[Illustration: FIG. 84.—Illustrating the effect of the sun’s motion in space.] If the observed proper motions of stars examined are not of this character, they cannot be explained as due _merely_ to the motion of the sun; but if they shew some tendency to move in this way, then the observations can be most simply explained by regarding the sun as in motion, and by assuming that the discrepancies between the effects resulting from the assumed motion of the sun and the observed proper motions are due to the motions in space of the several stars. From the few proper motions which Mayer had at his command he was, however, unable to derive any indication of a motion of the sun. Herschel used the proper motions, published by Maskelyne and Lalande, of 14 stars (13 if the double star Castor be counted as only one), and with extraordinary insight detected in them a certain uniformity of motion of the kind already described, such as would result from a motion of the sun. The point on the celestial sphere towards which the sun was assumed to be moving, the =apex= as he called it, was taken to be the point marked by the star λ in the constellation Hercules. A motion of the sun in this direction would, he found, produce in the 14 stars apparent motions which were in the majority of cases in general agreement with those observed.[158] This result was published in 1783, and a few months later _Pierre Prévost_ (1751-1839) deduced a very similar result from Tobias Mayer’s collection of proper motions. More than 20 years later (1805) Herschel took up the question again, using six of the brightest stars in a collection of the proper motions of 36 published by Maskelyne in 1790, which were much more reliable than any earlier ones, and employing more elaborate processes of calculation; again the apex was placed in the constellation Hercules, though at a distance of nearly 30° from the position given in 1783. Herschel’s results were avowedly to a large extent speculative, and were received by contemporary astronomers with a large measure of distrust; but a number of far more elaborate modern investigations of the same subject have confirmed the general correctness of his work, the earlier of his two estimates appearing, however, to be the more accurate. He also made some attempts in the same papers and in a third (published in 1806) to estimate the speed as well as the direction of the sun’s motion; but the work necessarily involved so many assumptions as to the probable distances of the stars—which were quite unknown—that it is not worth while to quote results more definite than the statement made in the paper of 1783, that “We may in a general way estimate that the solar motion can certainly not be less than that which the earth has in her annual orbit.”