SECT. I. ROTATION AND TRANSLATION. 7 



diameter. Such is the form of the earth and planets. The com- 

 pression (N. 31) or flattening at their poles is, however, so small, 

 that even Jupiter, whose rotation is the most rapid, and there- 

 fore the most elliptical of the planets, may, from his great 

 distance, be regarded as spherical. Although the planets attract 

 each other as if they were spheres, on account of their distances, 

 yet the satellites (N. 32) are near enough to he sensibly affected 

 in their motions by the forms of their primaries. The moon, for 

 example, is so near the earth, that the reciprocal attraction between 

 each of her particles, and each of the particles in the prominent 

 mass at the terrestrial equator, occasions considerable disturbances 

 in the motions of both bodies ; for the action of the moon on the 

 matter at the earth's equator produces a nutation (N. 33) in the 

 axis (N. 34) of rotation, and the reaction of that matter on the 

 moon is the cause of a corresponding nutation in the lunar orbit 

 (N. 35). 



If a sphere at rest in space receive an impulse passing through 

 its centre of gravity, all its parts will move with an equal velocity 

 in a straight line ; but, if the impulse does not pass through the 

 centre of gravity, its particles, having unequal velocities, will have 

 a rotatory or revolving motion, at the same time that it is trans- 

 lated (N. 36) in space. These motions are independent of one 

 another ; so that a contrary impulse, passing through its centre of 

 gravity, will impede its progress, without interfering with its 

 rotation. The sun rotates about an axis, and modern observa- 

 tions show that an impulse in a contrary direction has not been 

 given to his centre of gravity, for he moves in space, accompanied 

 by all those bodies which compose the solar system a circum- 

 stance which in no way interferes with their relative motions ; 

 for, in consequence of the principle that force is proportional to 

 velocity (N. 37), the reciprocal attractions of a system remain the 

 same whether its centre of gravity be at rest, or moving uni- 

 formly in space. It is computed that, had the earth received 

 its motion from a single impulse, that impulse must have passed 

 through a point about twenty-five miles from its centre. 



Since the motions of rotation and translation of the planets are 

 independent of each other, though probably communicated by 

 the same impulse, they form separate subjects of investigation. 



