OF CENTRAL FORCES. 31 



irregular curve, and not a true circle, round the sun : it LECT. 



n 

 being tne common center of gravity of the earth and 



moon that will then describe the same circle which the 

 earth would have moved in, if it had not been attended 

 by a moon. For, supposing the moon to describe a 

 quarter of her progressive orbit about the earth in the 

 time that the earth moves from e to f; it is plain, that 

 when the earth comes iof, the moon will be found at r; 

 in which time, their common center of gravity will have 

 described the dotted arc R 1 T, the earth the curve R 5/. 

 and the moon the curve q 14 r. In the time that the 

 moon describes another quarter of her orbit, the center 

 of gravity of the earth and moon will describe the dotted 

 arc T 2 U, the earth thecurvey 6 g, the moon the curve 

 r 15 s, and so on. And thus, whilst the moon goes once 

 round the earth in her progressive orbit, their common 

 center of gravity describes the regular portion of a cir- 

 cle R I T2 U 3 F4 W, the earth the irregular curve 

 R 5f6 g 7 h 8 i, and the moon the yet more irregular 

 curve q 14 r 15 s 16 t 17 u ; and then the same kind of 

 tracks over again. 



The center of gravity of the earth and moon is 6000 

 miles from the earth's center towards the moon ; there- 

 fore the circle 5 13 which the earth describes round that 

 center of gravity (in every course of the moon round 

 her orbit) is 12000 miles in diameter. Consequently 

 the earth is 12000 mil' s nearer the sun at the time of 

 full moon than at the time of new. [See the earth aif 

 and at h. 



To avoid confusion in so small a figure, we have sup- 

 posed the moon to go only twice and a half round the 

 earth, in the time that the earth goes once round the 

 sun : it being impossible to take in all the revolutions 

 which she makes in a year, and to give a true figure of 

 her path, unless we should make the semidiameter of 

 the earth's orbit at least 95 inches ; and then, the pro- 



