The student should not fail to note one important difference between proper motions and the motions determined spectroscopically: the latter are given directly in miles per second, or per hour, while the former are expressed in angular measure, seconds of arc, and there can be no direct comparison between the two until by means of the known distances of the stars their proper motions are converted from angular into linear measure. We are brought thus to the very heart of the matter; parallax, proper motion, and motion in the line of sight are intimately related quantities, all of which are essential to a knowledge of the real motions of the stars. [Illustration: FIG. 125.--Spectrum of Pollux.--PICKERING.] 194. STAR DRIFT.--An illustration of how they may be made to work together is furnished by some of the stars--which make up the Great Dipper--β, γ, ε, and ζ Ursæ Majoris, whose proper motions have long been known to point in nearly the same direction across the sky and to be nearly equal in amount. More recently it has been found that these stars are all moving toward the sun with approximately the same velocity--18 miles per second. One other star of the Dipper, δ Ursæ Majoris, shares in the common proper motion, but its velocity in the line of sight has not yet been determined with the spectroscope. These similar motions make it probable that the stars are really traveling together through space along parallel lines; and on the supposition that such is the case it is quite possible to write out a set of equations which shall involve their known proper motions and motions in the line of sight, together with their unknown distances and the unknown direction and velocity of their real motion along their orbits. Solving these equations for the values of the unknown quantities, it is found that the five stars probably lie in a plane which is turned nearly edgewise toward us, and that in this plane they are moving about twice as fast as the earth moves around the sun, and are at a distance from us represented by a parallax of less than 0.02"--i. e., six times as great as the outermost circle in Fig. 122. A most extraordinary system of stars which, although separated from each other by distances as great as the whole breadth of Fig. 122, yet move along in parallel paths which it is difficult to regard as the result of chance, and for which it is equally difficult to frame an explanation. [Illustration: FIG. 126.--The Great Dipper, past, present, and future.]