brium and at liberty, shall be perpendicular to that surface : and it 

 is grounded on this, that the forces must have no tendency to move 

 a particle in any direction upon the surface, that is, in a plane touch- 

 ing the surface. 



In the Principia, Sir Isaac Newton assumes that the earth, sup- 

 posed a homogeneous mass of fluid in equilibrium, has the figure of 

 an oblate elliptical spheroid of revolution which turns upon the less 

 axis : and, in order to deduce the oblateness of the spheroid from 

 the relation between the attractive force of the particles, and their 

 centrifugal force caused by the rotatory velocity, he lays down this 

 principle of equilibrium, that the weights or efforts of aU the small 

 columns extending from the centre to the surface, balance one an- 

 other round the centre. The exactness of this principle is evident 

 in the case of the elliptical spheroid, from the symmetry of its figure : 

 and it is not difficult to infer that the same principle is equally true 

 in every mass of fluid at liberty and in equilibrium by the action of 

 accelerating forces on its particles. In every such mass of fluid, the 

 pressure, which is zero at the surface, increases in descending below 

 the surface on all sides : from which it follows that there must be a 

 point in the interior at which the pressure is a maximum. Now 

 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 sufli- 

 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 j^rin- 

 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 from 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 



