ACCORDANCE OF QUANTITATIVE THEORIES, &c. 195 



square of the distance held true, and the reputed distance 

 of the moon was correct, he could infer that the moon 

 ought to fall towards the earth at the rate of fifteen feet 

 in one minute. Now, the actual divergence of the moon 

 from the tangent of its orbit appeared to amount only to 

 thirteen feet in one minute, and there was a discrepancy 

 of two feet in fifteen, which caused Newton to lay ' aside 

 at that time any further thoughts of this matter/ Many 

 years afterwards, probably fifteen or sixteen years, Newton 

 obtained more precise data from which he could calculate 

 the size of the moon's orbit, and he then found the dis- 

 crepancy to be inconsiderable. 



His theory of gravitation was then verified so far as 

 the moon was concerned ; but this was to him only the 

 beginning of a long course of deductive calculations, each 

 ending in a verification. If the earth and moon attract 

 each other, and also the sun and the earth, similarly there 

 is no reason why the sun and moon should not attract 

 each other. Newton followed out the consequences of 

 this inference, and showed that the moon would not move 

 as if attracted by the earth only, but sometimes faster 

 and sometimes slower. Comparisons with Flamsteed's 

 observations of the moon showed that such was the case. 

 Newton argued again, that as the waters of the ocean are 

 not rigidly attached to the earth, they might attract the 

 moon, and be attracted in return, independently of the 

 rest of the earth. Certain daily motions would then be 

 caused thereby exactly resembling the tides, and there 

 were the tides to verify the fact. It was the almost 

 superhuman power with which he traced out geome- 

 trically the consequences of his theory, and submitted 

 them to repeated comparison with experience, which con- 

 stitutes his pre-eminence over all philosophers b . 



The whole progress of physical astronomy has consisted 

 b ' Elementary Lessons in Logic,' p. 262. 

 2 



