stood that the length of this line is taken to represent the actual motion; the latter would be infinitesimal as compared with its length; we use it only to show direction. We may, however, use the line to represent on a magnified scale the actual amount of the motion during any unit of time, say, one year. It may be divided into two components; one, S, in the direction of the line of sight from us to the star, which for brevity we shall call the radial line, and the other, S M, at right angles to that line.
It must be understood that, as the term 'proper motion' is commonly used, only the component S M, can be referred to, because the radial component, S R, does not admit of being determined by telescopic vision. As we know from the preceding chapters, it can in the case of the brighter stars be determined by spectroscopic measurement of the radial motion. At present we leave this component out of consideration.
The visible component, S M, can also be resolved into two perpendicular components, the one east and west on the celestial sphere, the other north and south. The former is the proper motion in right ascension (the measured motion in this coordinate being multiplied by the co-sine of the declination to reduce it to a great circle), and the other is the proper motion in declination. In star catalogues these two motions are given, so far as practicable. Thus, altogether the actual motion of a star in space may be resolved into three components: that of right ascension, that of declension, and the radial component.
An additional consideration is now to be added. The proper motion of a star, as observed and given in catalogues, is a motion relative to our system. It has been shown in a former chapter that the latter has a proper motion of its own. When account is taken of this, and the motions are all reduced as well as we can to a common center of gravity of the whole stellar system, we conceive the observed proper motion of the star to be made up of two parts, of which one is the actual motion of the star relative to the common center, and the other due to the motion of the sun, carrying the earth with it. The direction of the latter appears to us opposite that of the motion of the sun. The sun's motion being directed to the constellation Lyra, it follows that the component in question in the case of the stars is directed toward the opposite constellation, Argo. This component, as we know, is termed the parallactic motion, being dependent on the distance or parallax of the star.
As in the case of other proper motions, we may measure the parallactic motion either in angular measure, as so many seconds per century, or in linear measure, as so many kilometers per second. The relation of the two measures depends on the distance of a star. The simplest conception of the relation may be gained by reflecting that the
