400 ON THE MEAN PLACES OF 84 FUNDAMENTAL STARS. [48 



The same corrections were subsequently published in the Monthly Notices 

 for January, 1853, and Mr Farley made the modifications which were required 

 in order that the results might coincide with those which would have been 

 found if the above mentioned small corrections to the places for 1755, 1840, 

 and 1845 had been first applied, and the calculations before described had 

 been made with the places so corrected. 



These modifications are as follows : 



As explained before, in the preliminary calculations Mr Farley applied 

 the constant correction 8- 02 to the Right Ascensions for 1755 given in 

 the Tabulae Regiomontance. Hence the correction to be further applied to 

 the Right Ascension for 1755 will be = Le Verrier's correction + O s '02. 



The corrections of Declination for 1755 will be 0, as well as the 

 corrections of Right Ascension for the same date of Stars not included in 

 Le Verrier's list. 



Again the correction of the place for 1845 as deduced from that for 

 1840 



correction for 1840 correction for 1755 



= correction for 1840 + 



17 



and the mean of this value and of the correction for 1845 derived 

 independently, as before mentioned, is to be taken according to the number 

 of observations on which they respectively depend, and we shall have the 

 adopted correction for 1845. 



Also, 



Adopted correction for 1845 



+ -$ (adopted correction for 1845 correction for 1755) 

 = correction for 1857 to be applied to former results. 



The correction of the Proper Motion before found will be 



= -^Q (adopted correction for 1845 correction for 1755). 



[Here follows a table shewing the results of calculations made in 

 conformity with the above.] 



