«s«t. iv] DISSERTATION SECOND. 91 



lofty mountains, without its intensity or direction suffer- 

 ing any sensible change, Why may it not reach to a 

 much greater distance, and even to the moon itself? 

 And, if so, may not the moon be retained in her orbit 

 by gravity, and forced to describe a curve like a pro- 

 jectile at the surface of the earth? 1 



Here another consideration very naturally occurred. 

 Though gravity be not sensibly weakened at the small 

 distances from the surface to which our experiments ex- 

 tend, it may be weakened at greater distances, and at 

 the moon may be greatly diminished. To estimate the 

 quantity, of this diminution, Newton appears to have rea- 

 soned thus : If the moon be retained in her orbit by her 

 gravitation to the earth, it is probable that the planets 

 are, in like manner, carried round the sun by a power 

 of the same kind with gravity, directed to the centre of 

 that luminary. He proceeded, therefore, to inquire, by 

 what law the tendency, or gravitation of the planets to 

 the sun, must diminish, in order that, describing, as they 

 do, orbits nearly circular round the sun, their times of 

 revolution and their distances may have the relation to 

 one another which they are known to have from obser- 

 vation, or from the third law of Kepler. 



This was an investigation which, to most even of the 

 philosophers and mathematicians of that age, would have 

 proved an insurmountable obstacle to their farther pro- 

 gress; but Newton was too familiar with the geometry of 

 evanescent or infinitely small quantities, not to discover 

 very soon, that the law now referred to, would require 

 the force of gravity to diminish exactly as the square of 

 the distance increased. The moon, therefore, being dis- 

 tant from the earth about sixty semidiameters of the 



1 Pemberton's View of Newton's Philosophy, Pref. 



