S22 Royal Society. 



surface, D = the distance between the opposed points, F = the 

 force of attraction. 



For the direct induction : 



For the reflected induction : 



For the attractive force between a charged and a neutral free 



conductor : 



Q2 T 

 F = — F . 



For the force between two unchangeable surfaces, one positive 

 the other negative : 



2. " On the Conditions of Equilibrium of an Incompressible Fluid, 

 the particles of which are acted upon by Accelerating Forces," By 

 James Ivory, Esq., K.H., M.A., F.R.S., &c. 



The intention of this paper is to examine the principles and me- 

 thods that have been proposed for solving the problem of which it 

 treats, with the view of obviating what is obscure and exceptionable 

 in the investigation usually given of it. 



The principle first advanced by Huyghens is clearly demonstrated, 

 and is attended with no difficulty. This principle requires that the 

 resultant of the forces in action at the surface of a fluid in equili- 

 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 «f the particles, and their 

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

 principle of equilibrium, that the weights or efforts of all 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 



