411 292 GEOGRAPHY AND ASTRONOMY. compasses and a scale of chords set up 62 from is to s : Also the declination of the sun that day being 231 degrees northward, set 231 from s downward, and it will find the point E, and the arch n E is the altitude of the equator above the horizon, or the colatitude of the place, viz. 381 degrees : Thence you find the latitude is E z or 511 degrees which completes a quadrant. Then if you draw the line E e it will represent the equator in that scheme. Suppose you take the meridian altitude of the sun on either of the equinoctial days, viz. in March or September, and you find it to be 381 degrees : Set up 311 from H to E, then the suit having no declination the meridian altitude itself shews you the height of the equator above the horizon, which is the complement of the latitude. Sùppose the meridian altitude of the sun at the shortest day be 15 degrees, set up 15 from H to v : Then the sun's declina- tion is 2I1 degrees southward ; therefore set 231 from v upward, and it finds.the point E : And the arch H E is the complement of the latitude as before, viz. 381degrees. For all these practices the chief rule is this. In the sum- mer half-year set your declination downward from the point of the meridian altitude, and it will find the equator's height above the horizon. In winter set your declination upward from the point of the meridian altitude, and it will shew you the height of the equator. The reason of it is most evident in the third and fourth figures. It may be proper in this place to recollect what I have al- ready demonstrated in Sect. V. figure iv. that the latitude of any place (that is the distance of its zenith from the equator) z E is equal tothe elevation ofthe pole ro above the horizon. Thereby it appears. that the elevation of the equator above the horizon of that place on one side as E H (which is the complement of the latitude) is equal to the complement of the pole's elevation on the other side as z P. If therefore the latitude (suppose of London) be R z or p o 511 the colatitude r z or ri E will be 381 for it must complete a quadrant or 90 degrees ; and there- fore if you set the point P 511 degrees above o on the other sideof the horizon, and draw the line p c, you have the axis of the world represented, or the north-pole in its proper elevation for London, and standing (as it ought) at right- angles with the equator E C. I have represented the solution of this sixth problem in a geometrical manner to shew the reason of this practice ; but this problem of finding the latitude by the meridian altitude is much easier performed arithmetically thus. In the winter half-year add the declination to the meridian altitude, and it gives you the colatitude. In the simmer half-year substract the sùn's declina- tion from the meridian altitude and-it gives the colatitude.-
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