50 CATALOGUE OF STARS WITHIN 
Table VIII contains the probable errors of Table VII. 
TABLE VIII.— Probable Errors of Table VII. 
1 6 no 2 and i6 no. 7 .. 
16 no. 7 and 21 no. 15 
21 no. 15 and 18 no. 3 
18 no. 3 and 16 no. 4. 
16 no. 4 and 16 no. 5 . 
16 no. 5 and 21 no. 13 
21 no. 13 and 18 no. i 
18 no. I and 16 no. 2 . 
90° and 16 no. 2. . . . 
90° and 1 6 no. 7 . . . . 
90° and 21 no. 15. . . 
90° and 1 8 no. 3 . . . . 
90° and 16 no. 4. . . . 
90° and 16 no. 5. . . . 
90° and 21 no. 13. . . 
90° and 18 no. i . . . . 
d^ or dr). 
dA' or (/w. 
mm. 
± . 0009 
.0007 
.0001 
.0010 
.0008 
.0007 
.0008 
.0007 
.0006 
.0007 
.0006 
.0009 
.0006 
.0007 
.0007 
.0007 
± . 0007 
.0006 
.0010 
.0008 
.0008 
.0007 
.0007 
.0006 
.0007 
.0008 
.0007 
.0011 
.0009 
.0009 
.0009 
.oooS 
0.173 
. 176 
.198 
.194 
.167 
.204 
.205 
•152 
.171 
.177 
•154 
.199 
. 162 
•177 
.205 
.183 
Since the values of the differential reduction constants given in 
Table VII enable us merely to form the best combination of results 
derived from pairs of adjacent plates, it becomes necessary to find a 
method of reducing all of these combinations to the most uniform 
standard. This may be performed as follows (c/. Col. Con. no. 21, 
p. 70). If a star is found on plates 16-2, 16-7, and 90°, we may con- 
sider that by substituting the proper values from Table VII in equa- 
tions (2) we may pass from plate 16-2 to 16-7, by a second negative 
substitution from 16-7 to 90°, and by a third substitution from 90° to 
16-2. The final « and r. should agree with the initial value of plate 
16-2. Since this substitution is valid for every star common to the 
three plates, we should have theoretically 
. ^ d^i — d:\o -j- rfig = o , 
dfji — drno -\- dr,9 = o , 
etc. 
The subscripts denote the respective combinations in Table VII in 
which they are numbered in order from i to 16. 
Let u represent a general expression for any differential constant. 
Since there are eight possible combinations of overlapping plates by 
means of which we may start with plate 16-2 and return to it, they 
