POSITION OF DOUBLE STARS* ♦ 



259 



lamed, that the vacancy between the apparent diameters, Obfcrvationsand 



when the firft angle of pofition was taken, was | diameter of j-pg^^""^^^' 



the fmall flar; aaid the lall angle of pojSt ion being 6° Sl^changcsof rela- 



. foulh following, with a diliance between the ftars of | diame- ^^^ fituation In 

 ,r n • r , "^''^ extremely 



. terot the fmall itar, we obtain (he two points or centres of the near each other. 



fmall ftars ^cjc', through which an ellipfis abxx'cd maybe 

 drawn about 7. This will be the apparent orbit in which the 

 fmall ftar will be feen to move about 7, by an eye placed at O. 

 And the inclination of the orbit to the line in which we fee the 

 double flar, will be had fufficienlly accurate to enable us to give 

 a calculation of the feveral angles of pofition that have been 

 taken. The ellipfis we have delineated ftiews that the fmall 

 flar, in its firtl fituation x, could not be much paft its conjunc- 

 tion at b, and that, confequently, in palling from x to x\ the 

 • parts of the apparent elliptical arch, which are projedions of 

 the real circular arch h A", would be defcribed in times nearly 

 proportional to the time in which the whole arch has been de- 

 fcribed. Upon thefe principles, the third column of the fol- 

 lowing table has been calculated. 



The difference between the calculated and obferved angles, 

 contained in the fourth column of the preceding table^ is fo little, 

 that we may look upon the gradual change of thefc angles as 

 eftablifhed by obfervation ; and we may form a calculated efti- 

 mate of the time which will be taken up by the mutual revo- 

 lution of the two ftars. The apparent places xx\ being referred 

 to their real ones, give the arch h h', which has been defcribed 

 in 21 years and 38 days ; and this arch, feen from the centre y, 

 is about 6* 20' : it follows, that the length of a whole revolu- 

 tion of our fmall ftar round y Leonis, will be about 1200 years. 



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