Sir Isaac Newton 11 



completed there seemed to be a discrepancy of about 11 per 

 cent, between the value of gravity at the surface of the earth 

 as deduced from the moon's orbit, and that which can be 

 observed directly. It has even been said that, for a time, 

 he rejected the theory altogether, but there is reason for 

 believing that the delay was due to one uncertain step in the 

 argument which might have caused an error and accounted 

 for the disagreement. Newton consequently deferred publi- 

 cation until he could satisfy himself with regard to this 

 doubtful point. The attraction of the earth as a whole is 

 made up of the attraction of its separate parts. When the 

 attracted body is at a distance, no great error can be committed 

 by assuming the earth's mass to be concentrated at its centre, 

 but it might be otherwise, if it is near the surface. Ulti- 

 mately, Newton proved that, when the law of attraction 

 is that of the inverse square, we may indeed take the 

 attraction of a sphere at all distances to be the same as that 

 of an equal mass placed at its centre. The real cause of the 

 disagreement was then found to be the inaccurate value 

 originally adopted for the circumference of the earth. When 

 the measurements of Picard became known the agreement 

 was found to be complete. 



The importance of Newton's discovery extended far 

 beyond its immediate results; its wider and far-reaching 

 effect lay in the demonstration it supplied that by means 

 of a rigorous mathematical analysis the facts of Nature can 

 be represented not only in the vague speculative manner 

 which then was considered sufficient by the majority of 

 philosophers, but definitely and quantitatively, allowing 

 a numerical test to be applied. Apart from the philosophic 

 value of a rigorous treatment, the human mind is always 

 strongly (on occasions too strongly) impressed by numerical 

 coincidences. Newton's investigation which enabled him to 

 calculate the force of gravity at the earth's surface from the 

 time of revolution of the moon therefore carried conviction, 

 and was accepted by the majority of his countrymen ; but 

 it took some time before the continent of Europe gave its 

 full assent, and the criticisms which were raised illustrate 

 the danger of taking up too definite an attitude with regard 

 to the ultimate starting point representing the simple 



