POSITION OF DOUBLE STARS. 253 



If, in confequence of our former arguments, and the prefent Obfervatlons and 

 remarks, we place £ Bootis among the ftars which hold a fmaller f^^^i^^g ^he " 

 one in combination, we may delineate its. orbit as in Plate VIII. change of rela-, 

 -n- Q ' tive fituation in 



*^^S' '^' ' / ftars extremely . 



Let P N F S reprefent a circle, projeded into the elliptical near each other, 



orbit axx'bcd. e is the large ftar ; and x xf are the firfl and 

 lafl meafured north preceding iiluations of the fmall one, as 

 given in the following table. 



The real motion from h to h' is projected into that from x to 

 x' I and, while the elliptical arch fubtends an angle of 12^' 33', 

 the circular one will be about 4'^ 50'. 



From the figure of the orbit, w^e may conclude that the fmall 

 flar, in its firft pofition, at x or A, was not more than between 

 30 and 40 years pall its conjundlion; and that, confequently, 

 the parts of the arch x a/, were nearly proportional to the times 

 of their being defcribed. The pofitions have been calculated 

 upon this principle; but with fome allowance for the firft ob- 

 ferved angle, which I fuppofe to have been a little too fmall ; 

 and, though the differences of the obferved and calculated 

 angles are pretty eonfiderable, the obfervations are ftill fuffi- 

 ciently confiftent to prove the gradual change of the fituation 

 of the fmall fi:ar. * . . 



The quantity of the change in 22 years and 207 days, will 

 Ihow that a periodical revolution cannot take up lefs than 1681 

 years. The real figure and fituation of the orbit, with many 

 other particulars, are ftill unknown ; it is, therefore, unneceff 

 fary to point out the uncertainties in which the inveftigation of 

 the periodical time of the fmajl ftar about « Bootis muft long 

 remain involved. 



^ Herculis^ 



