GRAVITY. 



or'particles of matter in the universe tend 

 towards one another. 



The existence of the same principles of 

 gravitation in the superior regions of the 

 heavens as on the earth is one of the 

 great discoveries of Newton, who made 

 the proof of it as easy as that on the earth. 

 This was at first only a conjecture in his 

 mind ; he observed, that all bodies near 

 the earth, and in its atmosphere, had the 

 property of tending directly towards it ; 

 he soon conjectured, that it probably ex- 

 tended much higher than to any distance 

 to which we could reach to make experi- 

 ments ; and so on, from one distance to 

 another, till he at length saw no reason 

 why it might not extend to the moon, by 

 means of which she might be retained in 

 her orbit, as a stone in a sling is retained 

 by the hand ; and if so, he next inferred, 



Shy might not a similar principle exist in 

 e other great bodies in the universe, the 

 sun, and all the other planets, both pri- 

 mary and secondary, which might all be 

 retained in their orbits, and perform their 

 revolutions by means of the same univer- 

 sal principle of gravitation. 



He soon realized and verified these by 

 mathematical proofs. Kepler had found 

 out, by contemplating the motions of the 

 planets about the sun, that the area de- 

 scribed by a line connecting the sun and 

 planet, as this revolved in its orbit, was 

 always proportional to the time of its de- 

 scription, or that it described equal areas 

 in equal times, in whatever part of its or- 

 bit the planet might be, moving always as 

 much the quicker as its distance from the 

 sun was less. And it is also found, that 

 the satellites, or secondary planets, re- 

 spect the same law in revolving about 

 their primaries. But it was soon proved, 

 by Newton, that all bodies moving in any 

 curve line described on a plane, and 

 which, by radii drawn to any certain point, 

 describes areas about the point propor- 

 tional to the times, are impelled or acted 

 on by some power tending towards that 

 point. Consequently, the power by which 

 all these planets revolve, and are retained 

 in their orbits, is directed to the centre 

 about which they move, viz. the primary 

 planets to the sun, and the satellites to 

 their several primaries. 



Again, Newton demonstrates, that if 

 several bodies revolve with an equal m 3- 

 tion in several circles about the same cen- 

 tre, and that if the squares of their perio- 

 dical times be in the same proportion as 

 the cubes of their distances from the com- 

 mon centre, then the centripetal forces 



of the revolving bodies, by which they 

 tend to their central body, will be in the 

 reciprocal or inverse ratio of the squares 

 of the distances. But it had been agreed 

 on by the astronomers, and particularly 

 Kepler, that both these cases obtain in all 

 the planets ; and therefore he inferred, 

 that the centripetal forces of all the pla- 

 nets were reciprocally proportional to 

 squares of the distances from the centres 

 of their orbits. 



Upon the whole, it appears that the 

 planets are retained in their orbits by 

 some power which is continually acting 

 upon them : that this power is directed 

 towards the centre of their orbits: that 

 the intensity or efficacy of this power in- 

 creases upon an approach towards the 

 centre, and diminishes on receding from 

 the same, and that in the reciprocal du- 

 plicate ratio of the distances; and that by 

 comparing this centripetal force with the 

 force of gravity on the earth, they are 

 found to be perfectly alike, as may easily 

 be shown in various instances. For ex- 

 ample, in the case of the moon, the near- 

 est of all the planets, the rectilinear spaces 

 described in any given time, by a body 

 urged by any power, reckoning from the 

 beginning of its descent, are porportion- 

 ate to those powers. Consequently, the 

 centripetal force of the moon, revolving 

 in its orbit, will be to the force of gravity 

 on the surface of the earth as the space 

 which the moon would describe in falling, 

 during any small time, by her centripetal 

 force towards the earth, if she had no mo- 

 tion at all, to the space a body near the 

 earth would describe in falling by its gra- 

 vity towards the same. 



Now, by an easy calculation of these 

 two spaces, it appears that the former 

 force is to the latter as the square of the 

 semi-diameter of the earth is to the square 

 of that of the moon's orbit. The moon's 

 centripetal force, therefore, is equal to 

 the force of gravity; and consequently 

 these forces are not different, but they 

 are one and the same ; for if they were 

 different bodies, acted on by the two pow- 

 ers conjointly, they would fall towards the 

 earth with a velocity double to that aris- 

 ing from the sole power of gravity. 



It is evident, therefore, that the moon's 

 centripetal force, by which she is retained 

 in her orbit, and prevented from running 

 off in tangents, is the very power of gra- 

 vity of the earth extended thither. See 

 " Newton's Principia," lib. i. prop. 45, cor. 

 2. and lib. iii. prop. 3 ; where the numeral 

 calculation may be seen at full length. 



