A CATALOGUE OF STANDARD STARS. 545 ` 
Comparing these with the new observations, as in Table II., the quantities 4 a’, 4 a’ 
cos 3’, 4 à will be readily formed. If the star be one of the four strictly treated, the 
equations can be at once formed, by the formule for that purpose. Then the quantities 
an, bn, cn, dn, etc., as also aa, ab, ac, etc., being computed for each new equation, 
and added in the proper place; the final equations in Table III. Part I. being ; 
0 = [an] + [aa] w + [as] £ + [ac] y + [ad] 
0 — [bn] + [ad] w+ [25] e+ [^c] y + [^d] » 
etc., etc., 
will give at once new final equations which can be solved. 
For the 21 other stars, the corrections in declination must first be computed, ac- 
cording to the values of a’ and y' given in Table III. Part IL. ; after this is done, the 
quantity 4 n for the new equations in AR. can be formed, and their solution will 
present no difficulty. It will in general make no difference whether the new values 
of æ and y, or those already given in Table III. Part IL. be used, to obtain 4n for 
declination. In either case there will be no difficulty in computing 4 n for the new 
observations, and thus forming the new equations according to the precepts for the old. 
An extreme case may occur, where it will be found that 4n for AR. would differ 
by a sensible amount when computed according to the new values of a and y. This, 
however, will not happen for a good many years. 
It remains merely to explain Tables V., VL, which contain the calculations of AR. 
for the clock-stars. (Table VL, Supplement, contains the positions of the more north- 
ern stars not often used as clock-stars.) = 
The method here pursued was, to form positions for the years 1838-40, 1850, 
1854-1858, and in some few cases for 1859, depending on the places of the Funda- 
menta for 1755, and the * Greenwich Results” for 1855. The positions of the Funda- 
menta were assumed as correct systematically, because the mean difference between the 
former reduction and Le Verrier’s and Peters’s new reductions of the 36 stars called 
« fundamental” is almost precisely zero; and so far as the casual errors of Bessel's 
places are concerned, it seemed possible to diminish their influence in great part by 
using comparatively late modern observations. 
One of the objects of the observations now in progress at Cambridge, for the reduc- 
tion of which these tables are designed, is to deduce new places of the fundamental 
stars, and to afford materials for a thorough examination of the relative systematic errors, 
whatever they may be, of the fundamental catalogue employed, so that for our purpose 
it is best to have a catalogue which is symmetrical as far as may be; which would not 
VOL. VIII. 71 
