VOL. LXIIl.] PHILOSOPHICAL TRANSACTIONS. 38Q 



right ascension to be 21"* 27' of sidereal time by the two former observations, 

 and ^l"" 16^^ by the two latter, the difterence in declination being 4Q' 48".7, by 

 a mean of the observations in May, the extremes differing only 4 seconds. It 

 appears from computation, that between the times of observation the variation 

 of yi Bootis in right ascension was 337 1". 7, and i4l7".3, in declination; of 

 Arcturus 3311 ".7 in right ascension, and J347".9 in declination; the difference 

 of variation in right ascension is l' O', and of declination l'9'''.4; by the former 

 the difterence in right ascension was diminished, and in declination increased by 

 the latter, agreeably to the places of the two stars. The difference in right as- 

 cension theretbre in 1768, if neither of the stars had moved, should have been 

 = 5° 23' 2".2, and 5l' 55" in declination; but they were observed to be 5° 2l' 

 43".4, and 49' 48".7. Arcturus therefore, by this observation, has in 78.257 

 years gone l' 18".8 to the west, and 2' 6 .3 to the south, supposing n Bootis not 

 to have any proper motion. 



On the 5th of April, 169I, the difference in right ascension between n Bootis 

 and Arcturus was 21"" 33* of mean solar time, = 5° 24' 14".0; and the differ- 

 ence of declination 50' 45".6, as in the preceding example. The difterence of 

 variation in right ascension is 59 ".1, and in declination l' 8".4. The difference 

 of right ascension therefore at the latter end of May, 1768, should have been 

 5° 23' 14".9, and 51' 54^.0 in declination; but, according to observatioli, they 

 were 5° 21' 43".4, and 49' 48".7. Arcturus therefore, according to this obser- 

 vation, has moved l'31".5 to the west, and 2' 5'.3 to the south in 77. 120 years. 



On the 4th of May, 1691, the difterence of right ascension between n Bootis 

 and Arcturus was 21"" 33* of mean solar time, = 5° 24' 14".3, when allowance 

 is made for the going of the clock and the error of the plane of the instrument, 

 and the difference of declination on the 3d of May = 50' 50''.6. According to 

 computation, those differences should have been 5° 23' 15 .2 and 51' 59 ".O res- 

 pectively; but they were observed to be 5° 21' 43 .4 and 49' 48 '.7. Arcturus 

 therefore, in 77.071 years, has moved l' 31 ".8 westward, and 2' 10".3 south- 

 ward. N. B. The zenith distance of Arcturus, as determined by Mr. Flamsteed, 

 on the 4 th of May, is manifestly erroneous. 



On the 27th of May, l6g2, n Bootis preceded Arcturus in right ascension by 

 21™ 32'.5 of mean solar time, = 5° 24' 10'. 1, the difference of declination 

 being 50' 50 ".6. In 75.978 years the difference of right ascension should have 

 been 5° 23' 11'''.8, and 5l' 58''.0 in declination; but those differences were ob- 

 served to be 5° 21' 43".4 and 49' 48".7. Arcturus therefore has moved l' 28''''.4 

 westward, and 2' 9".3 southward. - 



On the 27th of May, 1 6g2, Arcturus preceded -n- Bootis in right ascension by 

 24"^ 35*. 5 of mean solar time, = 6° q' 32*,2, when an allowance is made for 

 the going of the clock and the error of the plane of the instrument, the differ- 



