12. _The Vernier._--To enable the observer to read the fractions of the divisions on the circles, a device called a _vernier_ is often employed. It consists of a short, graduated arc, attached to the end of an arm _c_ (Fig. 17), which is carried by the axis, and turns with the telescope. This arc is of the length of _nine_ divisions on the circle, and it is divided into _ten_ equal parts. If 0 of the vernier coincides with any division, say 6, of the circle, 1 of the vernier will be 1/10 of a division to the left of 7, 2 will be 2/10 of a division to the left of 8, 3 will be 3/10, of a division to the left of 9, etc. Hence, when 1 coincides with 7, 0 will be at 6-1/10; when 2 coincides with 8, 0 will be at 6-2/10; when 3 coincides with 9, 0 will be at 6-3/10, etc. [Illustration: Fig. 17.] To ascertain the reading of the circle by means of the vernier, we first notice the zero line. If it exactly coincides with any division of the circle, the number of that division will be the reading of the circle. If there is not an exact coincidence of the zero line with any division of the circle, we run the eye along the vernier, and note which of its divisions does coincide with a division of the circle. The reading of the circle will then be the number of the first division on the circle behind the 0 of the vernier, and a number of tenths equal to the number of the division of the vernier, which coincides with a division of the circle. For instance, suppose 0 of the vernier beyond 6 of the circle, and 7 of the vernier to coincide with 13 of the circle. The reading of the circle will then be 6-7/10. 13. _Hour Circles._--Great circles perpendicular to the celestial equator are called _hour circles_. These circles all pass through the poles of the heavens, as shown in Fig. 18. _EQ_ is the celestial equator, and _P_ and _P'_ are the poles of the heavens. The point _A_ on the equinoctial (Fig. 19) is called the _vernal equinox_, or the _first point of Aries_. The hour circle, _APP'_, which passes through it, is called the _equinoctial colure_. [Illustration: Fig. 18.] 14. _Declination and Right Ascension._--The _declination_ of a heavenly body is its distance north or south of the celestial equator. The _polar distance_ of a heavenly body is its distance from the nearer pole. Declination and polar distance are measured on hour circles, and for the same heavenly body they are complements of each other. [Illustration: Fig. 19.] The _right ascension_ of a heavenly body is its distance eastward from the first point of Aries, measured from the equinoctial colure. It is equal to the arc of the celestial equator included between the first point of Aries and the hour circle which passes through the heavenly body. As right ascension is measured eastward entirely around the celestial sphere, it may have any value from 0° up to 360°. Right ascension corresponds to longitude on the earth, and declination to latitude.