2SG 



bring out the full power of the engine j the effect produced being sim- 

 ply that of increasing the speed of the wheel, and not that of the ves- 

 sel. 7thly. An increase of speed will be obtained by reducing the 

 diameter of the wheel ; at least within such limits as allow of the 

 floats remaining sufficiently immersed in the water; and provided the 

 velocity of the engine does not exceed that at which it can perform 

 its work properly. Sthly. An advantage would be gained by giving 

 to the wheel a larger diameter, as far as the immersion of the pad- 

 dles uroduced by loading the vessel would not so sensibly affect the 

 angle of inclination of the paddle ; but this advantage cannot be ob- 

 tained with an engine of the same length of stroke, because in order 

 to allow the engine to make its full number of strokes, it will then be 

 necessary to diminish the size of the paddles, which is a much 

 greater evil than having a wheel of smaller diameter with larger 

 paddles. 



The reading of a paper was then commenced, entitled, " On the 

 Equilibrium of a Mass of Homogeneous Fluid at liberty." Bv James 

 Ivory, Esq., K.H., M.A., F.R.S. 



June 5, 1834. 



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



John Marquess of Breadalbane ; Charles John Lord Teignmouth • 

 the Hon. George Elliot, R.N. ; the Rev. Frederick William Hope, 

 M.A, ; Joseph Jekyll, jun., Esq., M.A. j the Rev. Robert Murphy, 

 M.A.; the Hon. Sir George Rose; Richard Twining, Esq.; William 

 Robert Whatton. Esq.; and George Witt, M.D., were elected Fel- 

 lows of the Society. 



Mr. Ivory's paper, entitled, " On the Equilibrium of a Mass of 

 Homogeneous Fluid at liberty," was resumed and concluded. 



The author shows that Clairaut's theory of the equilibrium of fluids, 

 however seductive by its conciseness and neatness, and by the skill 

 displayed in its analytical construction, is yet insufficient to solve 

 the problem in all its generality. The equations of the upper surface 

 of the fluid, and of all the level surfaces underneath it, are derived, 

 in that theory, from the single expression of the hydrostatic pressure, 

 and are entirely dependent on the differential equation of the surface. 

 They require, therefore, that this latter equation be determinate and 

 explicitly given ; and accordingly they are sufficient to solve the 

 problem when the forces are known algebraical expressions of the 

 co-ordinates of the point of action ; but they are not sufficient when 

 the forces are not explicitly given, but depend, as they do in the 

 case of a homogeneous planet, on the ass umed figure of the fluid. In 

 this latter case, the solution of the problem requires, farther, that the 

 equations be brought to a determinate form by eliminating all that 

 varies with the unknown figure of the fluid ; and the means of doing 



