Light deviation and Schwarzschild metric

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How did Einstein compute the amount of light deviation due to the earth's gravitational field when the Schwarzschild metric was not known yet?
 

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He didn't get it right at the first try, in fact in his first calculations in 1908 he was off by a factor of 2. The correct result was obtained 1915 using the weak field approximation where all terms smaller than the order of 1/c³ were neglected, see http://home.fnal.gov/~syphers/Education/Notes/lightbend.pdf
 
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