THE TIDES 317 



square of the one number to the square of the other. The 

 forces are inversely as the squares of the distance, that 

 is the most commonly quoted part of the law of gravitation; 

 but the law is incomplete without the first part, which estab- 

 lishes the relation between two apparently different prop- 

 erties of matter. Newton founded this law upon a great 

 variety of different natural phenomena. The motion of the 

 planets round the sun, and the moon round the earth, proved 

 that for each planet the force varies inversely as the square 

 of its distance from the sun; and that from planet to planet 

 the forces on equal portions of their masses are inversely 

 as the squares of their distances. The last link in the great 

 chain of this theory is the tides. 



(2) Tide-Generating Force. And now we are nearly 

 ready to complete the theory of tide-generating force. The 

 first rough view of the case, which is not always incorrect, 

 is that the moon attracts the waters of the earth towards 

 herself and heaps them up, therefore, on one side of the 

 earth. It is not so. It would be so if the earth and moon 

 were at rest and prevented from falling together by a rigid 

 bar or column. If the earth and moon were stuck on the two 

 ends of a strong bar, and put at rest in space, then the 

 attraction of the moon would draw the waters of the earth 

 to the side of the earth next to the moon. But in reality 

 things are very different from that supposition. There is 

 no rigid bar connecting the moon and the earth. Why then 

 does not the moon fall towards the earth? According to 

 Newton's theory, the moon is always falling towards the 

 earth. Newton compared the fall of the moon, in his cele- 

 brated statement, with the fall of a stone at the earth's sur- 

 face, as he recounted, after the fall of an apple from the 

 tree, which he perceived when sitting in his garden musing 

 on his great theory. The moon is falling towards the earth, 

 and falls in an hour as far as a stone falls in a second. 

 It chances that the number 60 is nearly enough, as I have 

 said before, a numerical expression for the distance of the 

 moon from the earth in terms of the earth's radius. It is 

 only by that chance that the comparison between the second 

 and hour can be here introduced. Since there are 60 times 

 |6o seconds in an hour, and about 60 radii of the earth in 



