170 
ANNUAL REPORT SMITHSONTAN INSTITUTION, 1919. 
Plate U. 
Comparison with Oxford Plate K^, — Since Plate U shows some 
good images it has been examined, although owing to the absence 
of star 8 the weight is small. The measures were made at Principe. 
Theoretical plate-constants 
a= +2.8, 5. d= +8.9, e= +37.7. 
star. 
X. 
Ai. 
All. 
+240;/. 
E^. 
A^a;. 
Resid. 
11 
1.39 
17.34 
17.48 
19.87 
22.60 
2,905 
4,508 
4,626 
6,270 
7,110 
2,791 
4,292 
4,420 
5,992 
6,805 
2,976 
4,493 
4,224 
5,998 
6,530 
-101 
-72 
- 92 
+ 4 
+ 23 
- 84 
-129 
+288 
- 10 
+252 
-147 
4 
-192 
3 
+225 
6 
- 73 
10 
+189 
Star. 
11 
4 
3 
6 
10 
Ay. 
Ai2/. 
-240i. 
AiV- 
Resid. 
12.40 
18.72 
17.60 
24.99 
27.21 
9,026 
5,846 
5,985 
5,458 
4,911 
8,547 
4,986 
5,165 
4,339 
3,684 
- 334 
-4,162 
-4, 195 
-4,769 
-5, 424 
+ 6 
+ 234 
+272 
+ 136 
+ 114 
8,875 
8,914 
9,089 
8,972 
8,994 
- 55 
+120 
+ 3 
+ 25 
In this case it is not possible to determine the orientation with 
sufficient accuracy from the ^--measures ; the value here applied is an 
arbitrary preliminary value. We accordingly make a least-squares 
solution from both a?-and ^/-residuals to determine the correction to 
the orientation, SO, as well as 5c, 8/, and Ix. 
The result is 
Se= +2, 8x= +121. 
This gives the deflection 2.90". 
The probable error is, however, ±:0.87", so that the result is practi- 
cally worthless. Further, it is much more likely to be affected by 
systematic error than the previous results. 
The large probable error is partly due to the large residuals which 
are greater than in the previous measures; in particular star 3 is 
unduly faint. If the same accuracy had been obtained, the theo- 
retical weight would have been half that of Plates W and X; 
but having regard to j)ossible systematic error, probably a quarter 
weight would more nearly represent the true value. 
This determination is ignored in the subsequent discussion. 
36. It is easy to calculate the etfects of any errors in the adopted 
scale, orientation, etc., on the final result (deflection at the limb). 
We give some illu.strations. 
An error in the adopted scale of y of 10 units (in the fifth place of 
decimals) would lead to an error 0.68" in the result from either plate. 
Thus the probable error ±2.1 in the determination of e' gives a 
