The complete achievement of this result is, of course, a thing of the remote future, but sufficient progress in determining these motions has been made during the past century and a half to show that nearly every lucid star possesses some proper motion, although in most cases it is very small, there being less than 100 known stars in which it amounts to so much as 1" per annum--i. e., a rate of motion across the sky which would require nearly the whole Christian era to alter a star's direction from us by so much as the moon's angular diameter. The most rapid known proper motion is that of a telescopic star midway between the equator and the south pole, which changes its position at the rate of nearly 9" per annum, and the next greatest is that of another telescopic star, in the northern sky, No. 28 of Fig. 122. It is not until we reach the tenth place in a list of large proper motions that we find a bright lucid star, No. 1 of Fig. 122. It is a significant fact that for the most part the stars with large proper motions are precisely the ones shown in Fig. 122, which is designed to show stars near the earth. This connection between nearness and rapidity of proper motions is indeed what we should expect to find, since a given amount of real motion of the star along its orbit will produce a larger angular displacement, proper motion, the nearer the star is to the earth, and this fact has guided astronomers in selecting the stars to be observed for parallax, the proper motion being determined first and the parallax afterward. 192. THE PATHS OF THE STARS.--We have already seen reason for thinking that the orbit along which a star moves is practically a straight line, and from a study of proper motions, particularly their directions across the sky, it appears that these orbits point in all possible ways--north, south, east, and west--so that some of them are doubtless directed nearly toward or from the sun; others are square to the line joining sun and star; while the vast majority occupy some position intermediate between these two. Now, our relation to these real motions of the stars is well illustrated in Fig. 112, where the observer finds in some of the shooting stars a tremendous proper motion across the sky, but sees nothing of their rapid approach to him, while others appear to stand motionless, although, in fact, they are moving quite as rapidly as are their fellows. The fixed star resembles the shooting star in this respect, that its proper motion is only that part of its real motion which lies at right angles to the line of sight, and this needs to be supplemented by that other part of the motion which lies parallel to the line of sight, in order to give us any knowledge of the star's real orbit. [Illustration: FIG. 123.--Motion of Polaris in the line of sight as determined by the spectroscope. FROST.]