50 



H. JACOB!, 



precession is omitted in the reductions, the coordinates f and yj obtained 

 for the pole are those of the pole's position at the epoch of the catalogue. 

 Consequently, the right ascension and polar distance of the unknown stars 

 are given by the plates referred likewise to the epoch of the catalogue, and 

 these are not strictly valid for computing the refraction. 



To avoid this difficulty, we need only bring up to the date of the plate 

 the star-places taken from the catalogue. But this would necessitate exten- 

 sive computations of precession. Instead of doing this, we can apply a cor- 

 rection to our refraction formulas. If we let: 



t, t Q , be the year of the plate, and the year to the beginning of which 



the catalogue places are referred, 

 A", iz", be the right ascension and polar distance of the pole of the 



time t referred to the pole of the beginning of the year t, 







m, n, be the usual precession constants. 



Then we have with sufficient approximation for our present purpose: 



A" = 180° -*-±m(t — g, *" =n(t — Q. 



If we wish to be extremely accurate, we must also compute the usual 

 reduction from mean to apparent place», exclusive of aberration, for the 

 time t, and using the above values of A" and n". These being added to A' 

 and tt", will give the apparent place of the pole of the beginning of the 



m i in 



year t . "We shall call these corrected quantities A and ic . It can then 

 be shown without much difficulty that the following corrections must be 

 added to the right hand members of the refraction equations (5). 



For (a — a) -re sin 1 ", I sin (6 — a) — J cos (G 



a 



For tt — 7i, J sin (8 — a) -+- 1 cos (0 



where: 



I = Icsz" cosec 2 9 cos (6 — A'") sin 1 ", 



"f i r tW i ' /t\ t>l> 



J = for cot y [cos A cot e h- sin (0 — A ) tan 9] sin 1 . 



The computation of the aberration by means of equations (6) will not 

 offer any difficulties of practical importance, provided the longitude of the 

 sun used in the computations be referred to the epoch t . If the major terms 

 of the aberration have been computed by the Besselian formulas: 



(Cc+Dd), —{Cc'+Dd'), 



taking the values of G and D from the ephemeris belonging to the year of 

 the plate, it will be sufficient to correct the values of c, cZ, c\ d\ computed 

 in the usual way, by adding to them the corrections: 



*BJ.-iIaT. ctp. 50. IO 



