GNOMON
, in Astronomy, is an instrument or apparatus for measuring the altitudes, declinations, &c, of the sun and stars. The Gnomon is usually a pillar, or column, or pyramid, erected upon level ground, or a pavement. For making the more considerable observations, both the ancients and moderns have made great use of it, especially the former; and many have preferred it to the smaller quadrants, both as more accurate, easier made, and more easily applied.
The mostancient observation of this kind extant, is that made by Pytheas, in the time of Alexander the Great, at Marseilles, where he found the height of the Gnomon was in proportion to the meridian shadow at the summer solstice, as 213 1/8 to 600; just the same as Gassendi found it to be, by an observation made at the same place, almost 2000 years after, viz, in the year 1636. Ricciol. Almag. vol. 1, lib. 3, cap. 14.
Ulugh Beigh, king of Parthia, &c, used a Gnomon in the year 1437, which was 180 Roman feet high. That erected by Ignatius Dante, in the church of St. Petronius, at Bologna, in the year 1576, was 67 feet high. M. Cassini erected another of 20 feet high, in the same church, in the year 1655.
The Egyptian obelisks were also used as Gnomons; and it is thought by some modern travellers that this was the very use they were designed and built for; it has also been found that their four sides stand exactly facing the four cardinal points of the compass. It may be added, that the Spaniards in their conquest of Peru, found pillars of curious and costly workmanship, set up in several places, by the meridian shadows of which their amatas or philosophers had, by long experience and repeated observations, learned to determine the times of the equinoxes; which seasons of the year were celebrated with great festivity and rich offerings, in honour of the sun. Garcillasso de la Vega, Hist. Peru. lib. 2, cap. 22.
Use of the Gnomon, in taking the meridian altitude of the Sun, and thence finding the Latitude of the place.—— A meridian line being drawn through the centre of the Gnomon, note the point where the shadow of the Gnomon terminates when projected along the meridian line, and measure the distance of that extreme 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 shadow, the sun's altitude is thence easily found.
Suppose, ex. gr. AB the Gnomon, and AC the length of the shadow. Here in the right-angled triangle ABC, are given the base AC, and the perpendicular AB, to find the angle C, or the sun's altitude, which will be found by this analogy, as CA : AB : : radius: the tang. of [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.
The following example will serve to illustrate this proposition: Pliny says, Nat. Hist. lib. 2, cap. 72, that at Rome, at the time of the equinoxes, the shadow is to the Gnomon as 8 to 9; therefore as or radius : a tangent, to which answers the angle 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.
Riccioli remarks the following defects in the observations of the sun's height, made with the Gnomon by the ancients, and some of the moderns: viz, that they neglected the sun's parallax, which makes his apparent altitude less, by the quantity of the parallax, than it would be, if the Gnomon were placed at the centre of the earth: 2d, they neglected also the refraction, by which the apparent height of the sun is a little increased: and 3dly, they made the calculations from the length of the shadow, as if it were terminated by a ray coming from the centre of the sun's disc, whereas the shadow is really terminated by a ray coming from the upper edge of the sun's disc; so that, instead of the height of the sun's centre, their calculations gave the height of the upper edge of his disc. And therefore, to the altitude of the sun found by the Gnomon, the sun's parallax must be added, and from the sum must be subtracted the sun's semidiameter, and refraction, which is different at different altitudes; which being done, the correct height of the equator at Rome will be 48° 4′ 13″, the complement of which, or 41° 55′ 46″, is the latitude. Ricciol. Geogr. Refor. lib. 7, cap. 4.|
The preceding problem may be resolved more accurately by means of a ray of light let in through a small hole, than by a shadow, thus: Make a circular perforation in a brass plate, to transmit enough of the sun's rays to exhibit his image on the floor, or a stage; fix the plate parallel to the horizon in a high place, proper for observation, the height of which above the floor let be accurately measured with a plummet. Let the floor, or stage, be perfectly plane and horizontal, and coloured over with some white substance, to shew the sun more distinctly. Upon this horizontal plane draw a meridian line passing through the foot or centre of the Gnomon, i. e. the point upon which the plummet falls from the centre of the hole; and upon this line note the extreme points I and K of the sun's image or diameter, and from each end subtract the image of half the diameter of the aperture, viz KH and LI: then will HL be the image of the sun's diameter, which, when bisected in B, gives the point on which the rays fall from the centre of the sun.
Now having given the line AB, and the altitude of the Gnomon AG, beside the right angle A, the angle B, or the apparent altitude of the sun's centre, is easily found, thus: as AB : AG : : radius: tang. angle B.
Gnomon, in Dialling, is the style, pin, or cock of a dial, the shadow of which points out the hours. This is always supposed to represent the axis of the world, to which it is therefore parallel, or coincident, the two ends of it pointing straight to the north and south poles of the world.
Gnomon, in Geometry, is a figure formed of the two complements, in a parallelogram, together with either of the parallelograms about the diameter. Thus the parallelo- gram AC being divided into four parallelograms by the two lines DG, EF parallel to the sides, forming the two complements AB and BC, with the two DE, FG about the diameter HI: then the two Gnomons are , and .
Gnomonic Projection of the Sphere, is the representation of the circles of an hemisphere upon a plane touching it in the vertex, by the eye in the centre, or by lines or rays issuing from the centre of the hemisphere, to all the points in the surface.
In this projection of the sphere, all the great circles are projected into right lines, on the plane, of an indefinite length; and all lesser circles that are parallel to the plane, into circles; but if oblique to the plane, then are they projected either into ellipses or hyperbolas, according to their different obliquity. It has its name from Gnomonics, or Dialling, because the lines on the face of every dial are from a projection of this sort: for if the sphere be projected on any plane, and upon that side of it on which the sun is to shine; also the projected pole be made the centre of the dial, and the axis of the globe the style or Gnomon, and the radius of projection its height; you will have a dial drawn with all its furniture. See Emerson's Projection of the Sphere.
