xxiv 



THE PROGRESS OF 



ure of a degree by Norwood having now fur- 

 nished more exact data, he found that his cal- 

 culation pave the precise quantity for the moon's 

 momentary deflexion from the tangent of her 

 orbit, which was deduced from astronomical ob- 

 fervation. The moon, therefore, has a tendi-m -y 

 to descend to the earth from the same cause that 

 a stone at its surface has ; and if the descent of a 

 stone in a second be diminished in the ratio of 

 1 to 3600, it will give the quantity which the 

 moon descends in a second below the tangent of 

 her orbit. Thus is obtained an experimental 

 proof that gravity decreases as the square of the 

 distance increases. He had already found that 

 the times of the planetary revolutions, supposing 

 their orbits to be circular, led to the same con- 

 clusion. He now proceeded, with a view to the 

 solution of Hooke's problem, to inquire what 

 their orbits must be, supposing the centripetal 

 force to be inversely as the square of the dis- 

 tance, and the initial force to be any whatever. 

 On this subject, we are told, that he composed 

 about a dozen of propositions, probably those at 

 the beginning of the Principia. 



After this noble opening it is very surprising 

 that he again dropt the investigation, and was not 

 induced to take it up again till several years 

 after, when Dr Halley paid him a visit at Cam- 

 bridge, and prevailed upon him to renew and 

 extend his researches. 



He then found that the three laws of Kepler 

 are direct consequences of the system of gravita- 

 tion. He showed that they all followed from the 

 law that the planets gravitate to the sun, with a 

 force inversely as the square of the distances. It 

 added much to this evidence that the observa- 

 tions of Cassini had proved the same laws to pre- 

 vail among the satellites of Jupiter. 



Did the principle which appears to unite the 

 great bodies of the universe act only on these 

 bodies ? Did it reside merely in their centres, or 

 was it a force common to all the particles o: 

 matter? It could hardly be doubted that thii 

 tendency was common to all the particles o 

 matter. For the centres of the great bodies hac 

 no properties but those derived from the particle 

 distributed around them. But the question ad 

 mitted of being brought to a better test than mer 

 abstract reasoning. The bodies between whicl 

 this tendency had been observed to take place 

 were all round bodies, and nearly spherical, am 

 whether large or small, they seemed to gravitate 

 towards each other, according to the same law 

 The planets gravitate to the sun, the moon to the 

 earth, the satellites of Jupiter to that planet an< 

 gravity, in all these cases, varies inversely as th 

 square of the distances. It was, therefore, safe 

 to infer that however small the bodies, provide 

 they were round, they would gravitate to eacl 



tlier with forces varying inversely as the squares 



f the distances. It was probable, then, that 



gravity was the mutual tendency of all the par- 



icles of matter to each other. But this could 



not be concluded with certainty, till it was 



mown whether great spherical bodies, composed 



f particles gravitating according to this law, 



vould themselves gravitate according to the 



ame. 



This problem Newton undertook to solve. He 

 reduced it to the quadrature of curves, and 

 bund, no doubt, with delight, that the law was 

 ,he same for the sphere as for the particles which 

 compose it That the gravitation was directed 

 to the centre of the sphere, and was, as the 

 quantity of matter contained in it, divided by 

 the square of the distance from the centre. Thus 

 a complete expression was obtained for the law 

 of gravity, involving both the conditions on 

 which it must depend, the quantity of matter in 

 the gravitating bodies, and the distance at which 

 the bodies are placed. There could be no 

 doubt that this tendency was always mutual, and 

 there was no exception to the rule that action 

 and re-action are equal. So that if a stone 

 gravitates to the earth, the earth equally gravi- 

 tates to the stone ; or, in other words, the two 

 bodies approach each other with velocities which 

 are inversely as their quantities of matter. 



Newton went further, and showed how the 

 quantity of matter, and even the density of the 

 planets, might be determined. In the way 

 already explained, he was enabled to compare 

 the intensity of the earth's gravitation to the 

 sun, with that of the moon to the earth, each 

 being measured" by the momentary deflexion 

 from the tangent to the small arch of its orbit. 

 A more detailed investigation showed that the 

 intensity of the central force in different orbits, 

 is as the mean distance divided by the square of 

 the periodic time. And the same intensity being 

 also, as the quantities of matter divided by the 

 squares of the distances, it follows that these two 

 quotients are equal to each other; and that, 

 therefore, the quantities of matter are as the 

 mean distances divided by the squares of the 

 periodic times. Supposing, therefore, that the 

 ratio of the mean distance of the sun from the 

 earth, to the mean distance of the moon from 

 the earth is given ; as the ratio of their periodic 

 times is also known, the ratio of the quantity of 

 matter in the sun, to the quantity of matter in 

 the earth, of consequence is found. And the 

 same thing holds in all the planets which have 

 satellites moving round them. Hence also their 

 mean densities, or specific gravities, become 

 known. 



The Principia Philosophies Naturalis, which 

 contained all these discoveries, was published in 



