1. The purpose of the expeditions was to determine what effect, if any, is produced by a gravitational field on the path of a ray of light traversing it. Apart from possible surprises, there appeared to be three alternatives, which it was especially desired to discriminate between— (1) The path is uninfluenced by gravitation. (2) The energy or mass of light is subject to gravitation in the same way as ordinary matter. If the law of gravitation is strictly the Newtonian law, this leads to an apparent displacement of a star close to the sun’s limb amounting to 0"·87 outwards. (3) The course of a, ray of light is in accordance with Einstein’s generalised relativity theory. This leads to an apparent displacement of a star at the limb amounting to 1"·75 outwards. In either of the last two cases the displacement is inversely proportional to the distance of the star from the sun’s centre, the displacement under (3) being just double the displacement under (2).