ON HYDROSTATICS. 199 



bottom will be the same as if the vessel had remained in its original state, 

 'and were filled to the same height with the fluid. (Plate XIX. Fig. 242.) 



In order to understand this the more readily, we may suppose the portion 

 of the fluid, instead of being removed, to have been congealed into a solid mass 

 of equal density ; it is obvious that this congelation of the fluid would not 

 have altered the quantity of its pressure ; it would, therefore, have re- 

 mained in equilibrium with the water below ; the mass might also be 

 united with the sides of the vessel, so as to form a part of it, without in- 

 creasing or diminishing any of the pressures concerned : and we should 

 thus obtain a vessel similar to that which was the subject of our investi- 

 gation, the pressure on the bottom being always the same as if the mass, 

 supposed to be congealed, had remained fluid. Thus, the pressure on the 

 base of a conical or pyramidical vessel, full of water, is three times as 

 great as the weight of the water, since its content is one third of that of a 

 column of the same height, and standing on the same base. (Plate XIX. 

 Fig. 243.) 



In this manner the smallest given quantity of any fluid contained in a 

 pipe may be made to produce a pressure equivalent to any given weight, 

 however large, which rests on the cover of a close vessel communicating 

 with the pipe, and this may be done either by diminishing the diameter of 

 the pipe, and increasing its height, while the weight is supported by a sur- 

 face of a certain extent, or by increasing the magnitude of this surface, 

 without adding to the height of the pipe ; for in either case the ultimate 

 force of the fluid, in supporting the weight, will be equal to the weight of 

 a column of the same height, standing on the whole surface which is sub- 

 jected to its action. And if the effect of the column be increased by any 

 additional pressure, independent of its weight, that pressure may be 

 represented by supposing the height of the column to be augmented ; and 

 the effect of the additional pressure will also be increased in proportion to 

 the magnitude of the surface which supports the weight. It is on this 

 principle that the pressure of water has been applied by Mr. Bramah to 

 the construction of a very convenient press.* (Plate XIX. Fig. 244.) 



Although this property of fluids is the cause of some results which would 

 scarcely be expected by a person not accustomed to reflect on the subject, 

 and has, therefore, not improperly, been called the hydrostatic paradox, 

 yet it depends wholly on the general and acknowledged principles of 

 mechanical forces ; nor can we agree with those authors, who have asserted 

 that a very small quantity of a fluid may, " without acting at any mechani- 

 cal advantage " whatever, be made to balance a weight of any assignable 

 magnitude : for the immediate operation of the force very much resembles, 

 in the most common cases, the effect of a wedge, or of a moveable inclined 

 plane ; thus, a wedge remains in equilibrium, when the forces acting on 

 each side are in proportion to its length, like the hydrostatic pressure on a 

 vessel of a similar form. The conditions of the equilibrium of fluids may 

 also be determined, in all cases, from the general law of the descent of the 

 centre of gravity to the lowest point. Thus, it is easy to show that even 

 when two branches of a tube are of unequal diameter, a fluid must stand at 

 * He obtained a patent for this press in 1796. 



