GNOMON, in astronomy, a stile erected perpendicular to the horizon, in order to find the altitude of the sun. Thus in the right angled triangled A B C, fig. 2, are given A B, the length of the stile, B C, the length of its shadow, and the right angle, AB C. Hence, making C B, the radius, we have this analogy for finding the angle, A C B, the sun's altitude, viz. B C: A B : :radius:tangent of the angle C.
By means of a gnomon, the sun's meri dian altitude, and consequently the lati tude of the place, may be found more ex actly than with the smaller quadrants.
By the same instrument, the height of any object, G H, may be found ; for as D F, fig. 3, the distance of the observer's eye from the gnomon is to D E, the height of the stile, so is F H, the distance of the observer's eye from the object, to G fl, its height.
the Gnomon may be made useful in taking the meridian altitude of the sun, and thence finding the latitude of the place. Having a meridian line drawn through the centre of the gnomon, mark the point where the shadow of the gno mon terminates when projected along the meridian line, and measure the dis tance of that point from the centre of the gnomon, which will be the length of its shadow ; then, having the height of the gnomon, and the length of the sha dow, the sun's altitude is easily found.
Thus, if A B be the gnomon, and A C the length of the shadow, then in the right angled triangle, A B C, we have A B and B C given ; hence the angle C is easily found, for C B:BA:: radius : tangent of the angle C ; that is, as the length of the shadow is to the height of the gnomon, so is radius to the tangent of the sun's altitude above the horizon. Er. We learn from Pliny, at the time of the equinoxes, that the shadow was to the gnomon as 8 : 9, therefore we say as 8 :9::R 9 • —1 125, the tangent of an an : .
gle of 48° 22', which is the height of the equator at Rome, and its complement 41° 38' is therefore the height of the pole, or the latitude- of the place. This method, however, requires correction for the sun's parallax, and for refraction.