FIG. 162.—Double Star Measurement, _a a_, _b b_, first position of fixed, double wire when the vernier reads 0°, and the star runs between the wires; _c c_, _d d_, first position of movable wires. _a´ a´_, _b´ b´_, new position of fixed double wire which determines the angle of position; _c´ c´_, _d´ d´_, new positions of the movable wires which measure the distance. ] It is possible, by knowing the position angles at different dates, to find the angular velocity, and since the areas described by the radius vector are equal in equal times, the length of the radius vector must vary inversely as the square root of the angular velocity, and by taking a number of positions on the orbit of known angular velocity, we can set off radii vectores, and construct an ellipse, or part of one, by drawing a curve through the ends of the radii vectores; and from the part of the ellipse so constructed it is possible to make a good guess at the remainder. The angular size of this ellipse is obtained from the average of all the measures of distance of the stars. This ellipse is then the apparent ellipse described by the star, and the form and position of the true ellipse can be constructed from it from the consideration of the position of the larger star (which must _really_ be the focus), with reference to the focus of the _apparent_ ellipse; for if an ellipse be seen or projected on a plane other than its own, its real foci will no longer coincide with the foci of the projected ellipse. The methods adopted in practice, for which we must refer the reader to other works on the subject, are, however, much more laborious and lengthy than the above outline, which is intended merely to show the possibility, or the faint outline of a method of constructing the real ellipse. When the real ellipse or orbit is known, it is then of course possible to predict the relative positions of the two components. Let us consider in some little detail the actual work of measuring a double star. A useful form for entering observations upon, as taken, is the following, which is copied from one actually used. TEMPLE OBSERVATORY. No. 1. _April 12, 1875·276._ DOUBLE STARS. STRUVE 1338. R.A.—9h. 13m. 28s. DECL. 38° 41´ 20˝. Magnitudes—6·7, 7·2. POSITION. Zero, 109·8. [Illustration] DISTANCE. Direct. Indirect. ½ Diff. 17 97 10 16 97 9·5 ——————— 9·75 mean.