XXXIV PRELIMINARY GENERAL CATALOGUE OF STARS FOR 1900 
Proceeding in the usual manner, we shall have to add to the first of equations (D), 
6.0 Aao + 9.48 A/x 0 = -I-*180 
and to the second of equations (D), 
9.48 Aa 0 4 -14.98 A fi 0 = 4 - ^284 
The new normal equations become: 
36.0 Aa 0 +9.5 A/i 0 = 4 -?i 8 o 
9.5 Aa 0 4 - 34.8 A// 1 = 4- *284 
The solution of these gives 
Aao= -K003 (for 1870.4) 
A/x 0 = 4 -"0072 
A fjL = 4 -'0003 
The new mean epoch is 1877.0. For 1900 we should then have Aa= 4-*012, and 
consequently: 
Right-ascension =o h o ra 13-013 
1900 • Annual variation = 4 - 3*0712 
Proper-motion = — !ooio 
The probable error at the epoch, 1877, is ±'.05 (weight 36), and the probable 
error of centennial motion is ± '.'21 (weight = 2.02). The probable error for 
1910 is now ± '085 instead of ± '.'12 given in the Catalogue; consequently the weight 
for that date is nearly doubled. 
Owing to the rounding of the probable errors on the second decimal place, the 
weights for position at mean epoch and for centennial proper-motion may differ 
somewhat from the actual results from the solution-normals from which the 
catalogue-results were derived. But this difference will be larger for the best- 
determined stars, and there it will be of no material consequence. In the present 
case the normals actually derived from the computations for the Catalogue are: 
32.2 Aa 0 4 - 0.0 A/t 0 = 5 ooo 
0.0 Aa 0 4 - 20.2 A/x 0 = ?ooo 
If these be substituted for equations (D), the subsequent solution will not materially 
differ from the one already reached through (D). 
The process outlined in the foregoing is applicable to the introduction of any 
number of determinations additional to those employed in the construction of the 
Catalogue; and these may have dates previous to the mean epoch, as well as after 
it. Other methods to fit special requirements will suggest themselves to the expe¬ 
rienced computer. 
