SECT, i.] ATTKACTION OF A SPHERE. 



SECTION I. 



Attraction of a Sphere Form of Celestial Bodies Terrestrial Gravitation 

 retains the Moon in her Orbit The Heavenly Bodies move in Conic 

 Sections Gravitation Proportional to Mass Gravitation of the Particles of 

 Matter Figure of the Planets How it affects the Motions of their Satel- 

 litesRotation and Translation impressed by the same Impulse Motion of 

 the Sun and Solar System. 



IT has been proved by Newton, that a particle of matter 

 (N. 6) placed without the surface of a hollow sphere (N. 7), 

 is attracted by it in the same manner as if the mass of the 

 hollow sphere, or the whole matter it contains, were collected 

 into one dense particle in its centre. The same is therefore 

 true of a solid sphere, which may be supposed to consist of 

 an infinite number of concentric hollow spheres (N. 8). This, 

 however, is not the case with a spheroid (N. 9) ; but the 

 celestial bodies are so nearly spherical, and at such remote 

 distances from one another, that they attract and are attracted 

 as if each were condensed into a single particle situate in its 

 centre of gravity (N. 10) a circumstance which greatly faci- 

 litates the investigation of their motions. 



Newton has shown that the force which retains the moon 

 in her orbit, is the same with that which causes heavy sub- 

 stances to fall at the surface of the earth. If the earth were 

 a sphere, and at rest, a body would be equally attracted, 

 that is, it would have the same weight at every point of its 

 surface, because the surface of a sphere is everywhere equally 

 distant from its centre. But, as our planet is flattened at the 

 poles (N. 11), and bulges at the equator, the weight of the 

 same body gradually decreases from the poles, where it is 

 greatest, to the equator, where it is least. There is, how- 

 ever, a certain mean (N. 12) latitude (N. 13), or part of the 



