188. DISTANCES OF THE STARS.--Now, in order to separate the true from the false in this last mode of thinking about the stars, we need some knowledge of their real distances from the earth, and in seeking it we encounter what is perhaps the most delicate and difficult problem in the whole range of observational astronomy. As shown in Fig. 121, the principles involved in determining these distances are not fundamentally different from those employed in determining the moon's distance from the earth. Thus, the ellipse at the left of the figure represents the earth's orbit and the position of the earth at different times of the year. The direction of the star _A_ at these several times is shown by lines drawn through _A_ and prolonged to the background apparently furnished by the sky. A similar construction is made for the star _B_, and it is readily seen that owing to the changing position of the observer as he moves around the earth's orbit, both _A_ and _B_ will appear to move upon the background in orbits shaped like that of the earth as seen from the star, but having their size dependent upon the star's distance, the apparent orbit of _A_ being larger than that of _B_, because _A_ is nearer the earth. By measuring the angular distance between _A_ and _B_ at opposite seasons of the year (e. g., the angles _A--Jan.--B_, and _A--July--B_) the astronomer determines from the change in this angle how much larger is the one path than the other, and thus concludes how much nearer is _A_ than _B_. Strictly, the difference between the January and July angles is equal to the difference between the angles subtended at _A_ and _B_ by the diameter of the earth's orbit, and if _B_ were so far away that the angle _Jan.--B--July_ were nothing at all we should get immediately from the observations the angle _Jan.--A--July_, which would suffice to determine the stars' distance. Supposing the diameter of the earth's orbit and the angle at _A_ to be known, can you make a graphical construction that will determine the distance of _A_ from the earth? [Illustration: FIG. 121.--Determining a star's parallax.] The angle subtended at _A_ by the radius of the earth's orbit--i. e., 1/2 (_Jan.--A--July_)--is called the star's parallax, and this is commonly used by astronomers as a measure of the star's distance instead of expressing it in linear units such as miles or radii of the earth's orbit. The distance of a star is equal to the radius of the earth's orbit divided by the parallax, in seconds of arc, and multiplied by the number 206265.