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is refracted at G, it is rather a wonder how the very small part re-llected to H, should there, when refracted, be in quantity sufii-cient to excite any distinct ideas of colours at all. 8. The ap-pearance of the bows in that part of the heavens opposite to thesun. This necessarily happens from the incident and emergentray being both on one side of the drop ; for it is evident, that inorder to see the colours, we must look to that part against whichthe sunshines. 9. The bows never appear but when and whereit rains. This is because rain affords a sufficient plenty of drops,or aqueous spherules, proper to reflect and refract the light fit forthis purpose, which cannot be done without a requisite size, figure,and disposition of the particles, which the vapour of the clouddoes not admit, and therefore clouds alone exhibit no such ap-pearance. In the same manner innumerable hows might be from-ed by a greater number of reflections within the drops; but asthe secondary is so much fainter than the primary, that all thecolours in it are seldom seen, for the same reason a bow madewith three reflections would be fainter still, and in general alto-gether imperceptible. Since the rays of light, by various re-flections and refractions, are thus capable of forming, by meansof drops of rain, the bows which we so frequently see in the hea-vens, it is evident that there will be not only solar and lunarbows, but that many striking appearances will be produced bydrops upon the ground, or air on the agitated surface of the wa-ter. Thus a lunar bow will be formed by rays from the moonaffected by drops of rain ; but as its light is very faint in compa-rison with that of the sun, such a bow will very seldom be seen,and the colours of it, when seen, will be faint and dim. Thephenomena of haloes and parhelia depend also on the refractionand reflection of light. For an account of these see IIalo, andParheuum.
Of the Concave Figure of the Sky.
This apparent concavity is only ail optical deception foundedon the incapacity of our organs of vision to lake in very largedistances. Dr. Smith in his “ Complete System of Optics,” hathdemonstrated, that, if the surface of the earth was perfectly plane,the distance of the visible horizon from the eye would scarce ex-ceed the distance of 5000 times the height of the eye above theground supposing the height of the eye between five and six feet:beyond this distance all objects would appear in the visiblehorizon. For, let OP, (fig. 44, Plate CXXXI.) be the heightof the eye above the line PA drawn upon the ground ; andif an object AB, equal in height to PO, be removed to adistance PA equal to 5000 times that height, it will hardlybe visible by reason of the smallness of the angle AOB. Conse-quently any distance AC , how great soever, beyond A, will beinvisible. For since AC and BO are parallel, the ray C0 will al-ways cut AB in some point D between A and B; and thereforethe angle AOC, or AOD, will always he less than AOB, andtherefore A D or AC will be invisible. Of course all objects andclouds, as CE and FG, placed at all distances beyond A, if thevbe high enough to be visible, or to subtend a bigger angle at theeye than AOB, will appear at the horizon AB; because the dis-tance AC is invisible. Hence, if we suppose a vast long row of ob-jects, or a vast long wall ABZY, fig. 45, built upon this plane, andits perpendicular distance OA from the eye at O to be equal toor greater than the distance O a of the visible horizon, it will notappear straight, but circular, as if it were built upon the circum-ference of the horizon a c <■' g JJ '■ and if the wall I* continued toan immense distance, its extreme parts YZ will appear in the ho-rizon, at yz , where it is cut by a line ()// parallel to the wall. For,supposing a ray YO, the angle YO y will become insensiblysmall. Imagine this infinite plane OAY with the wall upon it,to he turned about the horizontal line O like the lid of a box, tillit becomes perpendicular to the other half of the horizontal planeLM i/, and the wall parallel to it, like a vast ceiling overhead;and then the wall will appear like the concave figure of the cloudsoverhead. But though the wall in the horizon appear in thefigure of a semicircle, yet the ceiling will not, but much flatter.Because the horizontal plane was a visible surface, which suggestedthe idea of the same di truces quite round the eye : but in the ver-tical plane extended between the eye and tile ceiling, there isnothing that affect, the sense with an idea of its parts but the com-mon line Otj\ consequently the apparent distances of the higher
■ - ■ ■■ ■ ■ ■ " , i i . .» 7 -; —
parts of the ceiling will be gradually diminished in ascending fromthat line. 'When the sky is quite overcast with the clouds oi equalgravities, they will all float in the air at equal heights above theearth, and consequently will compose a surface resembling a largeceiling, as flat as the visible surface of the earth. Its concavitytherefore is not real, but apparent: and when the heights of theclouds are unequal, since their real shapes and magnitudes are allunknown, the eye can seldom distinguish the unequal distancesot those clouds that appear in the same directions, unless thev arevery near us, or are driven by contrary currents of the air." 15othat the visible shape of the whole surface remains alike in bothcases. And when lire sky is either partly overc ast, or partly freefrom clouds, it is matter of fact that wc retain much the same ideaof its concavity, as when it was quite overcast. The concavity ofthe heavens appears to the eye, to be a less proportion of tbes’pbe-tical surface than a hemisphere. Dr. .Smith saw, that the centreof the concavity is much belocv the eye; and by taking a medi-um among several observations, he found the apparent distance olits parts at the'horizon to be generally between three and (mu-tinies greater than the apparent distance of its parts ovei head.For let the arch ABCD, flg. 4fi, represent the apparent concavityof the sky, O the place of the eye, bA and OC the horizontaland vertical apparent distances, whose proportion is required. Firstobserve when the sun or the moon, or any cloud or star, is in sucha position at B, that the apparent arches BA, BC, extended oneach side of this object towards the horizon and zenith, seemequal to the eye ; then taking the altitude of the object B with aquadrant, or finding if by astronomy from the given time of ob-servation, the angle AOB is knorvn. Drawing therefore the lineOB in the position thus determined, and taking in it anypoint B, at pleasure, in the vertical line CO produceddownwards, seek the centre E of a circle ABC, whosearches BA, BC, intercepted between B and the legs of the rightangle AOC, shall he equal to each other; then will this arehABCD represent the apparent figure of the sky. The centre Emay be found geometrically by constructing a cubic equation, oras quickly and sufficiently exact, by trying whether the chordsBA, BC,of the arch ABC drawn by conjecture are equal, and byaltering its radius BE till they are so. In making several obser-vations upon the sun, moon and stars, thev seemed to the Dr. tobisect the vertical arch ABC at B, when "their apparent altitude.,or the angle AOB was about 23 degrees; which gives theproportion of OC to OA as 3 to 10, or 1 to 3J nearly. Whenthe sun was but 30° high, the upper arch seemed always less thanthe under one; and, in Dr. Smith’s opinion, always greater whenthe sun was about 18° or 20° high.
Of the Irradiations of tiie Sun’s Light appearing
THROUGH THE INTERSTICES OF THE Cl-OUDS.
This is an appearance which every one must have observed,when the sky was pretty much overcast with clouds at some dis-tance from each other. At that time several large beams of light,something like the appearance of the light of the sun admitted iiitoasmoky room, will be seen generally with a very considerable degreeof divergence, as if the radiant point was situated at no great dis-tance above the clouds. l)r. Smith observes, that this appearanceis one of those which serve to demonstrate, that verv high andremote objects, in the heavens do not appear to us m their realshapes and positions, but according to their perspective projec-tions on the apparent concavity of the sky. He savs that thoughthese beams are generally seen diverging, as represented in fig. 47,Plate CXXXH. it is not always the case. lie himself once sawthem converging towards a point diametrically opposite to the sunlor, as near as he could conjecture,the point to which they con-verged was situated as much below the horizon, as the sun wasthen elevated above the opposite part of it. This pari is ret re-sented by the line iDi, fig. 48, and the point below it in opposi-tion to the sun is E; towards which all the beams v t , v t , &e. ap-peared to converge. “Observing (says he) that the ’point" ofconvergence was opposite to the sun, l began to suspect, that thisunusual phariotnenon was but a case of the usual apparent diver-gence of the beams of the sun, from his apparent place ammio- theclouds, as represented in fig. 47. I say an apparent divergence ;for though it is common for rays to diverge from a him,nous bodv!yet the divergence of these beams in such angles is not retd, bia
apparent: