Measurement of 42 hydrogen lines on 27 spectrograms of 40 Eri B leads to an observed red shift, AX/X, of 7 X 10- , corresponding to a velocity of 21 km/sec. This is to be compared to the value of 17 predicted on the basis of general relativity from the mass and radius of the star. The difference between observed and predicted values is less than the sum of their uncertainties, which are considerable fractions of the values themselves.
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Daniel M. Popper (1954) studied this question.