be visible by reason of the fmallness of the angle AOB. Confequently any diftance AC, how great foever, beyond A, will be invifible. For fince AC and EO are parallel, the ray CO will always cut AB in fome point D between A and B; and therefore the angle AOC, or AOD, will always be lefs than AOB, and therefore AD or AC will be invifible. Of courfe all objects and clouds, as CE and FG, placed at all distances beyond A, if they be high enough to be visible, or to fubtend a bigger angle at the eye than OB, will appear at the horizon AB; because the diftance AC is invifible. sob. Hence, if we fuppofe a vaft long row of objects, or a vaft long wall ABZY (fig. 1. Plate CCLVIII.) built upon this plane, and its perpendicular diftance OA from the eye at O to be equal to or greater than the distance Oa of the vifible horizon, it will not appear straight, but circular, as if it were built upon the circumference of the horizon a cegy: and if the wall be continued to an immenfe diftance, its extreme parts YZ will ap. pear in the horizon at yz, where it is cut by a line Oy parallel to the wall. For, fuppofing a ray YO, the angle YO, will become infenfibly small. Ima gine this infinite plane OAYy, with the wall upon it, to be turned about the horizontal line O like the lid of a box, till it becomes perpendicular to the other half of the horizontal plane LMy, and the wall parallel to it, like a vaft ceiling overhead; and then the wall will appear like the concave figure of the clouds overhead. But though the wall in the horizon appear in the figure of a femicircle, yet the ceiling will not, but much flatter. Be caufe the horizontal plane was a vifible furface, which fuggefted the idea of the fame diftances quite round the eye; but in the vertical plane extended between the eye and the ceiling, there is nothing that affects the sense with an idea of its parts but the common line Oy; confequently the apparent distances of the higher parts of the ceiling will be gradually diminished in afcending from that line. When the sky is quite overcaft with the clouds of equal gravities, they will all float in the air at equal heights above the earth, and confequently will compofe a furface refembling a large ceiling, as flat as the vifible furface of the carth. Its concavity therefore is not real, but apparent: and when the heights of the clouds are unequal, fince their real shapes and magnitudes are all unknown, the eye can seldom diftinguish the unequal distances of thofe clouds that appear in the fame directions, unless when they are very near us, or are driven by contrary currents of the air. So that the visible shape of the whole furface remains alike in both cafes. And when the sky is either partly overcaft, or partly free from clouds, it is matter of fact, that we retain much the fame idea of its concavity, as when it was quite overcaft.

507. The concavity of the heavens appears to the eye, to be a lefs portion of the spherical fur face than a hemifphere. Dr SMITH fays, that the centre of the concavity is much below the eye; and by taking a medium among feveral obferva tions, he found the apparent diftance of its parts at the horizon to be generally between 3 and 4 times greater than the apparent diftance of its parts overhead. For let the arch ABCD (fig. 10,

pl. 257.) reprefent the apparent concavity of the fky, O the place of the eye, OA and OC the hori zontal and vertical apparent distances, whofe proportion is required: First obferve when the fun or the moon, or any cloud or ftar, is in fuch a pofition that the apparent arches BA, BC, extended on each fide of this object towards the horizon and zenith, feem equal to the eye; then taking the altitude of the object B with a quadrant, or finding it by aftronomy from the given time of ob. fervation, the angle AOB is known. Drawing therefore the line OB in the position thus determined, and taking in it any point B at pleasure, in the vertical fine CO produced downwards, feek the centre E of a circle. ABC, whofe arches BA, BC, intercepted. between B and the legs of the right angle AOC, fhall be equal to each other; then will this arch ABCD reprefent the apparent figure of the fky. The centre E may be found geometrically by co ftructing a cubic equation, or as quickly, and fufficiently exact, by trying whe ther the chords BA, BC, of the arch ABC drawn by conjecture are equal, and by altering its radius BE till they are fo. In making feveral obfervations upon the fun, moon, and stars, they seemed to the Dr to bifect the vertical arch ABC at B, when their apparent altitudes, or the right angle AOB was about 23 degrees; which gives the proportion of OC to OA as 3 to 1o, or as 1 to 3 nearly. When the fun was but 30° high, the upper arch feemed always less than the under one; and, in Dr Smith's opinion, always greater when the fun was about 180 or 20° high.

V. Of the BLUE COLOUR of the SKY, and of BLUE and GREEN SHADOWS.

508. THE opinions of ancient writers concerning the colour of the sky merit no notice. The first who gave any rational explanation was FRÓMONDUS. By him it was fuppofed, that the bluenefs of the fky proceeded from a mixture of the white light of the fun with the black space beyond the atmosphere, where there is neither refraction nor reflection. This opinion prevailed very generally even in modern times, and was maintained by OTTO GUERICK and all his contemporaries, who afferted that white and black may be mixed in fuch a manner as to make a blue. Mr BOUGUER had recourfe to the vapours diffused through the atmo fphere, to account for the reflection of the blue rays rather than any other. He feems, however, to fuppofe, that it arifes from the conftitution of the air itself, whereby the fainter coloured rays are incapable of making their way through any conf derable tract of it. Hence he is of opinion, that the colour of the air is properly blue; to which opinion Dr Smith feems alfo to have inclined.

509. To this blue colour of the sky is owing the appearance of blue and green fhadows in the morn ings and evenings.-Thefe were first taken notice of by Count BUFFON, in July 1742, when he obferved, that the fhadows of trees which fell upon a white wall were green. He was then upon an eminence, and the fun was setting on the cleft of a mountain, so that he appeared confiderably lower than the horizon. The fky was clear, excepting in the W which, though free from clouds, was lightly fhaded with vapours of a yellow colour, inclining to red. Then the fun itself was exceed

of the body that produces them, that is, when the centre of the fun is 7° 8' above the horizon. This obfervation he made in the beginning of Auguft. 512. Befides these coloured fhadows, which are produced by the interception of the direct rays of the fun, our author obferved others fimilar to them at every hour of the day, in rooms into which the light of the fun was reflected from fome white body, if any part of the clear fky could be feen from the place, and all unneceffary light was excluded as much as poffible. Obferving these precautions, he fays that the blue fhadows may be feen at any hour of the day, even with the direct light of the fun; and that this colour will difappear in all thofe places of the fhadow from which the blue fky cannot be feen. All the obfervations he made upon the yellow or reddish borders of fhadows above-mentioned, led him to conclude, that they were occafioned by the interception of the fky-light, whereby part of the fhadow was illuminated either by the red rays reflected from the clouds, when the fun is near the horizon, or from fome terreftrial bodies in the neighbourhood. He mentions also another kind of fhadows which have the fame origin. These he often faw early in fpring, when he was reading by the light of a candle in the morning, and the twilight mixed with that of his candle. In these circumftances, the fhadow made by intercepting the light of his candle, at the distance of about fix feet, was of a beautiful and clear blue, which became deeper as the opaque body which made the shadow was brought nearer to the wall, and was exceedingly deep at the distance of a few inches only. But wherever the day-light did not come, the fhadows were all black without the leaft mixture of blue.

VI. Of the IRRADIATIONS of the SUN'S LIGHT appearing through the INTERSTICES of the CLOUDS. 513. This is an appearance which every one must have obferved, when the sky was pretty much overcaft with clouds at some distance from each other. At that time several large beams of light, fomething like the appearance of the light of the fun ad. mitted into a smoky room, will be feen generally with a very confiderable degree of divergence, as if the radiant point was fituated at no great diftance above the clouds. Dr Smith obferves, that this appearance is one of thofe which ferve to demonftrate, that very high and remote objects in the heavens do not appear to us in their real fhapes and pofitions, but according to their perspective projections on the apparent concavity of the fky. He fays that though these beams are generally feen diverging, as reprefented in fig. 11. Pl. 257. it is not always the cafe. He himself once faw them converging towards a point diametrically oppofite to the fun: for, as near as he could conjecture, the point to which they converged was fituated as much below the horizon, as the fun was then elevated above the oppofite part of it. This part is reprefented by the line tDr, fig. 12. and the point below it in oppofition to the fun is E; towards which all the beams vt, vt, &c. appeared to converge.

514. "Obferving (fays he) that the point of convergence was oppofite to the fun, I began to fufpect, that this unufual phenomenon was but a case of the usual apparent divergence of the beams of the fun, from his apparent place among the

clouds, as reprefented in fig. 11: I fay an apparens: divergence; for though nothing is more common than for rays to diverge from a luminous body, yet the divergence of these beams in fuch large angles is not real, but apparent: Because it is impoffible for the direct rays of the fun to crofa one another at any point of the apparent concavi ty of the sky, in a greater angle than about half a degree. For the diameter of the earth being fo extremely fmall, in comparison to the distance of the fun, as to fubtend an angle at any point of his body of but 20" or 22" at moft; and the diameter of our visible horizon being extremely fmaller than that of the earth; it is plain, that all the rays which fall upon the horizon, from any given point of the fun, must be inclined to each other in the fmalleft angles imaginable: the greatest of them being as much smaller than that angle of 22 leconds, as the diameter of the vifible horizon is fmaller than that of the earth. All the rays that come to us from any given point of the fun may therefore be confidered as parallel to each other; as the rays eBg (fig. 13. Pl. 257.) from the point e, or ƒBb from the oppofite point ƒ; and confequently the rays of these two pencils that come from oppofite points of the fun's real diameter, and cross each other in the fun's apparent place B among the clouds, can conftitute no greater an angle with each other than about half a degree; this angle of their interfection Bf being the fame as the fun would appear under to an eye placed among the clouds at B, or (which is much the fame) to an eye at O upon the ground: Because the fun's real diftance OS is inconceivably greater than his apparent distance OB. Therefore the rays of the fun, as Bg, Bh, do really diverge from his apparent place B in no greater angles gBb than about half a degree. Nevertheless they appear to diverge from the place B fig. 11. in all poffible an gles, and even in oppofite directions. Let us pro ceed then to an explanation of this apparent divergence, which is not felf-evident by any means; though at firft fight we are apt to think it is, by not diftinguishing the vaft difference between the true and apparent diftances of the fun.

515. Suppofing all the rays of the fun to fall accurately parallel to each other upon the vifible horizon, as they do very nearly, yet in both cafes they muft appear to diverge in all poffible angles. Let us imagine the heavens to be partly overcaft with a spacious bed of broken clouds v, v, v, &c. Pl. 261. fig. 4. lying parallel to the plane of the vifible horizon, here reprefented by the line AOD; and when the fun's rays fall upon these clouds in the parallel lines sv, sv, &c. let fome of them pafs through their intervals in the lines vt, vt, &c. and fall upon the plane of the horizon at the places t, t, &c. And fince the rest of the incident rays sv, sv, are supposed to be intercepted from the place of the fpectator at O by the cloud x, and from the intervals between the tranfmitted rays vt, vt, &c. by the cloud v, v, &c. a small part of thefe latter rays vt, vt, when reflected every way from fome certain kind of thin vapours floating in the air, may undoubtedly be fufficient to affect the eye with an appearance of lights and fhades, in the form of bright beams in the places vt, vt, &c. and of dark ones in the intervals be

tween.

pofite region to the fun, are more diminished by continual reflections from a longer tract of the atmosphere, than the incident rays upon the region next the fun.

517." The common phenomenon of diverging beams is more frequent in fummer than in winter, and alfo when the fun is lower than when higher up; probably because the lower vapours are denfer, and therefore more ftrongly reflective than the higher; because the lower ky-light is not fo bright as the upper; because the air is generally quieter in the mornings and evenings than about noonday; and, laftly, because many forts of vapours are exhaled in greater plenty in fummer than in winter, from many kinds of volatile vegetables; which vapours, when the air is cooled and condensed in the mornings and evenings, may become denie enough to reflect a fenfible light."

VII. Of the ILLUMINATION of the SHADOW of the EARTH by the REFRACTION of the AT

MOSPHERE.

tween them; juft as the like beams of light and fhade appear in a room by reflections of the fun's rays from a fmoky or duty air within it; the lights and fhades being here occafioned by the tranfmiffion of the rays through some parts of the window, and by their interruption at other parts. Now, if the apparent concavity of this bed of clouds v, v, to the eye at O, be reprefented by the arch ABCD, and be cut in the point B by the line OB drawn parallel to the beams tv, it will be evident by the rules of perspective, that these long beams will not appear in their real places, but upon the concave ABCD diverging every way from the place B, where the fun himself appears, or the cloud that covers his body, as reprefented feparately in full view, in fig. 11. pl. CCLVII. And for the fame reafon, if the line BO, fig. 4. plate CCLXI.be produced towards E, below the plane of the horizon AOD, and the eye be directed towards the region of the sky directly above E, the lower ends of the fame real beams vt, vt, will now appear upon the part DF of this concave; and will feem to converge towards the point E, fituated juft as much below the horizon as the oppofité point B is above it; which is feparately reprefented in full view, in fig. 12. pl. CCLVI. For if the beams vt, vt, be fuppofed to be visible throughout their whole lengths, and the eye be directed in a plane perpendicular to them, here reprefented by the line OF, Fig. 4. pl. CCLXI.; they and their intervals will appear broadeft in and about this plane, because these parts of them are the nearest to the eye; and there fore their remoter parts and intervals will appear gradually narrower towards the oppofite ends of the line BE. As a farther illuftration of this matter, we may conceive the spectator at O to be fituated upon the top of fo large a defcent OHI towards a remote valley IK, and the fun to be fo very low, that the point B oppofite to him may be seen above the horizon of this fhady valley. In this cafe it is manifeft, that the spectator at O would now fee these beams converging fo far as to meet each other at the point E in the sky itself.

316. "I do not remember to have ever feen any phenomenon of this kind by moon-light., Probably her light is too weak, to caufe a fenfible appearance of lights and fhades, fo as to form thefe beams. In the unufual phenomenon, the converging fun-beams towards the point below the horizon were not quite fo bright and ftrong as those ufually are that diverge from him; and the fky beyond them appeared very black (feveral fhowers having paffed that way), which certainly contributed to the evidence of this appearance. Hence it is probable, that the thinness and weaknefs of the reflected rays, from the vapours oppofite to the fun, is the chief cause that this appearance is so very uncommon in comparifon to that other of diverging beams; for, as the region of the sky round about the fun is always brighter than the oppofite one, fo the light of the diverging beams ought also to be brighter than that of the converging ones. For, though rays are refected from rough unpolished bodies in all poffible directions, yet it is a general obfervation, that more of them are reflected forwards obliquely, than are reflected more directly backwards. Befides, in the present case, the incident rays upon the op

518. THE ancient philofophers, who knew nothing of the refractive power of the atmosphere, were very much perplexed to account for the body of the moon being visible when totally eclipfed. At fuch times the generally appears of a dull red colour like tarnished copper, or of iron almost red-hot. This, they thought, was the moon's native light, by which the became visible when hid from the brighter light of the fun. PLUTARCH indeed, in his difcourse upon the face of the moon, attributes this appearance to the light of the fixed stars reflected to us by the moon; but this must be by far too weak to produce that effect. The true caufe of it is the scattered beams of the fun bent into the earth's fhadow by refractions through the atmosphere in the following manner.

519. "Let the body of the fun, fays Dr SMITH, be reprefented by the greater circle a b, fig. 1. pl. CCLVIII. and that of the earth by the leffer one cd; and let the lines ace and bde touch them both on their opposite fides, and meet in e beyond the earth; then the angular space ced will reprefent the conic figure of the earth's fhadow, which would be totally deprived of the fun's rays, were none of them bent into it by the refractive power of the atmosphere. Let this power just vanish at the circle bi concentric to the earth, fo that the rays a h and bi, which touch its oppofite fides, may proceed unrefracted, and meet each other at k. Then the two neareft rays to these that flow within them, from the fame points a and b being refracted inwards, through the margin of the atmosphere, will cross each other at a point 1, fomewhat nearer to the earth than k; and, in like manner, two oppofite rays next within the two laft will cross each other at a point m, fomewhat nearer to the earth than /, having fuffered greater refractions, by paffing through longer and denfer tracts of air, lying fomewhat nearer to the earth. The like approach of the fucceffive interfections k, l, m, is to be understood of innumerable couples of rays, till you come to the interfection n of the two innermoft; which we may suppose juft to touch the earth at the points and p. It is plain then, that the space bounded by these rays on, np, will

be

be the only part of the earth's fhadow wholly deprived of the fun's rays. Let fm g reprefent part of the moon's orbit when it is neareft to the earth, at a time when the earth's dark fhadow onp is the longeft; in this cafe I will show that the ratio of im to tn is about 4 to 3; and confequently that the moon, though centrally eclipfed at m, may yet be vifible by means of those scattered rays above-mentioned, first transmitted to the moon by refraction through the atmosphere, and from thence reflected to the earth. For, let the incident and emergent parts a q, rn, of the ray agorn (fig. 3. pl. CCLVIII.), that juft touches the earth at o, be produced till they meet at n, and let a qu produced meet the axis produced in x; and joining us and um, fince the refractions of an horizontal ray paffing from o to r, or from o to 9, would be alike and equal, the external angle nux is double the quantity of the ufual refraction of an horizontal ray, and the angle aus is the apparent measure of the fun's femidiameter seen from the earth; and the angle ust is that of the earth's femidiameter t u feen from the fun, (called his horizontal parallax); and, laftly, the angle umt is that of the earth's femidiameter feen from the moon, (called her horizontal parallax): because the elevation of the point u above the earth is too fmall to make a fenfible error in the quantity of thefe angles; whofe measures by aftronomical tables are as follow:

Sun's leaft app. femidiam.
His horizontal parallax

Their difference
Double the horiz. refract.

Their fum is

ang. tnu 83-10 Moon's greateft hor. par.. ang.tmu 62-10 520." Therefore (by a preceding prop.) we have tm:tn:: (ang. tnu: ang. tmu::83-10":62′10" :) 4: 3 in round numbers; which was to be proved. It is eafy to collect from the moon's greatest horizontal parallax of 62-10", that her leaft distance tm is about 55 femidiameters of the earth; and therefore the greatest length tn of the dark fhadow, being three quarters of tm, is about 41 femidiameters.

521." The difference of the laft mentioned angles tnu, tmu, is mun=21', that is, about two thirds of 31-40", the angle which the whole diameter of the fun fubtends at u. Whence it follows, that the middle point m of the moon, centrally eclipfed, is illuminated by rays which come from two thirds of every diameter of the fun's difk, and pafs by one fide of the earth; and alfo by rays that come from the oppofite two thirds of every one of the faid diameters, and pass by the other fide of the carth. This will appear by conceiving the ray aqorn to be be inflexible, and its middle point o to flide upon the earth, while the part rn is approaching to touch the point m; for then the oppofite part qa will trace over two thirds of the fun's diameter. The true proportion of the angles num, aus, could not be preferved in the figure, by reafon of the fun's immenfe diftance and mag. nitude with respect to the earth.

$22. "Having drawn the line at a (fg4 plate VOL. XVI. PART II.

CCLVIII.), it is obfervable, that all the incident rays, as a q, a x, flowing from any one point of the fun to the circumference of the earth, will be collected to a focus a, whofe diftance ta is lefs than tm in the ratio of 62 to 67 nearly; and thus an image of the fun will be formed at a 6, whofe rays will diverge upon the moon. For the angle ta u is the difference of the angles xua, uat found above, and ta:. tm:: ang. tmu: ang. ta u:: 62'-10′′: 67—30". The rays that flow next above aq and ax, by paffing through a thinner part of the atmosphere, will be united at a point in the axis a ta, fomewhat farther from the earth than the laft focus a; and the fame may be faid of the rays that pafs next above thefe, and fo on; whereby an infinite series of images of the fun will be formed, whofe diameters and degrees of brightnefs will increase with their distances from the earth.

523. "Hence it is manifeft why the MOON eclipfed in her perigee is obferved to appear always duller and darker than in her apogee. The reafon why her colour is always of the copper kind between a dull red and orange, I take to be this. The blue colour of a clear sky shows manifeftly, that the blue-making rays are more copiously reflected from pure air than thofe of any other colour; confequently they are lefs copiously transmitted through it among the reft that come from the fun, and fo much the lefs as the tract of air through which they país is the longer. Hence the common colour of the fun and moon is whiteft in the meridian, and grows gradually more inclined to diluted yellow, orange, and red, as they defcend lower, that is, as the rays are tranfmitted through a longer tract of air; which tract, being fill lengthened in paffing to the moon and back again, caufes a ftill greater lofs of the blue-making rays in proportion to the reft; and fo the refulting colour of the tranfmitted rays must lie between a dark orange and red, according to Sir Ifaac Newton's rule for finding the result of a mixture of colours. We have an inftance of the reverse of this cafe in leaf gold, which appears yellow by reflected, and blue by tranfmitted, rays. The circular edge of the fhadow in a partial eclipfe appears red; because the red-making rays are the leaft refracted of all others, and confequently are left alone in the conical furface of the thadow, al the reft being refracted into it."

§ VIII. Of the MEASURES of LIGHT. 524. THAT fome luminous bodies give a stronger and others a weaker light, and that fome reflect more light than others, was always obvious to mankind; but no perfon before M. BOUGUER hit upon a tolerable method of afcertaining the proportion that two or more lights bear to one another. The methods he ufed were the following a

525. He took two pieces of wood or pafteboard EC and CD (fig. 14. plate CCLVII.), in which he made two equal holes P and Q, over which he drew pieces of oiled or white paper. Upon these holes he contrived that the light of the different bodies he was comparing fhould fall; while he placed a third piece of pafteboard FC, fo as to prevent the two lights from mixing with one another. Then placing himself fometimes on one fide, and fometimes on the other, but generally on the oppofite Aide of this inftrument, with respect to the Ggg

light