6 TERRESTRIAL GRAVITATION. [SECT. i. 



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 dis- 

 tance (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 (N. 16) of 1 to 3600, 

 which is the square of the moon's distance (N. 17) from the 

 earth's centre, estimated in terrestrial radii, it is found to be 

 exactly the space the moon would fall through in the first 

 second of her descent to the earth, were she not prevented 

 by the centrifugal 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 centre 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 at- 

 tract 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 at- 

 tracted 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 law will cause it to move in a 

 curve of a different nature. Kepler found, by direct ob- 

 servation, that the planets describe 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 distances from its centre ; the sun, therefore, 

 is the centre of a force extending 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 



