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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 EfL 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 321 min. of a deg. in breadth, when at his mean distance from the Earth ; tity of re.
fraction. and 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. Appar.
Refrac- AP Refrac- Ap RefracAlt. tion.
tion. Alt. tion.
183. In all observations, to obtain the true alti- Plate II. tude of the Sun, Moon, or stars, the refraction must be subtracted from the observed altitude. But constancy the quantity of refraction is not always the same of refracat 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 caseiron were surprised to find, that afier a continual night refrac. of three months, the Sun began to rise seventeen
tions, 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 be. low 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 elevat. ed. When the refraction is so small as to be im.
perceptible, the Sun and Moon appear perfectly
round, as AEB F. Our ima. 185. When we have nothing but our imagination to gination
assist us in estimating distances, we are liable to be judge deceived; for bright objects seem nearer to us than of the dis. those which are less bright, or than the same objects tance of do when they appear less bright and worse defined, inaccessi. even though their distance be the same. And if in jects ; 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
The nearer an object is to the eye, the bigger it appears, and ways
it is seen under the greater angle. To illustrate this a little, suppose those
an arrow in the position I K, perpendicular to the right line HA, which are
drawn from the eye at H through the middle of the arrow at 0. lc accessi.
is plain that the arrow is seen under the angle IHK, and that HO, ble.
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 Ol; and A B (the same as I) 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 È F(the same as OI) will be seen under the angle EHF, or CHN, or AHM. Also ÉF. or 01, 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 10, 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 the object recedex.
under equal degrees of brightness, and under equal angles; although they be objects whose bulks we are generally acquainted with, such as houses or trees; for proof of which, the two following instances may suffice:
First, When a house is seen over a very broar? The reariver by a person standing on a low ground, who son as
signed. sees nothing of the river, nor knows of it beforehand; the breadth of the river being hid from him, because the banks seem contiguous, he loses the idea of a distance equal to that breadth; and the house seems small because he refers it to a less distance than it really is at. But if he goes to a place from which the river and interjacent ground can be seen, though no farther from the house, he then perceives the house to be at a greater distance than he bad imagined; and therefore fancies it to be bigger than he did at first; although in both cases it appears under the same angle, and consequently makes no bigger picture on the retina of his eye in the latter case than it did in the former. Many have been deceived by taking a red coat-of-arms, fixed upon the iron gate in Clare-Hall walks at Cambridge, for a brick house at a much greater distance.*
Plate II. Secondly, In foggy weather, at first sight, we generally imagine a small house which is just at
* The fields which are beyond the gate rise gradually till they are just seen over it; and the arms being red, are often mistaken for a house at a considerable distance in those fields.
I once met with a curious deception in a gentleman's garden at Hackney, occasioned by a large pane of glass in the garden wall at some distance from his house. The glass (through which the sky was seen from low ground) reflected a very faint image of the house'; but the image seemed to be in the clouds near the horizon, and at that distance looked as if it were a huge castle in the air..Yet the angle, under which the image appeared, was equal to that under which the house was seen : but the image being mentally referred to a much greater distance than the house, appeared much bigger to the imagination.