OF ARTS AND SCIENCES. 167 



Part II. 



In seeking for an explanation of the origin of periodic errors in observed 

 Right Ascensions, the following facts, drawn from the preceding discussion, will 

 not escape attention : — 



I. That for the observatories under consideration, the coefficients of sin a, 

 and also of cos a, have the same sign, varying only in magnitude. 



II. That for each observatory the maximum of negative erro i occurs at 

 about 6 hours of Right Ascension, the maximum of positive errors at about 18 

 hours, the zero of error varying but little from 3 hours. 



III. That the periodic error depending on the Dechnation, is zero at about 

 12° north. 



There seems to be only one circumstance that can vitiate these conclusions, 

 viz., tiiat tiie derived standard catalogue is itself subject to the errors in ques- 

 tion. In order to remove doubt on this point as far as possible, I give in Tables 

 I. and II. a comparison of the standard Right Ascensions with tlie following 

 authorities, viz. : Maskelyne, from 1765 to 1807; Struve, 1825; Struve, 1830; 

 Argelander, 1830; Pulkowa, 1845; and Newcomb, 1870. These authorities are 

 selected because there is good reason to suppose that the observations are in a 

 great measure free from errors of single period. Certainly no more severe test 

 than til is can well be applied ; for the standard catalogue has been formed quite 

 independently of them. If it is found that the Right Ascensions derived from 

 this discussion of only modern observations, satisfy observations distributed over 

 a range of nearly 100 years, they must be accepted as quite near the truth. If 

 the comparison indicates no periodic errors of greater magnitude than the prob- 

 able errors of observation, tlien the standard catalogue must also be regarded as 

 quite nearly free from these errors. 



Instead of using the various catalogues constructed from Maskelyne's obser- 

 vations, I give in Table I., in hundredths of seconds, the comparison for each 

 year, the data being derived from the Ledger of Stars, prepared with great care 

 by the Rev. Robert Main. The final Right Ascens: )ns given b}- Mr. Main are 

 corrected for quite a large number of errors found in Maskelyne's original com- 

 putations. This direct comparison will also enable us to form an estimate of 

 tlie 1 iative value of the individual observations. Argelander's places of a Canis 

 Majoris and a Canis Minoris have been corrected by +.04« and — .04* respec- 

 tively, on account of change of position between 1826 and 1830. Struve's posi- 

 tions for 1830 have been corrected by +.05* and — .05' respectively. From the 

 direct residuals have been subtracted the values of r'' derived from ^he following 

 equations : — 



s. s. 



Struve 1825, r" = -H.036 sin fJ —.007 cos S. 



Struve 1830, = -+-.074 sin d —.015 cos d. 



Argelander .... 1830, = — .028 sin 6 -h.OOd cos d. 



Pulkowa 1845, = —.023 sin (5 -1-.004 cos 6. 



Newcomb 1870, = -+-.014 sin 6 — .002 cos 6. 



