It must be admitted that the wide difference between the position of the apex from large and from small proper motions, as found by Porter, Boss and Stumpe, require explanation. Since the apparent motions of the stars are less the greater their distance, these results, if accepted as real, would lead to the conclusion that the position of the solar apex derived from stars near to us was much further south than when derived from more distant stars. This again would indicate that our sun is one of a cluster or group of stars, having, in the general average, a different proper motion from the more distant stars. But this conclusion is not to be accepted as real until the subject has been more exhaustively investigated. The result may depend on the selection of the stars; and there is, as yet, no general agreement among investigators as to the best way of making the determination. The next question which arises is that of the velocity of the solar motion. The data for this determination are more meagre and doubtful than those for the direction of the motion. The most obvious and direct method is to determine the parallactic motion of the stars of known parallax. Regarding any star 90° from the apex of the solar motion as in a state of absolute rest, we have the obvious rule that the quotient of its parallactic motion during any period, say a century, divided by its parallax, gives the solar motion during that period, in units of the earth’s distance from the sun. In fact, by a motion of the sun through one such unit, the star would have an apparent motion in the opposite direction equal to its annual parallax. If the star were not 90° from the apex we can easily reduce its observed parallactic motion by dividing it by the sign of its actual distance from the apex. Since every star has, presumably, a proper motion of its own, we can draw no conclusion from the apparent motion of any one star, owing to the impossibility of distinguishing its actual from its parallactic motion. We should, therefore, base our conclusion on the mean result from a great number of stars, whose average position or center of mass we might assume to be at rest. Here we meet the difficulty that there are only about 60 stars whose parallaxes can be said to be determined; and one-half of these are too near the apex, or have too small a parallax, to permit of any conclusion being drawn from them. A second method is based on the spectroscopic measures of the motion of stars in the line of sight, or the line from the earth to the star. A star at rest in the direction of the solar apex would be apparently moving toward us with a velocity equal to that of the solar motion. Assuming the center of mass of all the stars observed to be at rest, we should get the solar motion from the mean of all.