SECT, vi.] ROTATION OF A FLUID MASS. 51 



rotation, it decreases from the equator to the poles, where it 

 ceases. Now it is clear that these two forces are in direct 

 opposition to each other in the equator alone, and that gravity 

 is there diminished by the whole effect of the centrifugal 

 force, whereas, in every other part of the fluid, the centrifugal 

 force is resolved into two parts, one of which, being perpen- 

 dicular to the surface, diminishes the force of gravity ; but 

 the other, being at a tangent to the surface, urges the par- 

 ticles towards the equator, where they accumulate 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 

 greaterthere than else where, but because its whole effect is em- 

 ployed in diminishing gravity, whereas, in every other point of 

 thefluidmass, 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 in- 

 creases towards 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 towards the centre. The lunar inequali- 

 ties also prove the earth to be so constructed ; it was requi- 

 site, 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 centre ; but that the 



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