In a recent paper J. L. Synge (1952) has shown that the theories of Einstein and Whitehead predict practically the same phenomena in the solar field. He finds that the rotation of perihelion, the deflexion of light rays and the red-shift in the sun's spectrum are the same in both theories. In this paper the motion of the centre of mass of a double star is investigated. It is found that Whitehead's theory predicts a secular acceleration in the direction of the major axis of the orbit towards periastron of the larger mass. The possibility of a binary star having such an acceleration has already been considered by Levi-Civita (1937), and he has given an example in which it may become detectable in less than a century. On the other hand, it has been shown by Eddington and Clark (1938) that there is no secular acceleration according to Einstein's theory.