.22 Report S.A.A. Advancement of Science. 



proof demonstrating that if the planets move according to Kepler's 

 laws they must move under the influence of a force directed towards 

 the Sun and varying inversely as the square of the distance from the 

 Sun. 



Having obtained this law, Newton sought to verify it, and to 

 ascertain whether the attractive force of the Earth is similar in 

 kind to that of the Sun, and whether, therefore, the Moon moves 

 round the Earth in obedience to the same law. He had first to 

 prove, and with some difficulty and delay did prove mathematically, 

 that the attraction of a globe is the same as if its matter were all 



• concentrated at its centre. This dune, he obtained a measure of the 

 attractive force of the Earth at a distance from its centre equal to 

 its radius, by determining experimentally that any heavy body near 

 the Earth's surface droi)ped from a height would fall from rest about 

 16 feet in the first second of time; or, if the law of inverse squares 

 Avere true, the amount of fall would increase as the square of the 

 time, so that the fall of a heavy budy near the Earth's surface in 60 

 seconds would be 60-, or 3.600 times 16 feet. 



In Newton's time it was fairly well known that the mean distance 



• of the Moon from the Earth is approximately 60 radii of the Earth. 

 Therefore the force of the Earth's attraction on the Moon would 



^be 1/60- or 1/3600 part of that which it exerts on a body near the 

 Earth's surface. In other words, the Moon would fall towards the 

 Earth just as far in a minute of time as a stone near the Earths 

 surface would fall in a second of time — that is to say, 16 feet. 



Xewton next compared this hypothetical fall of the Moon 

 towards the Earth in a minute of time with the actual deflection 

 of the Moon's orbit from a straight line in the same unit of time. 

 With the data at his disposal he found the computed actual fall to be 

 13 feet instead of :6 feet, as he had determined that it should be 

 if his hypothesis was correct. 



Newton regarded this discrei)anc\ as so fatal that, in his own 

 words, he "laid aside at that time an\ further thought about the 

 matter."' 



In 1672 the result of Picards new measurement of an Arc of 

 Meridian in France was communicated to the Royal Society, and it 

 shewed that the length of a degree, instead of being 60 miles as 

 Newton had accepted it to be, was in fact 69 ^\ miles. Newton 

 does not appear to have known of Picard's result until his attention 

 was called to it by a letter from Hooke in 1679, and then Newton 

 at once realized its important influence on his original conclusions. 

 His previous unit of measure for the dimensions of the Moon's orbit, 

 and therefore for the actual fall of the Moon towards the Earth in 

 a minute of time, was erroneous by 16 per cent. It is said that Newton 

 was so excited when making the comparatively simple calculation 

 required to ascertain the effect of the new data upon his original 

 ronclusions. that he was unable to comjjlete it, and had to ask a 

 friend to do it for him. The result shejwed that, with the new data, 

 the actual fall of the Moon towards the Earth in a minute of time 

 -v'.-'p t6 feet per minute, agreeing exactly with the amount calculated 



