THE THEORY OF GRAVITATION. 143 



II. 



The following objection would of course have been raised by some to 

 this view: Part of these atoms must necessarily encounter the moon 

 before reaching the earth, and by their pelting would push her toward 

 us; and on the other hand the force exerted upon those terrestrial 

 objects which she shields would be less because of her interposition. 

 Consequently we ought to see the moon descending and a part of the 

 waters of the ocean rising to meet her, as if rendered lighter by the 

 interception of the atoms, and consequently yielding their place to the 

 adjacent waters. 1 In view of these objections the Epicureans would 

 have had to see if some phenomenon of this nature did not really exist. 

 They would have answered their opponents that the moon did not 

 recede from us on a tangent, but really did approach the earth at each 

 instant, and that the alternating motions of the ocean, so accordant 

 with those of the moon, exhibited this very effect in question, due to 

 the inequality introduced in the stream of atoms by the interposition 



of this great body. 



III. 



The example of a pebble projected horizontally, which circulates for 

 a few moments about the earth before falling, and longer in proportion 

 as the motion is more rapid, would have made it clear that the moon, 

 which occupies but a month in such a great journey, might not of 

 necessity actually approach the earth except in the sense of being 

 nearer than if she had gone off on a tangent. 



IV. 



A persistent antagonist, fortified by some theorems of centrifugal 

 force similar to those of Huygens (which are easily demonstrated by 

 elementary geometry for polygonal orbits such as would result from 

 intermittent collisions) might further have objected that the motion of 

 the moon was still 60 times too slow 2 to prevent her actual approach 

 to us, taking into consideration the very considerable force of gravita- 

 tion found at the surface of the earth. Upon this the Epicureaus 

 would not have been slow to reply that since the distance from the 



1 This is not precisely the actual state of affairs, but it is thus that the case would 

 present itself at first view. As an exact recognition of the laws of this phenomenon 

 would be more slowly acquired than an exact knowledge of the laws of atomism, 

 there would never be a time when that theory would have been found at fault in 

 this respect. 



2 If the force of gravitation were the same at all distances, the period would be 

 reciprocally proportional to the square root of the distance (Hugenii Theor. IV.) 

 Instead of to the three halves power as follows from the Newtonian law (Phil. nat. 

 Princ. Math. Prop. IV. Cor. 6). Then the period of the moon, as compared with that of 

 a body revolving at the surface of the earth, would be expressed by -v/60 instead of 

 60 i/60, the value derived from the Newtonian law of gravitation. 



