NEWTON AND THE LAW OF GRAVITATION 



body to fall towards the earth to the distance of thir- 

 teen feet in the first minute of its fall. Would such 

 be the force of gravitation acting at the distance of the 

 moon if the power of gravitation varies inversely as 

 the square of the distance? That was the tangible 

 form in which the problem presented itself to Newton. 

 The mathematical solution of the problem was simple 

 enough. It is based on a comparison of the moon's 

 distance with the length of the earth's radius. On 

 making this calculation, Newton found that the pull of 

 gravitation if that were really the force that controls 

 the moon gives that body a fall of slightly over 

 fifteen feet in the first minute, instead of thirteen feet. 

 Here was surely a suggestive approximation, yet, on 

 the other hand, the discrepancy seemed to be too 

 great to warrant him in the supposition that he had 

 found the true solution. He therefore dismissed the 

 matter from his mind for the time being, nor did he re- 

 turn to it definitely for some years. 



It was to appear in due time that Newton's hy- 

 pothesis was perfectly valid and that his method of 

 attempted demonstration was equally so. The dif- 

 ficulty was that the earth's proper dimensions were 

 not at that time known. A wrong estimate of the 

 earth's size vitiated all the other calculations involved, 

 since the measurement of the moon's distance depends 

 upon the observation of the parallax, which cannot 

 lead to a correct computation unless the length of the 

 earth's radius is accurately known. Newton's first 

 calculation was made as early as 1666, and it was not 

 until 1682 that his attention was called to a new and 

 apparently accurate measurement of a degree of the 



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