250 DETERMINATION OF THE LONGITUDE OF SEVERAL 



new argument. The values of T, T', &c. for the even hours, or twelfth 

 parts of the argument, are given by Bessel ; those of X, X', &c. by Ni- 

 colai, Astr. Nach., 37. Where a single, or few observations are re- 

 quired to be reduced for a particular station, the labour of computing 

 T, T', &c. may be saved by means of the following transformation, 

 which I do not recollect to have seen in any publication. 



The comparison of (1) and (2) gives, 



cT = c.X 



1 ) 



dT' =z d \ X' + 



3.4 



eT" = e $ X" — — Xf 

 i 2 . 3 S 



AT" = A j X" + -L X'" - — L_ X' + ' 



3.4 4.5.6 ' 4.5.6.7> 



iT' = i J X"- ^ X-+ ^ X« _ j-i-^ X 

 whence, making 



a = 6 4- -^ d— , \ ^ f-\ -i h—, &c. 



^3.4 4. 5. €''^4.5.6. 7 ' 



