EXERCISE 10.--The right ascension of the sun may be found by observing with the sidereal clock the time of its transit over the meridian. Use the equation in § 20, and substitute in place of _U_ the value of the clock correction found from observations of stars on a preceding or following night. If the clock gains or loses _with respect to sidereal time_, take this into account in the value of _U_. EXERCISE 11.--To determine the sun's declination, measure its altitude at the time it crosses the meridian. Use either the method of Exercise 4, or that used with Polaris in Exercise 8. The student should be able to show from Fig. 11 that the declination is equal to the sum of the altitude and the latitude of the place diminished by 90°, or in an equation Declination = Altitude + Latitude - 90°. If the declination as found from this equation is a negative number it indicates that the sun is on the south side of the equator. The right ascension and declination of the sun as observed on each day should be plotted on the map and the date, written opposite it. If the work has been correctly done, the plotted points should fall upon the curved line (ecliptic) which runs lengthwise of the map. This line, in fact, represents the sun's path among the stars. Note that the hours of right ascension increase from 0 up to 24, while the numbers on the clock dial go only from 0 to 12, and then repeat 0 to 12 again during the same day. When the sidereal time is 13 hours, 14 hours, etc., the clock will indicate 1 hour, 2 hours, etc., and 12 hours must then be added to the time shown on the dial. If observations of the sun's right ascension and declination are made in the latter part of either March or September the student will find that the sun crosses the equator at these times, and he should determine from his observations, as accurately as possible, the date and hour of this crossing and the point on the equator at which the sun crosses it. These points are called the equinoxes, Vernal Equinox and Autumnal Equinox for the spring and autumn crossings respectively, and the student will recall that the vernal equinox is the point from which right ascensions are measured. Its position among the stars is found by astronomers from observations like those above described, only made with much more elaborate apparatus.