Jf22 CAUSE »F THE CHANGES OP RELATITB 



Obfervationi C^) The laft rernaining trial we have to examine, is to fupi 



TtfptklnTthl P°^®'^ ^^ be nearer than »; the angle P aO, will then be lefa 

 changes of rela- than 90 degrees ; and the effe6l of a motion of O towards/, 



ftlr^ «Trerely'" ^^ ^^^ ^"^ ^^^^^ '" ^°' ^* "^'^^ ^^ ^" increafe of the diftanc« 

 ■ear each other, o^ ^he two ftars, and a diminution of their angle of pofition. 

 But tiie motion O^, which is alfo to be confidered, will add to 

 the fncreafe of the diftance and counteract the diminution of 

 the angle. It is therefore to be examined, whether fuch an 

 increafe of .diftance as we can allow to have efcaped obferva- 

 tion, will explain the change which we know to have hap- 

 pened in the angle, during the laft 23 1 year. By the fame 

 method of compounding the two motions as before, it imme- 

 diately appears, than we cannot place the fmall ftar more than 

 about 1 -tenth of the diftance Oa on the fide of Caftor, with^ 

 out occafioning fuch an increafe of the apparent diftance of 

 the two ftars as cannot poffibly be admitted ; and that, even 

 then, the angle of pofition, inftead of being lefs, will be a 

 few degrees larger, at the end of 23f years, than it was at 

 the beginning. This hypothefis, therefore, like all the fore- 

 going ones, muft alfo be given up, as inconfiftent with my 

 obfervations. 



It is moreover evident, that the obfervations of aftronomers 

 on the proper motion of the ftars in general, will not permit 

 us to aflume the folar motion at pleafure, merely for the fake of 

 accounting for the changes which have happened in the ap- 

 pearances of a double ftar. The proper motion of Caftor, 

 therefore, cannot be intirely afcribed to a contrary motion of 

 the fun. For we can affign no reafon why the proper motion 

 of this ftar alone, in preference, for inftance, to that of Arc- 

 turus, of Sirius, and of many others, Iliould be fuppofed to 

 arife from a motion of the folar fyftem. Now, if they are all 

 equally intitled to partake of this motion, we can only admit 

 it in fuch a direction, and of fuch a velocity, as will fatisfy 

 mean direction and velocity of the general proper motions of 

 the ftars ; and place all deviations to the account of a real 

 proper motion in each ftar feparately. 



Double Motion, 

 (/) In order to explain the phenomena of our double ftar, 

 according to No. 4, by the motion of two bodies, for inftancft 

 « and Xf it will be required that they both (hould move in given 



4 diredions^j 



