Two DEGREES OF THE NORTH POLE. 
55 
These values when substituted in equations (2) for the unknown 
stars will give the corrections to be added to the 90° places to produce 
the most improved values. To obtain the definitive corrections to 
the 89° plates it is necessary to subtract from these quantities the last 
eight sets of numbers in Table XII, u^ . . . uie, in turn. The results 
when substituted in equations (2) will give the corrections to be added 
to the places from the 89° plates. Table XIII contains these defini- 
tive correction constants. 
TABLE XIII. — ^Definitive Correction Constants. 
d^ 
dv 
dA' 
dw 
90° 
+ 
.0006 
+ 
•0033 

.0019 

.0013 
16-2 
+ 
.0005 
— 
.0022 
— 
.0010 
+ 
.0009 
16-7 
+ 
.0012 
+ 
.0065 
+ 
.0034 
+ 
.0041 
21-15 
+ 
.0023 
+ 
.0041 
— 
.0028 
+ 
.0051 
18-3 
+ 
.0020 
— 
.0051 
— 
.0032 
+ 
.0014 
16-4 
+ 
.0038 
— 
.0021 
+ 
.0019 
— 
.0036 
16-5 
+ 
.0116 
+ 
.0065 
+ 
.0024 
— 
.0073 
21-13 
+ 
.0070 
+ 
.0096 
+ 
.0065 
— 
.0080 
1 8-1 
+ 
.0026 
.0013 
+ 
.0015 
.0019 
The corrections thus obtained were added directly to the right 
ascensions and polar distances of which Table VI contains the means, 
J'j- sin -, having been previously multiplied by cosec -. The means 
of these corrected places form the final catalogue which is found in 
Table XVI. The residuals from the mean are given in Table XV, in 
the sense plate minus mean. A comparison of these residuals with 
those of Table VI shows that the process of inter-adjustment has 
considerably reduced them. The largest one, i".03, has become o".68, 
and only four residuals of the second solution are greater than o".6o 
as against thirty-five of the preliminary solution. The improvement 
may also be shown by comparing the sums of the squares of the resid- 
uals for all the stars, using the values which occur in Tables VI and 
XV, respectively : 
Preliminary solution. Final solution. 
Ja sin 7r 53". 10, 22". 82 , 
Jtt 46.25 , 23.46 . 
The following table shows the differences. Photographic minus 
Heliometer, of the standard stars from both preliminary and final 
solutions. The preliminary solution being based solely on the stand- 
ard stars gives results which agree more closely with the heliometer 
