ATTRACTION OP A SPHERE. SKCT. I. 



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 

 Satellites Rotation and Translation impressed by the same Impulse 

 Motion of the Sun and Solar System. 



IT has been proved by Newton, that a particle of mat- 

 ter (N. G) 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 con- 

 tains, were collected into one dense particle in its center. 

 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 center 

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

 tates 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 substances 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 center. 

 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, however, a 

 certain mean (N. 12) latitude (N. 13), or pait of the earth 

 intermediate between the pole and the equator, where 

 the attraction of the earth on bodies at its surface is the 

 same as if it were a sphere ; and experience shows that 

 bodies there fall through 16-0697 feet in a second. The 

 mean distance (N. 14) of the moon from the earth is 

 about sixty times the mean radius (N. 15) of the earth. 

 When the number 16-0697 is diminished in the ratio 



