258 



form of the terms, and the variable part of the arcs on which they de- 

 pend, may be deduced from the theory of equilibrium, yet the constant 

 epoch which occurs in each of these arcs, and which determines when 

 the inequality vanishes, and reaches its maximum, will probably have 

 to be determined, in all cases, by observation. 



In conclusion, the author gives a statement of what appears to 

 him to be the most important steps from which any great improve- 

 ment to our knowledge on the subject of the tides may be hoped ; 

 and recommends the discussion of extensive collections of observa- 

 tions made at a variety of places, in a manner similar to what has 

 been done by Mr. Dessiou with regard to those at London ; and the 

 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. Katharine's docks. 



January 16, 1834. 



JOHN WILLIAM LUBBOCK, Esq., M.A., V.P. and Treasurer, 

 in the Chair. 



A paper was read, entitled, " On a new property of the Arcs of the 

 Equilateral 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 abscissae of an equilateral hyperbola be 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. 



The reading of Mr. Faraday's Sixth Series of Experimental Re- 

 searches in Electricity was commenced. 



January 23, 1834. 

 FRANCIS BAILY, Esq., Vice-President, in the Chair. 



A paper was read, entitled, " 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 Charles 

 G. B. 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. 



