One of the little projects I got assigned in grad school was to
analyze the data that Eddington got in 1919 that he was so sure
verified Einstein's prediction of gravitational bending of light.
It was not particularly difficult to see that, since the solar corona
obscured the stars nearest to the sun, and only stars about three
solar radii out or farther could be analyzed, that the errors
inherent in the method were such that discriminating between the
maximum of .75 (?) arc-sec predicted by Newton, and 1.75 (?) arc-sec
predicted by Einstein was simply not possible. In fact, Eddington's
data were not inconsistent with no bending, although zero was near
the limits of the error bar. Fortunately for Eddington's reputation,
more recent measurements of the shift have shown that Einstein was
right.
I would have to say that either Eddington was deliberately fudging
his result, or, more likely, he wanted the result to be in accordance
with Einstein's theory so badly that he saw what really wasn't there.
There is also the story that when Einstein received the telegram from
Eddington confirming his prediction, that the grad student who was
with Einstein at the time noted that the great man was not
particularly moved by the news. The student queried him about why,
and Einstein is said to have replied, "Because I knew that the theory
was right." The student protested, "but Herr Professor, what if the
results had been different?" Einstein responded, "Then I would have
been sorry for the Dear Lord (Liebe Herr). The theory is correct."
Makes a great story, but it could easily be another of the numerous
legends that have grown up around Einstein.
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