306 GEOGRAPHY AND ASTRONOMY. azimuth, and many other astronomical problemsby the analemma for any day in the year. But this method which I proposed of performing them by finding the sun's place in the ecliptic by any short general scale or table, is liable to the mistakeof near halfa degree sometimes. Observe here, ifyou have by any means obtained and drawn the sun's path, viz. n a for any given day, you may find both the sun's place in the ecliptic and its right ascension by drawing c M the ecliptic. For then c x will be the sine of the sun's place or longitude to the common radius c M : And 6 x will be the sine of the sun's distance on the equator from the nearest equinoctial point, but the radius is6n : From hence you mayeasily compute its right ascension. Note, Though the little schemes and diagrams which belong to this book, are sufficient for a demonstration of the truth and reason of these operations, .yet if you have occasion to perform them inorder to find the hour or azimuth with great exactness, you must have a large flat board, or very stiff pasteboard witlt white paper pasted on it, that you may draw a semicircle upon it of 9 or 10, or rather 12 inches radius ; and the lines must not be drawn with ink, nor with a pencil ; for they cannot be drawn fine enough: But draw them only with the point of the compass; andyou must observe every part of the operation with the great- est accuracy, and take the sun's place or declination out of good tables : For a little error in some places will make a foul and large mistake in the final answer to the problem. Yet if the sun be within seven or eight days of either side of either solstice, you may make the tropic of cancer or capricorn serve for the path of the sun, without any sensible error ; for in 16 days together at the solstices, its declination does not alter above 12 or 15 minutes : But near the equinox you must be very exact ; for the declination alters greatly every day at that time of the year. There might be also various geographical practices or prob- lems, that relate to the earthlyglobe performed by the assistance of the analemma, and several other astronomical problems relating to the sun and to the fixed stars ; but some of them are more troublesome to perform ; and what 1 have already written on this subject is abundantly apf&cient togive the learner an acquaintance with thenature and reason of these lines, and the operations that are performed by them. And for my own part I must confess, there is nothing has contributed to establish ,all the ideas of the doctrineof the sphere in my mind, more than a.perfect acquaint- ance with the analemma. Problem XXII, "how to draw a meridian line, or a line directly pointing to north and south on a hOrizotatal plane by the altitude or azimuthof the sun beinggiven."
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