544 A CATALOGUE OF STANDARD STARS. 
c = Vw cos E, 
ct 
t= 30? 
n=you' 49; (e — o). 
The equations of equal precision for these four stars will be of the form 
0 =n -+ aw 4 br + cy + dz, 
whose solution by least squares is a mere matter of mechanical computation, according 
to Encke’s form in the Jahrbuch for 1836. 
For the polar stars excepting these four we shall put 
x= m cos à, S sc 
y = y cos à, == d, 
and the quantities æ y will be eliminated from the declination equations, and 2" y’ from 
those in right-ascension by the process mentioned above. We have, then, making 
— es dl 1 
a = y w cos & or y o! cos & sn (AR) = yu [+ S] sin E, 
t = Til ee 
b= a gy 4n (Dec.) = — y w' 1+ 39 sin § cos d, 
the following equations of equal precision in right-ascension 
0 =n 4 dAn 4 ax -+ by =n ax by, 
Q0 — n 4 4n— az! + by =n' + az! + by. 
and in declination 
The process of forming these is, — 1st, assume in declination 4 n — 0, and form 
and solve the declination-equations; 2d, substitute these values of a”, y' or u d in the 
equation for 4 » in AR., and form and solve the right-ascension equations. This 
gives the means of correcting the declination-equations. These last corrections were 
shown by trial to have no perceptible effect on the equations for AR., and the process 
of approximation ceased here. 
Tables IIL and IV. contain the formation and solution of the equations. In order 
to add new equations in future, we must, after determining the weights, compute for the 
epoch in question the theoretical AR. and Dec. derived from the numbers in Table I. 
