Page:Popular Science Monthly Volume 58.djvu/462

454 Certainly we can not learn all that we wish, yet we may learn something that will help us form some idea of the respective distances of the stars and the actual velocity of their motions. An obvious remark is that the more distant a star the slower it will seem to move. We must, therefore, distinguish between the linear or actual motion of a star, expressed as so many kilometers per second, and its apparent or angular motion of so many seconds per year, derived by measuring its change of direction as we see it with our instruments.

We shall now endeavor to explain Kapteyn's method in such a way that the reasoning shall be clear without repeating the algebraic operations which it involves. Let us conceive that Fig. 2 is drawn on the celestial sphere as we look up at the heavens. S is the direction of a star in the sky as we see it. Let us also suppose that the solar apex, situated in the constellation Lyra, lies anywhere horizontally to the left of the star, in the direction of the arrow-head marked Apex. Suppose

also that, were the solar system at rest, we should see the star moving along the line S D. Let the length of the line S D represent the motion in some unit of time, say, one year. Next, suppose the star at rest. Then in consequence of the motion of the solar system, by which we are carried toward the apex, the star would seem to be moving with its parallactic motion in the direction S B, away from the apex. Let the length of this line represent the parallactic motion in one year. Then by the theory of composition of motions, the star moving by its real motion from S to D, and by the motion of the earth having an apparent motion from S to B, will appear to us to move along the diagonal S A of the parallelogram. Thus, the line S A will represent the annual proper motion of the star as we observe it with our instruments, and which can be resolved into the apical motion, in the direction S B, and is cross-motion in the direction Sτ.

The apical motion consists of two parts, one the parallactic motion, equal to S B; the other real, and due to the motion of the star itself along the line S D, and equal to the distance of D from the line Sτ.

We have now to inquire how, in the case of a great number of stars, we may distinguish between the two parts.