Mr. Ivorj on the Equilibrium of an Incompressible Fluid. 323 



this point of maximum pressure, or centre, is impelled equally in all 

 directions by all the small columns standing upon it and reaching to 

 the surface ; and as the pressure in every one of these columns in- 

 creases continually from the surface to the centre, it follows that 

 the central point sustains the total effect of all the forces which 

 urge the whole body of fluid. It follows also, from the property of 

 a maximum, that the central point may be moved a little from its 

 place without any variation of the pressure upon it : which proves 

 that the forces at that point are zero. Thus the point of maximum 

 pressure is in stable equilibrium relatively to the action of the whole 

 mass of fluid : which establishes Newton's principle of the equi- 

 ponderance of the central columns in every instance of a fluid in 

 equilibrium and at liberty. 



The two principles of Huyghens and Newton being established 

 on sure grounds, the next inquiry is, whether they are alone suffi- 

 cient for determining the figure of equilibrium. Of this point there 

 is no direct and satisfactory investigation : and, in applying the two 

 principles to particular cases, it has been found that an equilibrium 

 determined by one, is not in all cases verified by the other ; and 

 even in some instances, that there is no equilibrium when both prin- 

 ciples concur in assigning the same figure to the fluid. Further re- 

 searches are therefore necessary to dispel the obscurity still inherent 

 in this subject. 



In a mass of fluid in equilibrium, if we suppose that small canals 

 are extended fi'om a particle to the surface of the mass, the particle 

 will be impelled with equal intensity by all the canals : for, other- 

 wise, it would not remain immoveable, as an equilibrium requires. 

 It has been inferred that the equal pressures of the surrounding fluid 

 upon a particle are sufficient to reduce it to a state of rest. Hence 

 has arisen the principle of equality of pressure, which is generally 

 admitted in this theory. Now, if the matter be considered ac- 

 curately, it will be found that the only point within a mass of fluid 

 in equilibrium which is at rest by the sole action of the surrounding 

 fluid, is the central point of Newton, or the point of maximum- 

 pressure. The reason is that, on account of the maximum, the 

 pressure of all the canals terminating in the central point, increases 

 continually as the depth increases ; so that, besides the pressures of 

 the canals, there is no other cause tending to move the particle. 

 With respect to any other particle, the pressure caused by the action 

 of the forces in some of the canals standing upon the particle, will 

 necessarily increase at first in descending below the surface, and 

 afterwards decrease ; so that the effective pressure transmitted to 

 the particle, is produced by the action of the forces upon a part only 

 of the fluid contained in such canals. If a level surface be drawn 

 through any particle, it is proved in the paper, that the equal press- 

 ures of the surrounding fluid on the particle, are caused solely by 

 the forces which urge the portion of the fluid on the outside of the 

 level surface, the fluid within the surface contributing nothing to the 

 same effect. Thus a particle in a level surface is immoveable by the 

 direct and transmitted action of the fluid on the outside of the level 



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