SECT. VI. ROTATION OF A FLUID MASS. 45 



the force of gravity ; but the other, being at a tangent to the sur- 

 face, urges the particles towards the equator, where they accu- 

 mulate 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 towards the poles, where it 

 ceases. On the contrary, gravity is least at the equator, because 

 the particles are farther from the centre of the mass, and increases 

 towards the poles, where it is greatest. It is evident, therefore, 

 that, as the centrifugal force is much less than the force of 

 gravity gravitation, which is the difference between the two, is 

 least at the equator, and continually increases towards the poles, 

 where it is a maximum. On these principles Sir Isaac Newton 

 proved that a homogeneous fluid (N. .119) mass in rotation 

 assumes the form of an ellipsoid of revolution (N. 120), whose 

 compression is ^B. Such, however, cannot be the form of the 

 earth, because the strata increase in density towards the centre. 

 The lunar inequalities also prove the earth to be so constructed ; 

 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 (N. 120) ; that the particles of equal 

 density would arrange themselves in concentric elliptical strata 

 (N. 121), the most dense being in the centre ; but that the com- 

 pression or flattening would be less than in the case of the 

 homogeneous fluid. The compression is still less when the mass 

 is considered to be, as it actually is, a solid nucleus, decreasing 

 regularly in density from the centre to the surface, 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 tendency to accumulate at the equator, though not 

 altogether ; otherwise the sea, by the superior mobility of its 

 particles, would flow towards the equator and leave the poles 

 dry. Besides, it is well known that the continents at the 

 equator are more elevated than they are in higher latitudes. It 

 is also necessary for the equilibrium of the ocean that its density 



