50 CATALOGUE OF STARS WITHIN 
Tabie VIII contains the probable errors of Table VII. 
TABLE VIII.—PROBABLE ERRORS OF TABLE VII. 
Pe sr Ma Fa ae en Ts eC <a SET SSo 

dé or dy. dA’ or dw, 9. 

mm, u" u" 
SOT 2 16 Oey oko ae + .0009 + .0007 + 0.173 
16-00, 7 and SY HO. 15 diese wt. .0007 .0006 P76 
FEO. ok SoA Bt a een ate .OOOI .OO1O .198 
18 DO BESO Oe Nf pane .OOIO .0008 194 
TOPs and NG NG's 0s... we .0008 .0008 .167 
SGinOR Giid coe Te ea ee .0007 .0007 . 204 
SY edi Fe Se to ee .0008 .0007 . 205 
TS OS and 16 NOA2a i ee ee .0007 .0006 .152 
003, Bila MO)? a Ae ot Paso . 0006 .0007 BR fed 
menage SL WF Co We 4 Seder pena. Le as .0007 .0008 aS A i, 
CF PATIL LST NG Te oes ee 8 . 0006 .0007 .154 
90° BI REGION 3 eee .0009 .OOI! .199 
90" PU Meg nes a er. eR” ne ear TS gS ee .0006 . 0009 .162 
GO van FOOLS een. oe ee + .0007 . 0009 Ty 
0) Ate weak Aone aa ey . 0007 . 0009 . 205 
OO RET AOR e ut ce Tanta .0007 | .0008 .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 finda 
method of reducing all of these combinations to the most uniform 
standard. This may be performed as follows (cf. Col. Con. no. 21, 
p.70). Ifa 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 togo°, and bya third substitution from 90° to 
16-2. ‘The final ¢ and =z 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=, — dijo + din =O, 
dyn, — dyio + dyg = 0, 
etc. 
The subscripts denote the respective combinations in Table VII in 
which they are numbered in order from 1 to 16. 
Let wu 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 
