures of the springs were 72° and 66° respectively ; and the gas 

 consisted of 92 parts of nitrogen, eight of oxygen, and three of car- 

 bonic acid. The author deduces from these facts arguments in con- 

 firmation of the views he has stated in the paper to which this is an 

 appendix. ■ 



GEOLOGICAL SOCIETY. 



Dec. 18, 1833. — A memoir " On the Geology of the Banks of the 

 Indus, the Indian Caucasus, and the Plains of Tartary to the Shores 

 of the Caspian," by Lieut. Alexander Burnes, was then read. 



The author has endeavoured in this paper to embody the geolo- 

 gical observations which he made on a journey during the years 1831 

 and 1832, up the river Indus and across the lofty range of Hindoo 

 Koosh to the Caspian Sea. 



He first describes the province of Cutcli, situated near the eastern 

 mouth of the Indus. lie states that it is mountainous; that the 

 soil is either rocky or sandy, with masses of lava scattered over its 

 surface; and that sulphur, coal, iron and alum are found in the 

 district. 



Nuinmulitcs occur in a ridge near the right banks of the Indus. 

 The dulta of the river is composed of a succession of beds of 

 earth, clay and sand of different colours, sometimes parallel, and 

 sometimes having one stratum dovetailed into another. The sea 



Third Series. Vol. 4. No. 21. March 183 1. 2 G 



