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oPTrcs.

cause its sides are inclined to each other, and therefore the imagein the focus of a single lens must be as compounded as light it-self, and consequently in some measure confused ; for eacli par-ticular species of rays” does in reality form a distinct image in itsown peculiar focus. And of course, when this compound imageis viewed with a deep magnifier, it will appear both coloured andconfused, as we find in the common microscopes, telescopes, &c.of the refracting sort, flow this is in some degree remedied, seebelow. But images formed by reflected light are not subject toeither of those imperfections, because there is no different reflec-tion of light while the angles of incidence are the same : andtherefore only one simple image is formed in the focus of a spe-culum : and so perfect, that it will bear to be magnified a secondtime with sufficient distinctness; and consequently a doublepower of magnifying in a reflecting telescope will have the sameeffect in a small length as we have in a very great length by re-fraction.

An Explication of several natural Phenomena, de-pending on the Principles of Optics.

Of the Rainbow.

This beautiful phenomenon hatli engaged the attention of allages. By some nations it hath been deified; though the more-sensible part always looked upon it as a natural appearance, andendeavoured, however imperfectly, to account for it. The ob-servations of the ancients and philosophers of the middle ages,concerning the rainbow, were such as could not have escaped thenotice of the most illiterate husbandman who gazed at the sky;and their various hypotheses deserve no notice. It was a consi-derable time even after the dawn of true philosophy in thiswestern part of the world, before we find any discovery of import-ance on this subject. Maurolycus was the first who pretended tohave measured the diameters of two rainbows with much exact-ness ; and he says, that he found that of the inner bow to be 45°,and that of the outer bow 56°; from which Descartes takes occa-sion to observe, how little we can depend upon the observations ofthose who were not acquainted with the cause of the appearances.One Clichtovxus (who distinguished himself by his opposition toLuther, and died in 1543,) had maintained, that the second bowis the image of the first, as he thought was evident from the in-verted order of the colours. For, said he, when we look into thewater, all the images that we see reflected by it are inverted withrespect to the objects themselves; the tops of the trees, for in-stance, that stand near the brink, appearing lower than the roots.That the rainbow is opposite to the sun, had always been observ-ed. It was, therefore, natural to imagine, that the colours of itwere produced by some kind of reflection of the rays of light fromdrops of rain, or vapour. The regular order of the colours wasanother circumstance that could not escape nolice. But, notwith-standing mere reflection had in no other case been observed toproduce colours, and it could not but have been observed that re-fraction is frequently attended with that phenomenon, yet no per-son seems to have thought of having recourse to a proper retrac-tion in this case, before one Fletcher of Breslau , who, in a treatisepublished in 1571. endeavoured to account for the colours of therainbow by a double refraction and one reflection. But he ima-gined that a ray of light, after entering a drop of rain, and suffer-ing a refraction both at its entrance and exit, was afterwards re-flected from another drop before it reached the eye of the specta-tor. He seems to have overlooked the reflection at the fartherside of the drop, or to have imagined that all the blendings of thelight within the drop would not make a sufficient curvature tobring the ray of the sun to the eye of the spectator. 7 hat heshould think of two refractions, was the necessary consequence othis supposing that the ray entered the drop at all. 1 his supposi-tion, therefore, was all the light he threw upon tiie subject. B.Porta supposed that the rainbow is produced by the retraction oflight in the whole body of rain or vapour, but not in the separatedrops. After all, a man who hud no pretension to philosophy,hit upon this curious discovery. This was Anthony De Dominis,bishop of Spalatro, whose treatise “ De Radiis Visus et Lucis,”was published by J. Bartolus in 1011. He first advanced, that thedouble refraction of Fletcher, with an intervening reflection, wassufficient to produce the colours of the bow, and also to bring therays that formed them to the eye of the spectator, without any

subsequent reflection. He distinctly describes the progress of aray of light entering the upper part of the drop, where it surfersone refraction, and after being thereby thrown upon the back paitof the inner surface, is from thence reflected to the lower part ofthe drop; at which place undergoing a second refraction, it isthereby bent, so as to come directly to the eye. To verily thishypothesis, the bishop proceeded in a very sensible and philoso-phical manner. For he procured a small globe of solid glass, andviewing it when it w'as exposed to the rays of the sun, in the samemanner in which he had supposed that the drops of rain weresituated with respect to them, he actually observed the same co-lours which he had seen in the true rainbow, and in the sameorder. Thus the circumstances in which the colours of the rain-bow were formed, and the progress of a ray of light through adrop of water, were clearly understood ; hut philosophers werelong at a loss to assign reasons for ail the particular colours and Ibrthe order of them. Indeed nothing but the doctrine of the dif-ferent refrangibility of the rays of light, a discovery reserved forthe great Sir Isaac Newton , could furnish a complete solid ion ofthis difficulty. De Dominis supposed that the reel rays werethose which had traversed the least space in the inside of a dropof water, and therefore retained more of their native force, andconsequently, striking the eye more briskly, gave it a strongersensation ; that the green and blue colours were produced by thoserays, the force of which had been, in some measure, obtumled inpassing through a greater body-of water; and that all the inter-mediate colours were composed (according to the hypothesiswhich prevailed at that time,) of a mixture of these three primaryones. That the different colours were caused by some differencein the impulse of light upon the eye, and the greater or less im-pression that was thereby made upon it, was an opinion which hadbeen adopted by many persons, wiio had ventured to depart fromthe authority of Aristotle . Afterwards De Dominis observed,that all the rays of the same colour must leave the drop of waterin a part similarly situated with respect to the eye, in order thateach of the colours may appear in a circle, the centre of which isa point of the heavens, in a line drawn from the sun through theeye of the spectator. The red rays, he observed, must issue fromthe drops nearest to the bottom of it, that the circle of red maybe the outermost, and therefore the most elevated in the bow.But though he conceived so justly of the manner in which theinner rainbow is formed, lie was far from having as just an idea ofthe cause of the exterior bow. This he endeavoured to explainin the same manner in which he had done the interior. When SirIsaac Newton discovered the different refrangibility of the rays oflight, lie immediately applied his new theory of light and coloursto the phenomena of the rainbow', taking this remarkable objectof philosophical inquiry, where De Dominis and Descartes wereobliged to leave their investigations imperfect. For they couldgive no good reason why the bow should be coloured, and muchless could they give any satisfactory account of the order in whichthe colours appear. It different particles of light had not differentdegrees of refrangibility, on which the colours depend, the rain-bow, besides being much narrower than it is, would be colour-less ; but the different refrangibility of differently coloured raysbeing admitted, the reason is obvious, both why the bow shouldbe coloured, and also why the colours should appear in the orderin which they are observed. Let a, Plate CXXXI, fig. 24, bea drop of water, and S a ray of Fight ; which, on its leaving thedrop of water, readies the eye of the spectator. This ray, at itsentrance into the drop, begins to be decomposed into its propercolours; and upon leaving the drop, after one reflection and asecond refraction, it is farther decomposed into as many smalldifferently colour-pencils as there are primitive colours in ‘thelight. Three of them only are drawn in this figure, of which theblue is the most, and the red the least retracted. 1 he doctrine ofthe different refrangibility of light enables us to give a reason forthe various phamomena of the'rainbow, which may be (bus ex-plained. Suppose BNFG, (Plate CXXX11. fig. 40,) to he aspherical drop ot falling rain, and AN a ray of the sun fallingupon it in the point. N ; which ray suppose refracted to F, fromthence reflected to G, anil there again refracted in the directionGR to the eye of a spectator ; and let IG be perpendicular to thedrop in Ihe point G ; then will the ray or beam of light, by itsrefraction at G, be separated into several sorts of rays, which willpaint their respective colours in that part of the drop ; of whichIt that