300 GEOGRAPHY AND ASTRONOMY. Problem XVIII. "The day of the month and the sun's altitude being given, how to find the hour or azimuth of the sun by the analemma. The two foregoing problems acquaint you how to fix the precise point of the sun's place any minute of any day in the year by theparallel of declination and parallel ofaltitude crossing each other. Now suppose the day. of the month be the 6th of May, and the sun's altitude34 degrees ih the morning. Describe the semi- circle x z o in figure xxiv. for the meridian. Make n c o the horizon. Draw E c making with s e an angle of the colatitude 34I degrees to represent the equator. Seek the declinationof the sun, and in the tables or scales you will find it near 161 degrees northward; set 161,from E to L ; draw n R for the path of the sun that day, parallel to E is the equator. Then set the altitude 34d. from u to A. draw A L parallel to it o the horizon, thus the point O shews the place of the sun as before. Now if you would find the hour, you must draw the line c N at right angles with the equator E c, which represents thesix o'clock hour line ; and the distance 6 0 is the sun's hour from six ; that is, his hour after six in the morning, or before six in the afternoon. If you are to seek the azimuth, then you must draw the line c z perpendicular to x o, which is the vertical circle of east or west ; then the extent e o is the sun's azimuth from east in the morning, or from west in the afternoon. Thus you see that in order to solve those two difficult prob- lems of the hour or azimuth, you need but a very few lines to perform the whole operation ; for if you want only the hour, e z may be omitted ; if you want only the azimuth, c N may be emitted. Yet in the winter half-year, suppose the 13th of November, when the declination is near 18 degrees south, it must be set downward. as E w from E toward x ; then you cannot so well find the hour without producing the six o'clock line N e below the horizon down to s,.that you may measure the hour from s or six. Observe also that this little diagram in figurexxiv. will solve a great variety of problems besides the hour and azimuth on the 6th of May : it strews the length of the day by the semi. diurnal arch n R.: The sun's ascensional difference is 6 a. His amplitude is c R. His azimuth from east or west at six is T 6. His altitude at east and west is v c. HIis meridian altitude is the arch n n : and his azimuth from east, or west at rising or setting is the line a R. ProblemXIX. " How to measure the number of degrees on any of the straight lines in the analemma."
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