108 



LECTURES 



the square of the distance^ or whether it varied in some more compli- 

 cated ratio of the distance. 



Bouilliau,*a French astronomer, cotemporary with Newton, though 

 older, is said to have been the first to suggest the inverse ratio 

 of the square of the distance as the law of variation, which he did in. 

 1645. Kepler maintained the opinion that the variation was inversely 

 as the distance simply. Hooke made the announcement that he had 

 demonstrated the law to be as the square inversely, but declined show- 

 ing his demonstration, and it finally appeared that he never had one. 

 It, indeed, seemed to be the prevailing opinion that the force must vary 

 inversely as the square of the distance. Wren concurred in this 

 opinion, but he could give no proof. Halley was in the same predica- 

 ment. They had both made the question a subject of special study. 

 Huyghens had once adopted this view of the question, but failing to 

 find any satisfactory proof had rejected it. Such was the state of the 

 problem when Newton entered upon its investigation. The progress 

 and result of his inquiries will always possess a singular interest in 

 the history of astronomy. 



It was in the summer of 1665, when the breaking out of the plague 

 in Cambridge had forced Newton to leave the place, that he retired 

 to his native village of Woolsthorpe. Witnessing the fall of an 

 apple, as the story is usually told and sanctioned by Brewster, 

 he conceived the idea that this same terrestrial gravity which caused 

 the apple to fall, and which certainly extended to the highest attain- 

 able elevations, might extend even to the moon, and be the force 

 which retained her in her orbit. To produce this effect there must 

 be a certain determinate force directed towards the earth, acting 

 constantly upon the moon, and deflecting her from a right line into 

 the curve which forms the orbit. With the distance of the moon and 

 the velocity of revolution this force could easily be computed. It only 

 remained to see whether the terrestrial gravity at that distance was 

 sufficient to produce precisely that effect. 



The principle upon which this conclusion rests will be readily 



understood by reference to figure 7. 

 Let E be the earth, M B a portion 

 of the moon's orbit, and suppose 

 that M B is so small a portion as to 

 be passed over by the moon in one 

 minute of time. It was a well es- 

 tablished principle in mechanics that 

 any body moving in a curved line 

 tends to recede from the centre, and 

 if not constantly restrained by some 

 force, to move in a straight line tan- 

 gent to the curve. Thus if the at- 

 traction of the earth should be sus- 

 pended at the instant the moon 

 reached the point, she would move 

 in the straight line M and not in the curved line M B. Now, if we 



TvaJ 



* Written also Bouilland and Boidliand, born 1605, died 1694. 



