JPOSITION 0F DONBLE STARS. 221 



fituatlon, the angle PaO will be more than 90 degrees. The Obfervations 



** , r- 1 ^"'^ inferences 



Itar X being lets than a, renders this hypolhefis the more refpeaing the 

 plAufible. Now, as a motion of Caftor, be it real or apparent, changes of re- 

 has adlually been afcertained, we cannot fet it alide ; the real j„ ^^^^^ extreme^ 

 motion of O, therefore, in order to account for the apparent one ly near eachi 

 of a, muft be of equal velocity, and in a contrary direction :° "* 

 that is, when decompofed, (y',l05 towards/, and (^\\2, to- 

 wards s. The effedl of the fun's moving from O towards/, 

 according to the 1ft Table in No. 3, is, that the diflance be- 

 tween the two liars will be diminifhed, and the angle of pofi- 

 tion increafed. But thefe are both contrary to the obferva- 

 tions I have given. The motion of O in declination towards 

 *, according to the fame Table, will ftill diminifh the diftance 

 of the two liars, but will alfo dirainifli the angle of pofition. 

 Then, lince a motion in right afcenfion increafes the angle, 

 while that in decimation diminiflies it, the fraall ftar may be 

 placed at fuch a dillance that the difTerence in the parallax, 

 arifing firom the folar mbtion, fhall bring the angle of pofition, 

 in 23f years, from 32^ 47' to 10" 53' ; which will explain the 

 obferved charige of that angle. The di fiance of the dar x, 

 for this purpofe, muft be above 2| times as much as that of 

 a from us. But, after having in this manner accounted for 

 the alteration of the angle of pofition, we are, in the next 

 place, to examine the effe6l which fuch a difference of parallax 

 muft produce in the apparent diftance of the two ftars from 

 each other. By a graphical method, which is quite fufficient 

 for our purpofe, it appears, that the union of the two motions 

 in right afcenfion and declination, muft have brought the 

 two ftars fo near, as to be only about half a diameter of the 

 large ftar from each other ; or^ to exprefs the fame in mea- 

 furesi the centers of the fiars muft now be V',S nearer than 

 they were 23| years ago. But this my obfervations cannot 

 allow ; for we have already fhown, that any change of more 

 than 3 or 4-tenths of a fecond muft have been perceived. 



If, on the other hand, we place the ftar x at fuch a diftance 

 that the folar parallax may only bring it about 4-tenths of a 

 fecond nearer to a, which is a quantity we may fuppofe to 

 have efcaped our notice in eftiraating the apparent diftance of 

 the two ftars, then will the angle of pofition be above 20 

 degrees too large. This fhows, that no diftance, beyond Caftor, 

 at which we can place the ftar, will explain the given obferva- 

 tions, • ^ 



