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Plate H. would appear as dark as in the night, and the stars would be seen as clear as in the nocturnal sky. In this case, we should have no twilight; but a sudden transition from the brightest sun-shine to the blackest darkness, immediately after sun-set; and from the blackest darkness to the brightest sun-shine, at sun-rising; which would be extremely inconvenient, if not blinding, to all mortals. But, by means of the atmosphere, we enjoy the Sun's light, reflected from the aerial particles, for some time before he rises, and after he sets. For, when the Earth by its rotation has withdrawn our sight from the Sun, the atmosphere being still higher than we, has the Sun's light imparted to it; which gradually decreases until he has got 18 degrees below the horizon; and then, all that part of the atmosphere which is above us is dark. From the length of twilight, the Doctor has calculated the height of the atmosphere (so far as it is dense enough to reflect any light) to be about 44 miles. But it is seldom dense enough at the height of two miles to bear up the clouds.
178. The atmosphere refracts the Sun's rays so, the Sun in as to bring him in sight every clear day, before he rises in the horizon; and to keep him in view for rises, and some minutes after he is really set below it. For, at keeps him in view some times of the year, we see the Sun ten minutes longer above the horizon than he would be if there were no refraction; and above six minutes every day
at a mean rate.
179. To illustrate this, let IEK be a part of the Earth's surface, covered with the atmosphere HGFC; and let HEO be the sensible horizon* of an observer at E. When the Sun is at A, really below the horizon, a ray of light, AC, proceeding from him comes straight to C, where it falls on the surface of the atmosphere, and there entering a denser medium, it is turned out of its rectilineal
As far as one can see round him on the Earth.
course ACdG, and bent down to the observer's eye at E; who then sees the Sun in the direction of the refracted ray Ede, which lies above the horizon, and being extended out to the heavens, shews the Sun at B, 171.
180. The higher the Sun rises, the less his rays are refracted, because they fall less obliquely on the surface of the atmosphere, § 172. Thus, when the Sun is in the direction of the line EƒL continued, he is so nearly perpendicular to the surface of the Earth at E, that his rays are but very little bent from a rectilineal course.
181. The Sun is about 32 min. of a deg. in The quan breadth, when at his mean distance from the Earth; tity of reand the horizontal refraction of his rays is 33 min. which being more than his whole diameter, brings all his disc in view, when his uppermost edge rises in the horizon. At ten deg. height, the refraction is not quite 5 min.; at 20 deg. only 2 min. 26 sec.; at 30 deg. but 1 min. 32 sec.; and at the zenith, it is nothing: the quantity throughout, is shewn by the following table, calculated by Sir ISAAC NEWTON.
182. A TABLE shewing the Refractions of the Sun, Moon, and Stars; adapted to their apparent Altitudes.
183. In all observations, to obtain the true alti- Plate II. tude of the Sun, Moon, or stars, the refraction The inmust be subtracted from the observed altitude. But constancy the quantity of refraction is not always the same of refrac at the same altitude; because heat diminishes the tions. air's refractive power and density, and cold increases both; and therefore no one table can serve precisely for the same place at all seasons, nor even at all times of the same day, much less for different climates; it having been observed that the horizontal refractions are near a third part less at the equator than at Paris. This is mentioned by Dr. SMITH in the 370th remark on his Optics, where the following account is given of an extraordinary refraction of the Sun-beams by cold. "There is a famous A very reobservation of this kind made by some Hollanders markable that wintered in Nova-Zembla in the year 1596, who cerning were surprised to find, that after a continual night refrac of three months, the Sun began to rise seventeen days sooner than according to computation, deduced from the altitude of the pole, observed to be 76°; which cannot otherwise be accounted for, than by an extraordinary refraction of the Sun's rays passing through the cold dense air in that climate. Kepler computes that the Sun was almost five degrees below the horizon when he first appeared; and consequently the refraction of his rays was about nine times greater than it is with us."
184. The Sun and Moon appear of an oval figure, as FCGD, just after their rising, and before their Fig. X. setting the reason of which is, the refraction being greater in the horizon than at any distance above it, the lower limb G is more elevated by it than the upper. But although the refraction shortens the vertical diameter FG, it has no sensible effect on the horizontal diameter CD, which is all equally elevated. When the refraction is so small as to be im
perceptible, the Sun and Moon appear perfectly round, as AEBF.
185. When we have nothing but our imagination to assist us in estimating distances, we are liable to be deceived; for bright objects seem nearer to us than those which are less bright, or than the same objects do when they appear less bright and worse defined, even though their distance be the same. And if in both cases they are seen under the same angle*, our imagination naturally suggests an idea of a greater distance between us and those objects which appear fainter and worse defined than those which appear brighter under the same angles; especially if they be such objects as we were never near to, and of whose real magnitudes we can be no judges by sight.
186. But it is not only in judging of the different apparent magnitudes of the same objects, which are better or worse defined by their being more or less bright, that we may be deceived: for we may make a wrong conclusion even when we view them
nor always of those
which are accessible.
The nearer an object is to the eye, the bigger it appears, and it is seen under the greater angle. To illustrate this a little, suppose an arrow in the position IK, perpendicular to the right line HA, drawn from the eye at H through the middle of the arrow at 0. It is plain that the arrow is seen under the angle IHK, and that HO, which is its distance from the eye, divides into halves both the arrow and the angle under which it is seen, viz. the arrow into 10, OK; and the angle into IHO and KHO: and this will be the case at whatever distance the arrow is placed. Let now three arrows, all of the same length with IK, be placed at the distances HA, HCE, H, still perpendicular to, and bisected by the right line HA; then will AB, CD, EF, be each equal to, and represent OI; and AB (the same as OI) will be seen from H under the angle AHB; but CD (the same as Of) will be seen under the angle CHD, or AHL; and EF (the same as OI) will be seen under the angle EHF, or CHA, or AHM. Also EF. or OI, at the distance HE, will appear as long as ON would at the distance HC, or as AM would at the distance HA; and CD, or IO, at the distance HC, will appear as long as AL would at the distance HA. So that as an object approaches the eye, both its magnitude and the angle under which it is seen increase; and the contrary as the object recedes.