170 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1919. 
Prats U. 
Comparison with Oxford Plate K,.—Since Plate U shows some 
good images it has been examined, althotieh owing to the absence 
of star 8 the weight is small. The measures were made at Principe. 
Theoretical plate-constants 
ee ed Peg” le hare 
Star. 2 At. Ait. +240y. Ez. Ast. Resid, 
TFTA a a 1.39 2, 905 2, 791 2, 976 —101 — 84 —147 
a RRR ex 17.34 4, 508 4, 292 4, 493 aN —129 —192 
SP Spl enycioh aia, See hetate 17. 48 4, 626 4, 420 4,224 — 92 +288 +225 
Beta st aie Ys a 19. 87 6, 270 5, 992 5, 998 ae =)40 ae 
(Gur es 22. 60 7,110 6, 805 6, 530 fae +252 +189 
Star y AY Ay —240x. Ky AW Resid. 
1113S SMe ON 12. 40 9, 026 8,547 — 334 a6 8, 875 — 
TIC A AT 18. 72 5, 846 4, 986 —4, 162 +234 8,914 — 55 
Sih ete Lee. 17. 60 5, 985 5, 165 —4,195 +272 9, 089 +120 
CANON I PEN 24. 99 5, 458 4, 339 —4,769 +136 8, 972 +. 3 
ACT) SESS Sy eee tae 27, 21 4,911 3, 684 —5, 424 +114 8, 994 + 25 
In this case it is not possible to determine the orientation with 
sufficient accuracy from the v-measures; the value here applied is an 
arbitrary preliminary value. We accordingly make a least-squares 
solution from both w-and y-residuals to determine the correction to 
the orientation, 86, as well as 8c, éf, = On. 
The result is 
S0= +2, du== +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 possible 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 effects of any errors in the adopted 
scale, orientation, etc., on the final result (deflection at the limb). 
We give some illustrations. 
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 
