172 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1919. 
The average y-residual is ±0.22'', which gives a probable error for 
y of ±0.21''. It is satisfactory that this agrees so nearly with the 
probable error (±0.22") of the check plates, showing that the images 
are of about the same degree of difficulty and therefore presumably 
comparable. The probable error of x is ±0.25", but we are not so 
much concerned with this. 
The weight of the determination of Ak is about 3 (strictly 3.23 for 
plate X and 2.87 for plate W). The probable error of k is therefore 
±0.12", which corresponds to a probable error of ±0.38" in the 
final values of the deflection. 
As the four determinations involve only two eclipse plates and 
are not wholly independent, and further small accidental errors may 
arise through inaccurate determination of the orientation, the prob- 
able error of our mean result will be about ±0.25". There is 
further the error of ±0.14" affecting all four results equally, arising 
from the determination of scale. Taking this into account, and in- 
cluding the small correction —0.04" previously mentioned, our result 
may be written 1.61"±0.30". 
It will be seen that the error deduced in this way from the residuals 
is considerably larger than at first seemed likely from the accordance 
of the four results. Nevertheless the accuracy seems sufficient to 
give a fairly trustworthy confirmation of Einstein's theory, and to 
render the half-deflection at least very improbable. 
38. It remains to consider the question of systematic error. The 
results obtained with a similar instrument at Sobral are considered 
to be largely vitiated by systematic errors. T\^at ground then have 
we — apart from the agreement with the far superior determination 
with the 4-inch lens at Sobral — for thinking that the present results 
are more trustworthy? 
At first sight everything is in favor of the Sobral astrographic 
plates. There are 12 stars shown against 5, and the images, though 
far from perfect, are probably superior to the Principe images. The 
multiplicity of plates is less important, since it is mainly a question 
of systematic error. Against this must be set the fact that the five 
stars shown on plates W and X include all the most essential stars ; 
stars 3 and 5 give the extreme range of deflection, and there is no 
great gain in including extra stars which play a passive part. 
Further, the gain of nearly two extra magnitudes at Sobral must 
have meant over-exposure for the brighter stars, which happen to be 
the really important ones ; and this would tend to accentuate system- 
atic errors, whilst rendering the defects of the images less easily 
recognized by the measurer. Perhaps, therefore, the cloud was not 
so unkind to us after all. 
Another important difference is made by the use of the extraneous 
determination of scale for the Principe reductions. Granting its 
