ATTRACTION OF A SPHERE. SECT. I. 



SECTION I. 



Attraction of a Sphere Form of Celestial Bodies Terrestrial Gravi- 

 tation 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 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 facilitates 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 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, however, a certain mean (N. 12) latitude (N. 13), or 

 part 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 '069 7 is di- 



