The uses of the position micrometer as it is called are very various. In examination of the sun it is used to ascertain the position of spots on the surface, and the rate of their motion and change. The lunar craters require mapping, and their distances and bearing from certain fixed points measuring, for this then the position micrometer comes into use. The varying diameters and the inclinations of the axes of the planets and the periods of revolution of the satellites are determined, and the position of their orbits fixed, in like manner. When a comet appears it is of importance to determine not only the direction of its motion among the stars, but the position of its axis of figure, and the angles of position and dimensions of its jets. The following diagram gives an example of the manner in which the position of its axis of figure is determined. First the nucleus is made to run along the fixed wire, so that it may be seen that the north vernier truly reads zero under this condition; if it does not its index error is noted. The system of wires is then rotated till one of the wires passes through the nucleus and fairly bisects the dark part behind the nucleus. [Illustration: FIG. 161.—Measurement of the Angle of Position of the Axis of Figure of a Comet, _a a_, positions of fixed wire when the north vernier is at zero; _d d_ position of movable wire under like conditions; _a´ a´_, _d´ d´_, positions of these wires which enable the angle of position of the comet’s axis to be measured. The angle _a a´_ or _d d´_ is the angle required. ] It need scarcely be said that these observations are also of importance with reference to the motion of the binary stars, those compound bodies, those suns revolving round each other, the discovery of which we owe to the elder Herschel. We may thus have two stars a small distance apart; at another time we may have them closer still; and at another we may have them gradually separating, with their relative position completely changed. By means of the wire micrometer and the arrangement for turning the system of wires into different positions with regard to the parallel of declination, we have a means of determining the positions occupied by the binary stars in all parts of their apparent orbit, as well as their distances in seconds of arc. It is found, however, by experience that the errors of observation made in estimating distances are so large, relatively to the very small quantities measured, that it is absolutely necessary to make the determination of the orbit depend chiefly on the positions. And this is done in the following way. [Illustration: