cxx COMPARISON-STARS. 



The incompatibility of some of these determinations is apparent, and the first five equations 

 require therefore to be combined with one another, according to the method of least squares, 

 after giving to each an appropriate weight. The values resulting from this combination have 

 been adopted. They are: 



Bessel Washington = 0".76 



Bessel Santiago = 0".06 



Bessel Greenwich =-f-0".23 



Hence we also have, 



Bessel Maclear = 0" . 1 6 . 



For southern stars we obtain, by 20 observations, 



Argelander Washington = + F.74 0".40, 



and by 12 observations, 



Washington Ann Arbor = + F.58 0".35, 



whence, 



Argelander Ann Arbor = + 3". 32. 



These corrections were uniformly applied, as also were the following equations as previously 

 determined for the declinations under consideration, excepting for the one zone of Lalande 

 already mentioned. 



They are taken from Argelander's Positiones Medice and Southern Zones, Struve's Posiiiones 

 Medice, and Madler's Fixstern-system II, as cited by Dr. Forster in his excellent paper in N. 

 1026 of the Astronomische Nachrichten. 



Bessel Taylor = F.32 



Bessel Twelve-Year = 0".40 

 Bessel Eiimker = 0".70 

 Bessel Piazzi = Bessel Lalande 



= 3". 6 for 3= + 15 



3".3 +20 



2".8 +25 



Argelander Taylor = + 0".50 0".0256 (d + 19) 

 Argelander Piazzi = Argelander Lalande 



= 1". 52 for 3 = 16 



1 .23 18 



0.84 20 



0.25 22 

 + .54 24 

 -I- 1 .30 26 

 + 1 .90 -28 



Lalande's zone of 1796, March 4, contains the stars N 03 - 70, 74, 81, 89, 94, 97, 100, 101. 

 To these has been applied the correction 2". 3 in order to reduce them to positions correspond- 

 ing differentially to the places adopted for the fundamental stars in the reduction. Twenty of 

 these were from Riimker, five from the Twelve- Year Catalogue, and one from Argelander's Posi- 

 tiones Medice. The mean by weights of the reductions to Bessel for the totality of these stars 

 is, 0".60, making the entire correction to Lalande, 2". 9. 



The observations thus corrected may be advantageously combined by allowing to each deter- 

 mination a weight proportionate to the product of the number of observations by a factor 

 constant for each authority. This factor should depend not only on the probable error of the 

 authority, but also, in some measure, upon the time elapsed since the observation that the 

 influence of undetected proper motions may not be too prejudicial. 



Combining the materials in this way, we may deduce a table of definite places of great pre- 

 cision, which may be practically treated like careful determinations by one and the same 

 observer. So important is it, however, in the present discussion, that all the comparison-stars 



