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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
First, When a house is seen over a very broad The reariver by a person standing on a low ground, who son assigned. 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.*
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.
Plate II. hand, to be a great castle at a distance; because it appears so dull and ill-defined when seen through the mist, that we refer it to a much greater distance than it really is at; and therefore, under the same angle, we judge it to be much bigger. For, the near object FE, seen by the eye ABD, appears ' under the same angle GCH that the remote object GHI does: and the rays GFCN and HECM, crossing one another at C in the pupil of the eye, limit the size of the picture MN on the retina, which is the picture of the object FE; and if FE were taken away, would be the picture of the object GHI, only worse defined; because GHI being farther off, appears duller and fainter than FE did. But when a fog, as KL, comes between the eye and the object FE, the object appears dull and illdefined like GHI; which causes our imagination to refer FE to the greater distance CH, instead of the small distance CE, which it really is at. And consequently, as misjudging the distance does not in the least diminish the angle under which the object appears, the small hay-rick FE seems to be as big , as GHI
187. The Sun and Moon appear bigger in the horizon than at any considerable height above it. These luminaries, although at great distances from the Earth, appear floating, as it were, on the surface
of our atmosphere HG Ffe C, a little way beyond Why the the clouds; of which those about F, directly over Sun and our heads at E, are nearer us than those about Hor Moon ape in the horizon HEe. Therefore, when the Sun pear biggest in the or Moon appears in the horizon at e, they are not horizon. only seen in a part of the sky, which is really farther
from us than if they were at any considerable altitude, as about f; but they are also seen through a greater quantity of air and vapours at e than at f Here we have two concurring appearances which deceive our imagination, and cause us to refer the Sun
and Moon to a greater distance at their rising or setting about e, than when they are considerably high as at f: first, their seeming to be on a part of the atmosphere at e, which is really farther than from a spectator at E; and secondly, their being seen through a grosser medium, when at e, than when at f; which, by rendering them dimmer, causes us to imagine them to be at a yet greater distance. And as, in both cases, they are seen much under the same angle, we naturally judge them to be biggest when they seem farthest from us; like the abovementioned house, § 186, seen from a higher ground, which shewed it to be farther off than it appeared from low ground; or the hay-rick, which appeared at a greater distance by means of an interposing fog.
than in the
188. Any one may satisfy himself that the Moon Their apappears under no greater angle in the horizon than parent dion the meridian, by taking a large sheet of paper, are not and rolling it up in the form of a tube, of such a less on the width, that observing the Moon through it when she meridian rises, she may, as it were, just fill the tube; then tie horizon. a thread round it to keep it of that size; and when the Moon comes to the meridian, and appears much less to the eye, look at her again through the same tube, and she will fill it just as much, if not more, than she did at her rising.
189. When the full Moon is in perigee, or at her least distance from the Earth, she is seen under a larger angle, and must therefore appear bigger than when she is full at other times; and if that part of the atmosphere where she rises be more replete with
*The Sun and Moon subtend a greater angle on the meridian than in the horizon, being nearer the observer's place in the former case than in the latter.
vapours than usual, she appears so much the diminer; and therefore we fancy her to be still the bigger, by referring her to an unusually great distance, knowing that no objects which are very far distant can appear big unless they be really so.
The Method of finding the Distances of the Sun, Moon, and Planets.
HOSE who have not learnt how to take the altitude of any celestial phenomenon by a common quadrant, nor know any thing of plane trigonometry, may pass over the first article of this short chapter, and take the astronomer's word for it, that the distances of the Sun and planets are as stated in the first chapter of this book. But, to every one who knows how to take the altitude of the Sun, the Moon, or a star, and can solve a plane right
The altitude of any celestial object, is an arc of the sky intercepted between the horizon and the object. 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 plane; 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 ECD, 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 which they stand on. To the centre E is fixed one end of a thread F, called the plumb-line, which has a small weight or plummet P fixed to its other end. Now, if an observer hold 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 0, in the edge EC; but if he elevate the quadrant so as to look through the sight-holes at any part of the heavens, suppose the Sun at S, just so many degrees as he elevates the sight-hole b above the horizontal line HOX,
angled triangle, the following method of finding the Plate IV. distances of the Sun and Moon will be easily understood.
Let BAG be one half of the Earth, AC its semidiameter, S the Sun, m the Moon, and EKOL a quarter of the circle described by the Moon in revolving from the meridian to the meridian again.Let CRS be the rational horizon of an observer at A, extended to the Sun in the heavens; and HAO his sensible horizon, extended to the Moon's orbit. ALC is the angle under which the Earth's semidiameter AC is seen from the Moon at L, which is equal to the angle OAL, because the right lines AO and CL, which include both these angles, are parallel. ASC is the angle under which the Earth's semidiameter AC is seen from the Sun at S, and is equal to the angle OAf; because the lines AO and CRS are parallel. Now, it is found by observation, that the angle OAL is much greater than the angle OAƒ; but OAL is equal to ALC, and OAf is equal to ASC. Now, as ASC is much less than ALC, it that the Earth's semidiameter AC appears proves much greater as seen from the Moon at L, than from the Sun at S; and therefore the Earth is much farther from the Sun than from the Moon.* The
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 centre of the celestial arc XYV, (and he may be said to be in the centre 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 smoked 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.
See the Note on § 185.