191. PROPER MOTIONS.--It is evident that these stars are too far apart for their mutual attractions to have much influence one upon another, and that we have here a case in which, according to § 34, each star is free to keep unchanged its state of rest or motion with unvarying velocity along a straight line. Their very name, _fixed stars_, implies that they are at rest, and so astronomers long believed. Hipparchus (125 B. C.) and Ptolemy (130 A. D.) observed and recorded many allineations among the stars, in order to give to future generations a means of settling this very question of a possible motion of the stars and a resulting change in their relative positions upon the sky. For example, they found at the beginning of the Christian era that the four stars, Capella, ε Persei, α and β Arietis, stood in a straight line--i. e., upon a great circle of the sky. Verify this by direct reference to the sky, and see how nearly these stars have kept the same position for nearly twenty centuries. Three of them may be identified from the star maps, and the fourth, ε Persei, is a third-magnitude star between Capella and the other two. 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.