Other allineations given by Ptolemy are: Spica, Arcturus and β Bootis; Spica, δ Corvi and γ Corvi; α Libræ, Arcturus and ζ Ursæ Majoris. Arcturus does not now fit very well to these alignments, and nearly two centuries ago it, together with Aldebaran and Sirius, was on other grounds suspected to have changed its place in the sky since the days of Ptolemy. This discovery, long since fully confirmed, gave a great impetus to observing with all possible accuracy the right ascensions and declinations of the stars, with a view to finding other cases of what was called proper motion—i. e., a motion peculiar to the individual star as contrasted with the change of right ascension and declination produced for all stars by the precession.
Since the middle of the eighteenth century there have been made many thousands of observations of this kind, whose results have gone into star charts and star catalogues, and which are now being supplemented by a photographic survey of the sky that is intended to record permanently upon photographic plates the position and magnitude of every star in the heavens down to the fourteenth magnitude, with a view to ultimately determining all their proper motions.
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.
193. Motion in the line of sight.—It is only within the last 25 years that anything whatever has been accomplished in determining these stellar motions of approach or recession, but within that time much progress has been made by applying the Doppler principle ([§ 89]) to the study of stellar spectra, and at the present time nearly every great telescope in the world is engaged upon work of this kind. The shifting of the lines of the spectrum toward the violet or toward the red end of the spectrum indicates with certainty the approach or recession of the star, but this shifting, which must be determined by comparing the star's spectrum with that of some artificial light showing corresponding lines, is so small in amount that its accurate measurement is a matter of extreme difficulty, as may be seen from [Fig. 123]. This cut shows along its central line a part of the spectrum of Polaris, between wave lengths 4,450 and 4,600 tenth meters, while above and below are the corresponding parts of the spectrum of an electric spark whose light passed through the same spectroscope and was photographed upon the same plate with that of Polaris. This comparison spectrum is, as it should be, a discontinuous or bright-line one, while the spectrum of the star is a continuous one, broken only by dark gaps or lines, many of which have no corresponding lines in the comparison spectrum. But a certain number of lines in the two spectra do correspond, save that the dark line is always pushed a very little toward the direction of shorter wave lengths, showing that this star is approaching the earth. This spectrum was photographed for the express purpose of determining the star's motion in the line of sight, and with it there should be compared Figs. [124] and [125], which show in the upper part of each a photograph obtained without comparison spectra by allowing the star's light to pass through some prisms placed just in front of the telescope. The lower section of each figure shows an enlargement of the original photograph, bringing out its details in a way not visible to the unaided eye. In the enlarged spectrum of β Aurigæ a rate of motion equal to that of the earth in its orbit would be represented by a shifting of 0.03 of a millimeter in the position of the broad, hazy lines.
Despite the difficulty of dealing with such small quantities as the above, very satisfactory results are now obtained, and from them it is known that the velocities of stars in the line of sight are of the same order of magnitude as the velocities of the planets in their orbits, ranging all the way from 0 to 60 miles per second—more than 200,000 miles per hour—which latter velocity, according to Campbell, is the rate at which μ Cassiopeiæ is approaching the sun.