SECT. I. UNIVERSAL GRAVITATION. 5 



(N. 16) of 1 to 3600, which is the square of the moon's 

 distance (N. 17) from the earth's center, estimated in 

 terrestrial radii, it is found to be exactly the space the 

 noon would fall through in the first second of her de- 

 scent to the earth, were she not prevented by the cen- 

 trifugal force (N. 18) arising from the velocity with 

 which she moves in her orbit. The moon is thus re- 

 tained in her orbit by a force having the same origin, 

 and regulated by the same law, with that which causes 

 a stone to fall at the earth's surface. The earth may 

 therefore be regarded as the center of a force which 

 extends to the moon ; and, as experience shows that the 

 action and reaction of matter are equal and contrary 

 (N. 19), the moon must attract the earth with an equal 

 and contrary force. 



Newton also ascertained that a body projected (N. 20) 

 in space (N. 21), will move in a conic section (N. 22), if 

 attracted by a force proceeding from a fixed point, with an 

 intensity inversely as the square of the distance (N. 23) ; 

 but that any deviation from that Iftw will cause it to move 

 in a curve of a different nature. Kepler found, by direct 

 observation, that the planets descripe ellipses (N. 24), or 

 oval paths, round the sun. Later observations show 

 that comets also move in conic sections. It consequently 

 follows, that the sun attracts all the planets and comets 

 inversely as the square of their distance? from his cen- 

 ter ; the sun, therefore, is the center of a force extend- 

 ing indefinitely in space, and including all the bodies of 

 the system in its action. 



Kepler also deduced from observation, that the squares 

 of the periodic times (N. 25) of the planets, or the times 

 of their revolutions round the sun, are proportional to 

 the cubes of their mean distances from his center 

 (N. 26). Hence the intensity of gravitation of all the 

 bodies toward the sun is the same at equal distances. 

 Consequently, gravitation is proportional to the masses 

 (N. 27); for, if the planets and comets were at equal 

 distances from the sun, and left to the effects of gravity, 

 they would arrive at his surface at the same time 

 (N. 28). The satellites also gravitate to their primaries 

 (N. 29) according to the same law that their primaries 

 do to the sun. Thus, by the law of action and reaction, 

 Afl 



