Note 47 — CHAP. IX. The Method of finding the Distances of the Sun, Moon, and Planets.

The Altitude of any celestial Phenomenon is an arc of the Sky intercepted between the Horizon and the Phenomenon. In Fig. VI. of Plate II. let HOX be a horizontal line, supposed to be extended from the eye at A to X, where the Sky and Earth seem to meet at the end of a long and level plain; and let S be the Sun. The arc XY will be the Sun’s height above the Horizon at X, and is found by the instrument EDC, which is a quadrantal board, or plate of metal, divided into 90 equal parts or degrees on its limb DPC; and has a couple of little brass plates, as a and b, with a small hole in each of them, called Sight-Holes, for looking through, parallel to the edge of the Quadrant whereon they stand. To the center E is fixed one end of a thread F, called the Plumb-Line, which has a small weight or plummet P fixed to it’s other end. Now, if an observer holds the Quadrant upright, without inclining it to either side, and so that the Horizon at X is seen through the sight-holes a and b, the plumb-line will cut or hang over the beginning of the degrees at o, in the edge EC; but if he elevates the Quadrant so as to look through the sight-holes at any part of the Heavens, suppose to the Sun at S; just so many degrees as he elevates the sight-hole b above the horizontal line HOX, so many degrees will the plumb-line cut in the limb CP of the Quadrant. For, let the observer’s eye at A be in the center of the celestial arc XYV (and he may be said to be in the center of the Sun’s apparent diurnal Orbit, let him be on what part of the Earth he will) in which arc the Sun is at that time, suppose 25 degrees high, and let the observer hold the Quadrant so that he may see the Sun through the sight-holes; the plumb-line freely playing on the quadrant will cut the 25th degree in the limb CP equal to the number of degrees of the Sun’s Altitude at the time of observation. N. B. Whoever looks at the Sun, must have a smoaked glass before his eyes to save them from hurt. The better way is not to look at the Sun through the sight-holes, but to hold the Quadrant facing the eye, at a little distance, and so that the Sun shining through one hole, the ray may be seen to fall on the other.