SECT. I. TERRESTRIAL GRAVITATION. 5 



rninished 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 retained 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 expe- 

 rience 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 law will cause it to move in a curve of a different 

 nature. Kepler found, by direct observation, 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 revo- 

 lutions round the sun, are proportional to the cubes of their mean 

 distances from its centre (N. 26). Hence the intensity of gravi- 

 tation of all the bodies towards 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 gravi- 

 tate 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, each body is itself the centre of an attractive force ex- 

 tending indefinitely in space, causing all the mutual disturbances 

 which render the celestial motions so complicated, and their in- 

 vestigation so difficult. 



