165. Light consists of exceeding small particles of matter issuing from a luminous body; as from a lighted candle such particles of matter continually flow in all directions. Dr. Niewentyt[34] computes, that in one second of time there flows 418,660,000,000,000,000,000,000,000,000,000,000,000,000,000 particles of light out of a burning candle; which number contains at least 6,337,242,000,000 times the number of grains of sand in the whole Earth; supposing 100 grains of sand to be equal in length to an inch, and consequently, every cubic inch of the Earth to contain one million of such grains.
166. These amazingly small particles, by striking upon our eyes, excite in our minds the idea of light: and, if they were so large as the smallest particles of matter discernible by our best microscopes, instead of being serviceable to us, they would soon deprive us of sight by the force arising from their immense velocity, which is above 164 thousand miles every second[35], or 1,230,000 times swifter than the motion of a cannon bullet. And therefore, if the particles of light were so large, that a million of them were equal in bulk to an ordinary grain of land, we durst no more open our eyes to the light than suffer sand to be shot point blank against them.
167. When these small particles, flowing from the Sun or from a candle, fall upon bodies, and are thereby reflected to our eyes, they excite in us the idea of that body by forming it’s picture on the retina[36]. And since bodies are visible on all sides, light must be reflected from them in all directions.
168. A ray of light is a continued stream of these particles, flowing from any visible body in straight lines. That they move in straight, and not in crooked lines, unless they be refracted, is evident from bodies not being visible if we endeavour to look at them through the bore of a bended pipe; and from their ceasing to be seen by the interposition of other bodies, as the fixed Stars by the interposition of the Moon and Planets, and the Sun wholly or in part by the interposition of the Moon, Mercury, or Venus. And that these rays do not interfere, or jostle one another out of their ways, in flowing from different bodies all around, is plain from the following Experiment. Make a little hole in a thin plate of metal, and set the plate upright on a table, facing a row of lighted candles standing by one another; then place a sheet of paper or pasteboard at a little distance from the other side of the plate, and the rays of all the candles, flowing through the hole, will form as many specks of light on the paper as there are candles before the plate, each speck as distinct and large, as if there were only one candle to cast one speck; which shews that the rays are no hinderance to each other in their motions, although they all cross in the hole.
169. Light, and therefore heat so far as it depends on the Sun’s rays (§ 85, towards the end) decreases in proportion to the squares of the distances of the Planets from the Sun. This is easily demonstrated by a Figure which, together with it’s description, I have taken from Dr. Smith’s Optics[37]. Let the light which flows from a point A, and passes through a square hole B, be received upon a plane C, parallel to the plane of the hole; or, if you please, let the figure C be the shadow of the plane B; and when the distance C is double of B, the length and breadth of the shadow C will be each double of the length and breadth of the plane B; and treble when AD is treble of AB; and so on: which may be easily examined by the light of a candle placed at A. Therefore the surface of the shadow C, at the distance AC double of AB, is divisible into four squares, and at a treble distance, into nine squares, severally equal to the square B, as represented in the Figure. The light then which falls upon the plane B, being suffered to pass to double that distance, will be uniformly spread over four times the space, and consequently will be four times thinner in every part of that space, and at a treble distance it will be nine times thinner, and at a quadruple distance sixteen times thinner, than it was at first; and so on, according to the increase of the square surfaces B, C, D, E, built upon the distances AB, AC, AD, AE. Consequently, the quantities of this rarefied light received upon a surface of any given size and shape whatever, removed successively to these several distances, will be but one quarter, one ninth, one sixteenth of the whole quantity received by it at the first distance AB. Or in general words, the densities and quantities of light, received upon any given plane, are diminished in the same proportion as the squares of the distances of that plane, from the luminous body, are increased: and on the contrary, are increased in the same proportion as these squares are diminished.
170. The more a telescope magnifies the disks of the Moon and Planets, they appear so much dimmer than to the bare eye; because the telescope cannot magnify the quantity of light, as it does the surface; and, by spreading the same quantity of light over a surface so much larger than the naked eye beheld, just so much dimmer must it appear when viewed by a telescope than by the bare eye.
171. When a ray of light passes out of one medium[38] into another, it is refracted, or turned out of it’s first course, more or less, as it falls more or less obliquely on the refracting surface which divides the two mediums. This may be proved by several experiments; of which we shall only give three for example’s sake. 1. In a bason FGH put a piece of money as DB, and then retire from it as to A, till the edge of the bason at E just hides the money from your sight: then, keeping your head steady, let another person fill the bason gently with water. As he fills it, you will see more and more of the piece DB; which will be all in view when the bason is full, and appear as if lifted up to C. For, the ray AEB, which was straight whilst the bason was empty, is now bent at the surface of the water in E, and turned out of it’s rectilineal course into the direction ED. Or, in other words, the ray DEK, that proceeded in a straight line from the edge D whilst the bason was empty, and went above the eye at A, is now bent at E; and instead of going on in the rectilineal direction DEK, goes in the angled direction DEA, and by entering the eye at A renders the object DB visible. Or, 2dly, place the bason where the Sun shines obliquely, and observe where the shadow of the rim E falls on the bottom, as at B: then fill it with water, and the shadow will fall at D; which proves, that the rays of light, falling obliquely on the surface of the water, are refracted, or bent downwards into it.
172. The less obliquely the rays of light fall upon the surface of any medium, the less they are refracted; and if they fall perpendicularly thereon, they are not refracted at all. For, in the last experiment, the higher the Sun rises, the less will be the difference between the places where the edge of the shadow falls, in the empty and full bason. And, 3dly, if a stick be laid over the bason, and the Sun’s rays be reflected perpendicularly into it from a looking-glass, the shadow of the stick will fall upon the same place of the bottom, whether the bason be full or empty.
173. The denser that any medium is, the more is light refracted in passing through it.
174. The Earth is surrounded by a thin fluid mass of matter, called the Air, or Atmosphere, which gravitates to the Earth, revolves with it in it’s diurnal motion, and goes round the Sun with it every year. This fluid is of an elastic or springy nature, and it’s lowermost parts being pressed by the weight of all the Air above them, are squeezed the closer together; and are therefore densest of all at the Earth’s surface, and gradually rarer the higher up. “It is well known[39] that the Air near the surface of our Earth possesses a space about 1200 times greater than water of the same weight. And therefore, a cylindric column of Air 1200 foot high is of equal weight with a cylinder of water of the same breadth and but one foot high. But a cylinder of Air reaching to the top of the Atmosphere is of equal weight with a cylinder of water about 33 foot high[40]; and therefore if from the whole cylinder of Air, the lower part of 1200 foot high is taken away, the remaining upper part will be of equal weight with a cylinder of water 32 foot high; wherefore, at the height of 1200 feet or two furlongs, the weight of the incumbent Air is less, and consequently the rarity of the compressed Air is greater than near the Earth’s surface in the ratio of 33 to 32. And having this ratio we may compute the rarity of the Air at all heights whatsoever, supposing the expansion thereof to be reciprocally proportional to its compression; and this proportion has been proved by the experiments of Dr. Hooke and others. The result of the computation I have set down in the annexed Table, in the first column of which you have the height of the Air in miles, whereof 4000 make a semi-diameter of the Earth; in the second the compression of the Air or the incumbent weight; in the third it’s rarity or expansion, supposing gravity to decrease in the duplicate ratio of the distances from the Earth’s center. And the small numeral figures are here used to shew what number of cyphers must be joined to the numbers expressed by the larger figures, as 0.171224 for 0.000000000000000001224, and 2695615 for 26956000000000000000.
| Air’s | ||
|---|---|---|
| Height. | Compression. | Expansion. |
| 0 | 33 | 1 |
| 5 | 17.8515 | 1.8486 |
| 10 | 9.6717 | 3.4151 |
| 20 | 2.852 | 11.571 |
| 40 | 0.2525 | 136.83 |
| 400 | 0.171224 | 2695615 |
| 4000 | 0.1054465 | 73907102 |
| 40000 | 0.1921628 | 26263189 |
| 400000 | 0.2107895 | 41798207 |
| 4000000 | 0.2129878 | 33414209 |
| Infinite. | 0.2126041 | 54622209 |
From this Table it appears that the Air in proceeding upwards is rarefied in such manner, that a sphere of that Air which is nearest the Earth but of one inch diameter, if dilated to an equal rarefaction with that of the Air at the height of ten semi-diameters of the Earth, would fill up more space than is contained in the whole Heavens on this side the fixed Stars, according to the preceding computation of their distance[41].” And it likewise appears that the Moon does not move in a perfectly free and un-resisting medium; although the air at a height equal to her distance, is at least 34000190 times thinner than at the Earth’s surface; and therefore cannot resist her motion so as to be sensible in many ages.
175. The weight of the Air, at the Earth’s surface, is found by experiments made with the air-pump; and also by the quantity of mercury that the Atmosphere balances in the barometer; in which, at a mean state; the mercury stands 291⁄2 inches high. And if the tube were a square inch wide, it would at that height contain 291⁄2 cubic inches of mercury, which is just 15 pound weight; and so much weight of air every square inch of the Earth’s surface sustains; and every square foot 144 times as much, because it contains 144 square inches. Now as the Earth’s surface contains about 199,409,400 square miles, it must be of no less than 5,559,215,016,960,000 square feet; which, multiplied by 2016, the number of pounds on every foot, amounts to 11,207,377,474,191,360,000; or 11 trillion 207 thousand 377 billion 474 thousand 191 million and 360 thousand pounds, for the weight of the whole Atmosphere. At this rate, a middle sized man, whose surface may be about 14 square feet, is pressed by 28,224 pound weight of Air all round; for fluids press equally up and down and on all sides. But, because this enormous weight is equal on all sides, and counterbalanced by the spring of the internal Air in our blood vessels, it is not felt.
176. Oftentimes the state of the Air is such that we feel ourselves languid and dull; which is commonly thought to be occasioned by the Air’s being foggy and heavy about us. But that the Air is then too light, is evident from the mercury’s sinking in the barometer, at which time it is generally found that the Air has not sufficient strength to bear up the vapours which compose the Clouds: for, when it is otherwise, the Clouds mount high, the Air is more elastic and weighty about us, by which means it balances the internal spring of the Air within us, braces up our blood-vessels and nerves, and makes us brisk and lively.
177. According to [42]Dr. Keill, and other astronomical writers, it is entirely owing to the Atmosphere that the Heavens appear bright in the day-time. For, without an Atmosphere, only that part of the Heavens would shine in which the Sun was placed: and if an observer could live without Air, and should turn his back towards the Sun, the whole Heavens 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 sunshine 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, before he rises and after he sets. For, when the Earth by its rotation has withdrawn the Sun from our sight, the Atmosphere being still higher than we, has his 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 two miles height to bear up the Clouds.
178. The Atmosphere refracts the Sun’s rays so, as to bring him in sight every clear day, before he rises in the Horizon; and to keep him in view for some minutes after he is really set below it. For, at some times of the year, we see the Sun ten minutes longer above the Horizon than he would be if there were no refractions: and about 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[43] 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 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 321⁄4 min. of a deg. in breadth, when at his mean distance from the Earth; and the horizontal refraction of his rays is 333⁄4 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.; between which and the Zenith, it is scarce sensible: the quantity throughout, is shewn by the annexed table, calculated by Sir Isaac Newton.
182. A Table shewing the Refractions of the Sun, Moon, and Stars; adapted to their apparent Altitudes.
| Appar. Alt. | Refraction. | Ap. Alt. | Refraction. | Ap. Alt. | Refraction. | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| D. | M. | M. | S. | D. | M. | S. | D. | M. | S. | ||
| 0 | 0 | 33 | 45 | 21 | 2 | 18 | 56 | 0 | 36 | ||
| 0 | 15 | 30 | 24 | 22 | 2 | 11 | 57 | 0 | 35 | ||
| 0 | 30 | 27 | 35 | 23 | 2 | 5 | 58 | 0 | 34 | ||
| 0 | 45 | 25 | 11 | 24 | 1 | 59 | 59 | 0 | 32 | ||
| 1 | 0 | 23 | 7 | 25 | 1 | 54 | 60 | 0 | 31 | ||
| 1 | 15 | 21 | 20 | 26 | 1 | 49 | 61 | 0 | 30 | ||
| 1 | 30 | 19 | 46 | 27 | 1 | 44 | 62 | 0 | 28 | ||
| 1 | 45 | 18 | 22 | 28 | 1 | 40 | 63 | 0 | 27 | ||
| 2 | 0 | 17 | 8 | 29 | 1 | 36 | 64 | 0 | 26 | ||
| 2 | 30 | 15 | 2 | 30 | 1 | 32 | 65 | 0 | 25 | ||
| 3 | 0 | 13 | 20 | 31 | 1 | 28 | 66 | 0 | 24 | ||
| 3 | 30 | 11 | 57 | 32 | 1 | 25 | 67 | 0 | 23 | ||
| 4 | 0 | 10 | 48 | 33 | 1 | 22 | 68 | 0 | 22 | ||
| 4 | 30 | 9 | 50 | 34 | 1 | 19 | 69 | 0 | 21 | ||
| 5 | 0 | 9 | 2 | 35 | 1 | 16 | 70 | 0 | 20 | ||
| 5 | 30 | 8 | 21 | 36 | 1 | 13 | 71 | 0 | 19 | ||
| 6 | 0 | 7 | 45 | 37 | 1 | 11 | 72 | 0 | 18 | ||
| 6 | 30 | 7 | 14 | 38 | 1 | 8 | 73 | 0 | 17 | ||
| 7 | 0 | 6 | 47 | 39 | 1 | 6 | 74 | 0 | 16 | ||
| 7 | 30 | 6 | 22 | 40 | 1 | 4 | 75 | 0 | 15 | ||
| 8 | 0 | 6 | 0 | 41 | 1 | 2 | 76 | 0 | 14 | ||
| 8 | 30 | 5 | 40 | 42 | 1 | 0 | 77 | 0 | 13 | ||
| 9 | 0 | 5 | 22 | 43 | 0 | 58 | 78 | 0 | 12 | ||
| 9 | 30 | 5 | 6 | 44 | 0 | 56 | 79 | 0 | 11 | ||
| 10 | 0 | 4 | 52 | 45 | 0 | 54 | 80 | 0 | 10 | ||
| 11 | 0 | 4 | 27 | 46 | 0 | 52 | 81 | 0 | 9 | ||
| 12 | 0 | 4 | 5 | 47 | 0 | 50 | 82 | 0 | 8 | ||
| 13 | 0 | 3 | 47 | 48 | 0 | 48 | 83 | 0 | 7 | ||
| 14 | 0 | 3 | 31 | 49 | 0 | 47 | 84 | 0 | 6 | ||
| 15 | 0 | 3 | 17 | 50 | 0 | 45 | 85 | 0 | 5 | ||
| 16 | 0 | 3 | 4 | 51 | 0 | 44 | 86 | 0 | 4 | ||
| 17 | 0 | 2 | 53 | 52 | 0 | 42 | 87 | 0 | 3 | ||
| 18 | 0 | 2 | 43 | 53 | 0 | 40 | 88 | 0 | 2 | ||
| 19 | 0 | 2 | 34 | 54 | 0 | 39 | 89 | 1 | 1 | ||
| 20 | 0 | 2 | 26 | 55 | 0 | 38 | 90 | 0 | 0 | ||
183. In all observations, to have the true altitude of the Sun, Moon, or Stars, the refraction must be subtracted from the observed altitude. But the quantity of refraction is not always the same at the same altitude; because heat diminishes the 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, as 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 observation of this kind made by some Hollanders that wintered in Nova Zembla in the year 1596, who were surprised to find, that after a continual night 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 quantity of refraction of the Sun’s rays, passing thro’ 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 setting: the reason is, that the refraction being greater in the Horizon than at any distance above it, the lowermost limb G appears more elevated than the uppermost. 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 imperceptible, the Sun and Moon appear perfectly round, as AEBF.
185. We daily observe, that the objects which appear most distinct are generally those which are nearest to us; and consequently, when we have nothing but our imagination to assist us in estimating of distances, 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 in both cases be the same. And as in both cases they are seen under the same angle[44], 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 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 broad river by a person standing on low ground, who 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 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[45].
Secondly, In foggy weather, at first sight, we generally imagine a small house, which is just at 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 if a Fog, as KL, comes between the eye and the object FE, it appears dull and ill defined 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 mis-judging 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 HGFfeC, a little way beyond the Clouds; of which, those about F, directly over our heads at E, are nearer us than those about H or e in the Horizon HEe. Therefore, when the Sun or Moon appear in the Horizon at e, they are not 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 f 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[46] much under the same Angle, we naturally judge them to be biggest when they seem farthest from us; like the above-mentioned 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.
188. Any one may satisfy himself that the Moon appears under no greater Angle in the Horizon than on the Meridian, by taking a large sheet of paper, and rolling it up in the form of a Tube, of such a width, that observing the Moon through it when she rises, she may, as it were, just fill the Tube; then tie 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 perigeo, 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 vapours than usual, she appears so much the dimmer; 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.
Plate IIII.
J. Ferguson delin.
J. Mynde Sculp.