196 HISTORY OF SCIENCE. 



and Halley, entertained the idea of planetary gravitation, the last two 

 nearly at the period at which it occurred to Newton. It was in the 

 year 1666, after the plague had driven him from Cambridge to his 

 house at Woolsthorpe, that Newton began to reflect upon gravitation 

 as the cause of the planetary motions. There is a well-known story 

 that Newton, sitting one day in his orchard, and observing an apple 

 dropping from a tree, was led by that incident into a train of profound 

 thought, which resulted in the discovery of the system of the world. 

 He was led to reflect that the power which draws heavy bodies to the 

 earth, extends some distance above its surface, even to the tops of the 

 highest mountains ; nay, above them, to the highest regions of the at- 

 mosphere. From this he conjectured that it might extend to the moon ; 

 that it might, in fact, be this very force which retained the moon in her 

 orbit by balancing the so-called centrifugal force. He reflected, also, 

 that although the force drawing bodies to the earth did not appear sen- 

 sibly lessened at the heights to which we could reach, yet these heights 

 were too small to enable us to conclude that the action of this force 

 could be everywhere the same. It remained, therefore, to discover, if 

 possible, the law by which it varied, and, in thinking of this, it occurred 

 to Newton that, if it was the weight of the moon which retained her 

 in her orbit round our earth, it must be a like attraction between the 

 planet Jupiter and his satellites which retained them in theirorbits. Now, 

 the periods in which each satellite revolves about Jupiter being known, 

 and the distances known, it was easy to calculate the relative centrifugal 

 forces which must be balanced by the attraction. Newton found that 

 the attractive force would vary inversely as the square of the distance. 

 Having thus obtained the law of the diminution of the force, it remained 

 to see whether such force of gravity, so acting between the earth and 

 the moon, would correspond with that required for retaining the moon. 

 Now, the moon's distance being known to be 60 semi-diameters of the 

 earth, the effect of gravity ought at that distance to be -geVo^ 1 f that 

 at the earth's surface. The power of gravity being represented by the 

 space through which it will cause a body to fall in one second, or the 

 space through which it would cause the moon to fall from rest in one 

 second, would be less than that which it would cause a body at the 

 surface of the earth to fall through, in proportion as the square of the 

 distance from the centre in the latter case is less than in the former. 



Now, the velocity of the moon in her orbit is known, and this velo- 

 city would of itself, the instant some other force ceased to prevent it, 

 cause our satellite to pass off through space in a straight line. Taking 

 the position of the moon in her orbit at any instant, the distance by 

 which she is during the next second deflected from the straight line 

 or tangent, in order to continue in her orbit, may be considered as the 

 space through which she has fallen towards the earth, as if from rest. 

 Now, the dimensions of the lunar orbit and the moon's velocity in it 

 being known, it was not difficult for Newton to calculate the space 



