540 A CATALOGUE OF STANDARD STARS. 
has been transferred by Wolfers, is greatly preferable to the more direct one. It 
needs a little more care, however, in the computation. 
We have now positions for 1755, referred to the ecliptic of 1855, which agree 
with all the data of the Fundamenta referring to these stars. We have also some 
modern observations referred with more or less accuracy to the ecliptic of the same 
epoch, or which we can easily refer to that ecliptic approximately. These give us the 
means of obtaining a formula which shall be of the form 
a — a? +2 (t — 1755), 5 = 8° + i? (t — 1755). 
Where a” à? are (Bessel’s). Bradley’s positions of 1755, in cases where they are 
complete, referred to the co-ordinate-planes of 1855; or, in case the Fundamenta 
position of 1755 is incomplete, «° is the AR. for 1755 referred to the ecliptic and 
equator of 1855, by means of 3”, as explained above; 8° being here arbitrary within 
certain small limits: where again A? i? are assumed proper motions referred to the 
ecliptic and equator of 1855, but so assumed as to nearly represent more modern 
observations. For stars not in the Fundamenta, a? 9? are both arbitrary. 
In other words, if all observed positions are referred to 1855 by precession alone, 
the formule 
a — a? + ete, à — 0” + etc., 
would represent those taken from the Fundamenta exactly, and all others nearly. But 
as certain positions are exceptionally incomplete, and others so as a rule, we shall 
not attempt so to refer them, but shall proceed in the opposite way. We shall 
compute theoretical places of each star for the epochs of the catalogues. This will 
be done most conveniently by computing places for epochs at equal intervals, which can 
then be tested, and afterwards interpolated ; thus saving labor, and securing accuracy. 
Table I. contains the assumed values of a? 8° A? i?. For the stars contained in 
Bradley, the values of e and 2^ have been verified by Mr. A. Hall, now Aide at the 
U. S. Naval Observatory, Washington; who has recomputed the positions referred 
to the ecliptic of 1755 from them. 
From these values positions for 1810, 1830, 1850, 1870 were computed, and in 
some cases for 1820, 1840, 1860; using Struve and Peters's constants. The positions 
for 1815 were computed independently, and also interpolated as a check. The proper 
motions (N i), and secular variation (in AR.) were computed for 1830 and 1850; 
the former by formule which will afterwards be cited with some modifications from 
Bessel, and the latter by the formula, 
0.0284 + 07.1950 [tg 0^ -+ 4] sin 2 u/-]- 0.4481 sin (a/-]- 91° 6^) tg0'-1- 0.01944 [X tg 0 cos a" - i sec 0^ sin a’. 
