OPTICS.

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apparent: Because it is impossible for the direct rays of the sunto cross one another at any point of the apparent concavity of theskv, in a greater angle than about half a degree. For the diame-ter of the earth being so extremely small, in comparison to the dis-tance of the sun, as to subtend an angle at any point of his bodyof about 20" or 22'at most; and the diameter of our visible hori-zon being extremely smaller than that of the earth ; it is plain, thatall the ra\s which fall upon the horizon, from any given point ofthe sun, must be inclined to each other in the smallest angles ima-ginable : the greatest of them being as much smaller than thatangle of 22 seconds, as the diameter of the visible horizon issmallerthan that of the earth. All the rays that come to us from anygiven point of the sun may therefore be considered as parallel toeach other; as the rayseBg, fig. 49, from the point e, or/B/i fromthe opposite point/; and consequently the rays of these two pen-cils that come from apposite points of the sun’s real diameter, andcross each other in the sun’s apparent place B among the clouds,can constitute no greater an angle with each other than abouthalf a degree ; this angle of their intersection eRf being thesame as the sun would appear under to an eye placed among theclouds at B, or (which is much the same) to an eye at O upon theground: Because the sun’s real distance OS is inconceivablyareater than his apparent distance O B. Therefore the rays of thev.m, as lig-, BA, do really diverge from his apparent place B in nogreater anglesgBA than about half a degree. Nevertheless theyappear to diverge from the place B, fig, 47, in all possible angles,and even in opposite directions. Let us proceed then to an ex-planation oi this apparent divergence, which is not self-evident byany means; though at first sight we are apt to think it is, by not dis-tinguishing the vast difference between the true and apparent dis-tances of the sun. Supposing all the rays of the sun to fall accu-rately parallel to each other upon the visible horizon, as they dovery nearly, yet in both cases they must appear to diverge in allpossible angles. Let us imagine the heavens to be partly overcastwith a spacious bed of broken clouds v, v, v, Sec. fig. 50, lyingparallel to the plane of the visible horizon, here represented bythe line AOD ; and when the sun’s rays fall upon these clouds inthe parallel lines x v, s v, Sec. let some of them pass through theirintervals in the lines v t, v t, See. and falling upon the plane of thehorizon at the places t, t, Sec. And since the rest of the incidentrays x v, i t, are supposed to be intercepted from the place of thespectator atO by the cloud ,r, and from the intervals between thetransmitted rays, v t, v t, Sec. by the cloud v, v, Sec. a small partof these latter rays v t, v t, when reflected every way fromsome certain kind of thin vapours floating in the air, may undoubt-edly be sufficient to affect the eye with an appearance of lights andshades, in the form of bright beams in the places » t, v l, Sec. andof dark ones in the intervals between them ; just as the like beamsof light and shade appear in a room by reflections of the sun’s raysfrom a smoky or dusty air within it; the lights and shades beinghere occasioned by the transmission of the rays through some partsof the window, and by their interruption at other parts. Now,if the apparent concavity of this bed of clouds v, v, to the eye atO, be represented by the arch A'BCD, and be cut in the point Bby the line OBr drawn parallel to the beams tv, it will be evi-dent by the rules of perspective, that these long beams will notappear in their real places, but upon the concave A BCD tliverg-ingevery way from the place B, where the sun himself appears, orthe cloud x that covers his body,.as represented separately in fullview in fig. 47, Plate CXXXIl. And for the same reason, if theline BO rig. 50, be produced towards the point F,, below theplane of the horizon AOD, and the eye be directed towards theregion of the sky directly above E, the lower ends of the same realbeams vt, v t, will now appear upon the part DF of this concave;and will seem to converge towards the point E, situated just asmuch below the horizon as the opposite point B is above it: whichis separately represented for the sake of illustration in fig. 48,For if the beams v t, v t, be supposed to be visible throughout theirwhole lengths, and the eye be directed in a plane perpendicular tothem, here represented by the line OF, fig. 50, they andtheir intervals will evidently appear broadest in and about thisplane, because these parts of them are the nearest to the eye ; andtherefore their remoter parts and intervals will appear graduallynarrower towards the opposite ends of the line BE. Asa fartherillustration of this matter, we may couceive the spectator at O toVOL. IV.— no. 103,

be situated upon the top of so large a descent OH1 towards a remote valley IK, and the sun to be so very low, that the point E,opposite to him, may be seen above the horizon of this shady val-ley. In this case it is manifest, that the spectator at O would now-see these beams converging so far as to meet each other at thepoint E in the sky itself.

Of Optical Instruments.

1. The Multiplying Glass. This is made by grinding downthe round side A i k, tig. 51, Plate CXXXI1. of a plano-convexglass AB, into several flat surfaces, as hb,bd, d k. An objectC will not appear magnified when seen through this glass by theeye at H ; but it will appear multiplied into as many differentobjects as the glass contains plane surfaces. For, since rays willflow from the object C to all parts of the glass, and each plane sur-face will refract these rays to the eye, the same object will appearto the eye in the direction of the rays which enter it through eachsurface. Thus, a ray gi H, falling perpendicularly on the mid-dle surface, will go through the glass to the eye without sullcringany retraction ; and will therefore shew the object in its true placeat C : whilst a ray a b flowing from the same object, and tailingobliquely on the plane surface b h, will be refracted in the direc-tion II,’by passing through the glass; and upon leaving it, willgo on to the eye in the direction e H : which will cause the sameobject C to appear also at E, in the direction of the ray H e, pro-duced in the right line H e n. And the ray c d, flowing from theobject C, and falling obliquely on tjie plane surface d A, will herefracted (by passing through the glass, and leaving it at f) to theeye at II; which will cause the same object to appear at D, inthe direction l\fm .—If the glass be turned round the lineg/ 11,as an axis, the object C will keep its place,because the surface bidis not removed ; hut all the other objects will seem to go round C,because the oblique planes, on which the rays acbd fall, will goround by the turning of the glass.

2. Mirrors. There are three mirrors principally used in opti-cal experiments, the plane mirror, the spherical convex mirror,and the spherical concave mirror. Of these the plane mirror mostclaims our attention, as it is more common, and undoubtedlymore ancient, than the other two. It has been said that the imagereflected by this mirror appears as far behind the surface as theobject is before it; that the image will appear of the same size,and in the same position with the object; that every such mirrorwill reflect an image of twice its own length and breadth ; and thatin certain circumstances it will reflect several images of the sameobject. For these phamomena we shall endeavour to account bythe laws of reflection. Let AB, fig. 52, bean object before thereflecting surface g h i of the plane mirror CD ; and let the eyebe at o. Let Ah be a ray of fight flowing from the top A of theobject, and falling upon the mirror at h, and h m be a perpendi-cular to the surface of the mirror at A ; the ray Ah will be re-flected from the mirror to the eye at o, making an angle m h oequal to the angle A h m : then will the top of the image E appearto the eye in the direction of the reflected ray o h produced to F.,where the right line A p E, from the top of the object, cuts theright line o h E, at E. Let B i be a ray of light proceeding fromthe foot of the object at B to the mirror at i; and n i a perpendi-cular to the mirror from the point i, where the ray Bz falls uponit: this ray will be reflected in the line i o, making an angle?; i aequal the angle B i n, with that perpendicular, and entering theeye at o; then will the foot F of the image appear in the directionof the reflected rav o i, produced to F, where this right line BFcuts the reflected ray produced to F. All the other rays thatflow from the intermediate points of the object, AB, and fall uponthe mirror between h and i, will be reflected to the eye at o ; andall the intermediate points of (he image EF will appear to the eyein the direction of these reflected rays produced. But all the raysthat flow from the object, and fall upon the mirror above h, willhe reflected back above the eye at o; and all the rays that flowfrom the object, and fall upon the mirror below will be reflectedback below the eye at o; so that none of the rays that fall above A,or below i, can be reflected to the eye at o ; and the distance be-tween A and i is equal to half the length of the object AB. Henceit appears, that if a man sees his whole image in a plane looking-glass, the part of the glass that reflects his image must be just halfas long and half as broad as himself, let him stand at any distance

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