32 OF CENTRAL FORCES. 



LECT. portional semidiameter of the moon's orbit would be 

 v^^J^, only a quarter of an inch. For a true figure of the 

 moon's path, I refer the reader to my Treatise of As- 

 tronomy. 



If the moon made any complete number of revolu- 

 tions about the earth in the time that the earth makes 

 one revolution about the sun, the paths of the sun and 

 moon would return into themselves at the end of every 

 year ; and so be the same over again : but they return 

 not into themselves in less than nineteen years nearly ; 

 in which time, the earth makes nearly nineteen revo- 

 lutions about the sun, and the moon 235 about the earth. 

 A double If the planet A 20 be attracted towards the sun, with 

 Force balan- such a force as would make it fall from A to B, in the 

 cesa ( i uad - time that the projectile impulse would have carried it 

 er of gravi- from A to F, it will describe the arc A G by the com- 

 *? bined action of these forces, in the same time that the 



former would have caused it to fall from A to B, or 

 the latter have carried it from A to F. But, if the pro- 

 jectile force had been twice as great, that is, such as 

 would have carried the planet from A to H, in the 

 same time that now, by the supposition, it carries it 

 only from A to F; the sun's attraction must then have 

 been four times as strong as formerly, to have kept the 

 planet in the circle A T W ; that is, it must have been 

 such as would have caused the planet to fall from A to 

 jK, which is four times the distance of A from B, in 

 the time that the projectile force singly would have 

 carried it from A to H, which is only twice the distance 

 of A from JF. " Thus, a double projectile force will 

 balance a quadruple power of gravity in the same cir- 

 cle ; as appears plain by the figure, and shall soon be 

 confirmed by an experiment. 



Note 20. See engraving at page 28. 



Note 21. Here the arcs A G, A I must be supposed to be very small ; 

 otherwise A E, which is equal to // /, will more than quadruple A B, 

 \\hich is equal to F G. 



