44 ROTATION OF A FLUID MASS. SECT. VI. 



ity ; but the other, being at a tangent to the surface, 

 urges the particles toward the equator, where they ac- 

 cumulate till their numbers compensate the diminution 

 of gravity, which makes the mass bulge at the equator, 

 and become flattened at the poles. It appears, then, that 

 the influence of the centrifugal force is most powerful at 

 the equator, not only because it is actually greater there 

 than elsewhere, but because its whole effect is employed 

 in diminishing gravity, whereas, in every other point of 

 the fluid mass, it is only a part that is so employed. For 

 both these reasons, it gradually decreases toward the 

 poles, where it ceases. On the contraiy, gravity is least 

 at the equator, because the particles are farther from 

 the center of the mass, and increases toward the poles, 

 where it is greatest. It is evident, therefore, that, as 

 the centrifugal force is much less than the force of grav- 

 ity gravitation, which is the difference between the 

 two, is least at the equator, and continually increases 

 toward the poles, where it is a maximum. On these 

 principles Sir Isaac Newton proved that a homogeneous 

 fluid (N. 118) mass in rotation assumes the form of an 

 ellipsoid of revolution (N. 119), whose compression is 

 -5 . Such, however, cannot be the form of the earth, 

 because the strata increase in density toward the center. 

 The lunar inequalities also prove the earth to be so con- 

 structed ; it was requisite, therefore, to consider the fluid 

 mass to be of variable density. Including this condition, 

 it has been found that the mass, when in rotation, would 

 still assume the form of an ellipsoid of revolution ; that 

 the particles of equal density would arrange themselves 

 in concentric elliptical strata (N. 120), the most dense 

 being in the center; but. that the compression or flat- 

 tening would be less than in the case of the homogene- 

 ous fluid. The compression is still less when the mass 

 is considered to be, as it actually is, a solid nucleus, de- 

 creasing regularly in density from the center to the sur- 

 face, and partially covered by the ocean, because the 

 solid parts, by their cohesion, nearly destroy that part 

 of the centrifugal force which gives the particles a ten- 

 dency to accumulate at the equator, though not alto- 

 gether ; otherwise the sea, by the superior mobility of 

 its particles, would flow toward the equator and leave 



