*226 PHILOSOPHICAL TRANSACTIONS. [aNNO 178/. 



of all other celestial objects with the transit instrument. The result in brief is as 

 follows : I first settled the relative right ascensions of about 30 of the brightest 

 fixed stars, and lying nearest the equator, by a great number of observations with 

 the transit instrument, referring them to a, Aquilae as the fundamental star, whose 

 right ascension I assumed from Dr. Bradley's determination. Hence, by observed 

 transits of the sun and the same stars, in the spring and autumn, when his daily 

 motion in declination was at least l6' or ^ of the greatest, I inferred the sun's 

 right ascensions relative to the right ascensions of those stars settled in the man- 

 ner just mentioned. Also from the sun's observed zenith distances taken with 

 the brass mural quadrant on the same days, and corrected by refraction, parallax, 

 and error of line of collimation, with Dr. Bradley's obliquity of the ecliptic, and 

 latitude of the observatory, I computed the sun's declinations, and thence the 

 right ascensions corresponding to them. 



Now, if the assumed right ascension of a Aquilae, and thence those of the 

 other stars were affected with some small error, as might be supposed, the sun's 

 right ascensions deduced from the observed transits would differ the same way 

 from the truth at both seasons of the year, viz. by the unknown error- of the 

 assumed right ascension of a Aquilae ; but his right ascensions inferred from his 

 observed zenith distances would be affected contrary ways at the two opposite 

 seasons of the year, by the unknown errors in the refractions, parallaxes, latitude 

 of the place, and obliquity of the ecliptic. Hence, the mean of the two correc- 

 tions of the sun's right ascension, found from the observed declinations about the 

 vernal and autumnal equinox, would be the true correction of the assumed right 

 ascension of « Aquilae ; and the difference of the same corrections would, by an 

 easy calculation, show how much the computed declinations were too great or 

 too little for the truth, and consequently what the true declinations were, and 

 what the true zenith distance of the sun was, when in the equator, or the latitude 

 of the place, on supposition that Dr. Bradley's refractions were truly stated ; for 

 any small uncertainty in the obliquity of the ecliptic, as stated by him, could not 

 affect this result, which was deduced equally from observations of the sun in 

 north and south declination, when the same error of the obliquity would affect 

 the sun's right ascensions deduced from the observed declinations contrary ways. 

 I took the sun's parallax from the 24th of my tables annexed to my observations, 

 constructed on a horizontal parallax 8'''.84, which I had deduced from the obser- 

 vations of the first transit of Venus, that in 176J, and differing insensibly from 

 8^'', which I deduced from the observations of the total durations of the transit 

 between the internal contacts observed at Wardhus and Otaheite in 1769, con- 

 sequently more correct than the horizontal parallax of lO-i-'' used by Dr. Bradley. 

 It is also evident, that the true zenith distance of the equator thus found, di- 

 minished by Dr. Bradley's mean refraction, will be the apparent zenith distance 

 of the equator, affected only by the mean refraction. 



