34-6 Mr. Ivory's Bemarfo on the TJieory 



forces acting upon every particle in the outer surface, shall be 

 perpendicular to that surface ; and we may suppose that this 

 condition is expressed by the equation 



where <p is a function of the three rectangular co-ordinates of 

 a point in the surface, and C an arbitrary quantity introduced 

 in the integration. All the level surfaces will be determined 

 by the same equation, the function p remaining the same, 

 while C decreases by insensible degrees : whence it follows 

 that the resultant of "the accelerating forces will be perpendi- 

 cular to every level surface ; and that every level stratum will 

 press equally upon the fluid below it. In this first case there- 

 fore, in which the level strata act upon one another only by 

 pressure, there is no doubt that all the conditions of equili- 

 brium are contained in the equation of the outer surface ; which 

 is agreeable to the received theory. 



We may next suppose, as in Newton's theory of the earth, 

 a homogeneous fluid mass subjected to a centrifugal force, and 

 to an attraction between the particles in the inverse propor- 

 tion of the square of the distance. The condition that the re- 

 sultant of the accelerating forces is perpendicular to the outer 

 surface, will, as before, be expressed by an equation, viz. 



? = C: 

 and the several level surfaces will be determined by making 

 C decrease by insensible degrees. In the interior of the fluid 

 body, the gravitation, or the resultant of the accelerating forces, 

 at any level surface, will be perpendicular to it; and hence 

 the thin level stratum immediately above, will press equally 

 Upon the fluid below. But it is to be observed that the pres- 

 sure is caused by the gravitation at the level surface acting 

 upon the matter of the thin stratum above, and that it is inde- 

 pendent of any active forces inherent in the matter of the 

 stratum. Wherefore, since every particle attracts every other 

 particle, the level stratum will act upon the fluid below it 

 both by pressure and by attraction ; and, in this respect, there 

 is an essential difference between the present case and the for- 

 mer one. There are here two distinct forces independent of 

 another ; and the adjustment of the equilibrium requires that 

 both be taken into account. The equality of pressure is a 

 consequence of the equation of the outer surface; but the 

 equilibrium with respect to the attractive forces of the stratum 

 can be obtained only by supposing that the stratum has such 

 a figure as to attract all particles in the inside with equal 

 forces in opposite directions. The received theory is there- 

 fore defective and insufficient in the case of a homogeneous 



fluid 



