APPENDIX. 65 



ftant turned out of its rectilineal courfe. Thus, the curvature 

 of the earth's orbit, or, which is the fame thing, the radius 

 of that orbit, that is, the diftance of the fun from th| earth, 

 would be determined. But the fact is, that the inftantaneous 

 effects of the fun's difturbing force are too minute to be mea- 

 fured ; and that it is only the effect of that force, continued 

 for an entire revolution, or fome confiderable portion of a re- 

 volution, which Aftronomers are able to obferve. 



THERE is yet a greater difficulty which embarraffes the folution 

 of this problem. For, as it is only by the difference of the forces 

 exerted by the fun on the earth and on the moon, that the mo- 

 tions of the latter are difturbed, the farther off the fun is fup- 

 pofed, the lefs will be the force by which he difturbs the 

 moon's motions ; yet that force will not diminifli beyond a 

 fixed limit, and a certain difturbance would obtain, even if the 

 diftance of the fun were infinite. Now the fun is actually 

 placed at fo great a diftance, that all the difturbances, which 

 he produces on the lunar motions are very near to this 

 limit, and therefore a fmall miftake in eftimating their quanti- 

 ty, or in reafoning about them, may give the diftance of the 

 fun infinite, or even impoffible. But all this did not deter Dr 

 STEWART from undertaking the folution of the problem, with 

 no other affiftance than that which Geometry could afford. In- 

 deed, the idea of fuch a problem had firft occurred to Mr MACHIN, 

 1 who, in his book on the Laws of the Moon's Motion, has juft 

 mentioned it, and given the refult of a rude calculation, (the 

 method of which he does not explain) which affigns 8" for 

 the parallax of the fun. He made ufe of the motion of 

 the nodes, but Dr STEWART confidered the motion of the 

 apogee, or of the longer axis of the moon's orbit, as the 

 irregularity' beft adapted to his purpofe. It is well known, 

 that the orbit of the moon is not immoveable, but that, 

 in confequence of the difturbing force of the fun, the long- 

 er axis of that orbit has an angular motion, by which it 



(I) goes 



