48] ON THE MEAN PLACES OF 84 FUNDAMENTAL STARS. 387 



Sirius and Procyon. Indeed one of the principal objects which I had in 

 view in the formation of this Catalogue was to test how far the observed 

 proper motions of those stars which had been long and carefully observed, 

 could be reconciled with the hypothesis that the proper motion, when 

 referred to the equator or ecliptic of a given date, was really uniform. 



The rule laid down in my instructions to Mr Farley embodies a very 

 simple mode of representing the apparent variability of proper motion arising 

 from the change of position of the great circles to which the star is referred, 

 whenever the star is not very near to the pole. 



When the star is very near the pole, the Right Ascension and Decli- 

 nation for the time 1800-M when referred to the Equator and Equinox 

 of 1800 is first found by adding the proper motions in R. A. and Decl. 

 for t years to the Right Ascension and Declination for 1800, and then 

 this Right Ascension arid Declination is converted into the corresponding 

 Right Ascension and Declination referred to the Equator and Equinox of 

 1800-M by the proper Trigonometrical formulae given below. These formulae 

 are founded upon the elements of precession given by Dr Peters in his 

 classical work Numerus Constans Nutationis. It should be noticed that 

 the corresponding formulae given by Mr Carrington at p. xxx of the Intro- 

 duction to his valuable Catalogue of Circumpolar Stars are not sufficiently 

 accurate. The quantities which he denotes by z + v, z' i/ and 0, and which 

 he employs in reducing the place of a star from one epoch 1800 + 1 to 

 another 1800 + i', ought to vanish identically when t = t', whereas, according 

 to Mr Carrington's Table of Precession Constants, when t = t' = 55, the value 

 of z + v i s _o"73 and that of z'-v' is + 0"'73. 



In the rule which I gave to Mr Farley for forming the value of the 

 secular variation of the Precession to be employed in reducing the observed 

 Right Ascension and Declination from 1840 to 1845, it is not taken into 

 account that different Elements of Precession are employed by Argelander 

 and Bessel from those which are employed in the Nautical Almanac. The 

 slight inaccuracy thence arising will, however, scarcely be appreciable. 



It should be remarked that the Polar Star 51 Cephei was not observed 

 by Bradley, and consequently that this star, although included among the 

 84 Stars to which Mr Farley's calculations refer, does not, properly speaking, 

 fall within the scope of my plan. The coordinates of this star for 1800, 

 which I gave to Mr Farley as part of his fundamental data, were the 

 means of two discordant determinations of those elements by Piazzi. Hence 

 it is not surprising that the predicted places of this star when tested by 



492 



