PHYSICAL ASTRONOMY. 297 



on a solid body like the Earth, it may throw some 

 light on the matter, to inquire into the figure 

 which a homogeneous fluid would put on, its parts 

 being all supposed to gravitate to one another, and 

 at the same time to be under the influence of a 

 centrifugal force, by which they all tended to re- 

 cede from an axis given in position. 



To the equilibrium of a fluid mass, it is necessary 

 that any two columns reaching to the surface from 

 any point in the interior of the fluid, should ba- 

 lance one another, or should press equally on that 

 point. Conversely, when this is the case, however 

 many the forces may be that act on the particles of 

 the fluid, the mass must remain in equilibria. 



It follows from this, when a fluid is at rest its surface 

 is at every point perpendicular to the direction 

 of the diagonal resulting from all the forces which 

 act at that point. 



299* This equilibrium of the columns will take 

 place in a mass of homogeneous fluid revolving 

 on an axis, if it be formed into an oblate sphe- 

 roid, such that the polar semi-axis is to the ra- 

 dius of the equator, as the attraction at the 

 equator diminished by the centrifugal force at 

 the same place, to the attraction at the pole. 



This proposition was first demonstrated by MAC- 

 LAURIN. Fluxions, torn, u, 636 to 641. 



300. Hence 



