70 MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES. 



cerning the positions of the more southern stars that come under consideration in the following 

 discussion, I have consulted the skies directly. 



It is well to premise here, that of the 23 stars that Baily left unidentified, Flamsteed gave to 

 3 the magnitude of 5, to 1 the magnitude of 5.J, to 9 the magnitude of 6, to 1 the magnitude 

 of 6J, to 3 the magnitude of 7, and of 5 (2 of which belong to the group of Prcesepe) the 

 magnitudes are not recorded. 



Fortunately, what discrepancies Baily detected in the manuscripts are communicated in the 

 copious notes to the new edition of the British Catalogue, so that for the stars in question we may 

 take the figures as they are given for time and zenit distance in Volume TI of the Historia Ccelestis 

 for the actually recorded ones, without any apprehension of errors of print. 



For none of these stars is there more than one observation, and the record of it may involve a 

 mistake, either in noting the clock time, or in circle reading, or in hearing and writing by the 

 amanuensis. For the reading of the circle "j^er lineas diagonales^^ a check is given by that "per 

 strias cochleae." This, however, may not always hold good, as, for example, there are indications 

 that sometimes (perhaps when the stars came in quick succession, or for some other reason) only 

 the fraction was read off or put down for the screw, and the whole number of revolutions afterwards 

 filled in from the corresponding reading of the division. 



When, by some hypothesis of a mistake, we try to bring about an agreement with a star known 

 by modern determinations, the question naturally presents itself. What difference are we allowed 

 to admit"? or, in other words, since the modern observations in this comparison may be assumed 

 as perfectly accurate, what is the probable error of a position in Flamsteed's Catalogue "? For ob- 

 taining approximately an idea of this, may serve the dift'erences from Bradley, which Baily has 

 added in his edition. By taking from twenty pages (about every fifth page) the mean of these 

 differences, without regard to sign, excluding, however, the stars of high northern declination, also 

 avoiding those with a known considerable proper motion and those which clearly appear to be 

 affected with some gross accidental mistake, I find 44" in right ascension and 17" in declination. 

 By another count, viz., by taking the means of differences for all the sixth-magnitude stars that 

 were observed only once (about 400 in number), I find 50" and 18", respectively. Disregarding as 

 small what the comparison with Bradley may have added, these figures give an approximate 

 measui'e of the mean uncertainty of a position in the British Catalogue. Considerably much smaller 

 is the pure mean observation error of Flamsteed, which Argelander has computed, viz., ± 10".4 

 in right ascension and ± 7".8 in declination.* These values are independent of the situation of the 

 Quadrant, while the others are affected, besides, by the imperfection of the elements Flamsteed 

 used in his computations. The contrast is a proof how greatly the usefulness of the Catalogus Bri- 

 tannicus could be increased by a re-reduction of the original observations. 



Proceeding now to the examination of each of the 22 stars in particular, it seemed necessary 

 to communicate the discussion with some detail, in order to leave as little doubt as the subject in 

 each case permits. Every one accustomed to observe is aware of the facility of committing mis- 

 takes, however careful he may believe he has been. The assumption, therefore, of some other- 

 wise plausiiile error of Flamsteed which leads to a modern star-place is to be held much more 

 reasonable than the vague acquiescence in a supposed disappearance of the star. In that sense 

 I think I have succeeded in finding for every case at least a probable explanation. 



1) B. Fl. 314. 



This star in the British Catalogue is called 28 Arietis, and its position given thus : 



6 mag 330 33' 20"; +18° 23' 40" 



which reduced to 1800 would be 



3504/44//. +180 59' 3" 



* Argelander (De oljservatiouibus astron. a Flamsteedio institutis dissertatio. Regioiuont., 1^22) finds the probable 

 error of a poiatiug in right asooasiou J; 0'.3i():5, or of the right ascension itself, being the result of the ditferentiatioa 

 from a so-called "deteruilning star, " J- 0=.32G3 -/a = ± Os.4614 = ± 6".U, of the zoait distaace or decliuatioa J; 5". 20. 

 Hence follow the main errors as given ia the text. 



