fo confused and indiftinct that I could not read them; but in the former, they appeared fo diftinct that I could read readily, and thought I faw them as diftinct as when I viewed them with my naked eye: in both cafes I viewed the fame objects through the fame prifm, at the fame diftance from me, and in the fame fituation. There was no difference but in the lights by which the objects were illuminated, and which in one cafe was fimple, in the other compound; and therefore the diftinct vifion in the former cafe, and confused in the latter, could arife from nothing elfe than from that difference in the lights. Which proves the whole propofition.

421. "In thefe three experiments, it is farther very remarkable, that the colour of homogeneal light was never changed by the refraction. And as these colours were not changed by refractions, fo neither were they by reflections. For all white, grey, red, yellow, green, blue, violet bodies, as paper, ashes, red lead, orpiment, indigo, bice, gold, filver, copper, grafs, blue flowers, violets, bubbles of water tinged with various colours, peacock's feathers, the tincture of lignum nephriticum, and fuch like, in red homogeneal light appeared totally red, in blue light totally blue, in green light totally green, and fo of other colours. In the homogeneal light of any colour they all appeared totally of that fame colour; with this only difference, that fome of them re. flected that light more ftrongly, others more faint ly. I never yet found any body which, by reflecting homogeneal light could fenfibly change its colour. From all which it is manifeft, that if the fun's light confifted of but one fort of rays, there would be but one colour in the world, nor would it be poffible to produce any new colour by reflec. tions and refractions; and by confequence, that the variety of colours depends upon the compofition of light.

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422. The folar image Pt, formed by the feparated rays in the 5th experiment, did in the progrefs from its end P, on which the most refrangible rays fell, unto its end t, on which the leaft refrangible rays fell, appear tinged with this feries of colours; violet, indigo, blue, green, yellow, orange, red, together with all their intermediate degrees in a continual fucceffion, perpetually varying; fo that there appeared as many degrees of colours as there were forts of rays differing in refrangibility. And fince these colours could not be changed by refractions nor by reflections, it follows, that all homogeneal light has its proper colour answering to its degree of refrangibility.

423. Every homogeneal ray confidered apart is refracted, according to one and the fame rule, fo that its fine of incidence is to its fine of refraction in a given ratio; that is, every different coloured ray has a different ratio belonging to it. Tois our author has proved by experiment, and by other experiments has determined by what numbers thofe given ratios are expreffed. For instance, if an heterogeneal white ray of the fun emerges out of glafs into air; or, which is the fame thing, if rays of all colours be fuppofed to ucceed one another in the fame line AC, and AD

(Plate 256. fig. 15.) their common fine of incicence in glafs be divided into 50 equal parts, then EF and GH, the fines of refraction into air, of the leaft and most refrangible rays, will be 77 to 78 fuch parts refpectively. And fince every colour has feveral degrees, the fines of retraction of all the degrees of red will have all intermediate degrees of magnitude from 77 to 77, of all the degrees of orange from 77 to 77}, of yellow from 774 to 77, of green from 77% to 77%, of blue from 774 to 773, of indigo from 773 to 777, and of violet from 77% to 78."

PART II.

SECT. I. The APPLICATION of the PRECEDING THEORY to feveral NATURAL PHENOMENA.

1. Of the RAINBOW.

424. THIS beautiful phenomenon hath engaged the attention of all ages. By some nations it hath been deified; though the more fenfible part always looked upon it as a natural appearance, and endeavoured, however imperfectly, to account for it. The obfervations of the ancients and phi lofophers of the middle ages, concerning the rain. bow, were fuch as could not have escaped the notice of the moft illiterate husbandman who gazed at the sky; and their various hypothefes deferve no notice. It was a confiderable time even after the dawn of true philofophy in this weftern part of the world, before we find any discovery of importance on this fubject. MAUROLYCUS was the firft who pretended to have measured the diameters of two rainbows with much exa&nefs; and he fays, that he found that of the inner bow to be 45°, and that of the outer bow 56°; from which Defcartes takes occalion to obferve, how little we can depend upon the obfervations of thofe who were not acquainted with the caufe of the appearances.

425. One CLICHTOVAUS (who diftinguished himfelf by his oppofition to Luther, and died in 1543) had maintained, that the 2d bow is the image of the firft, as he thought was evident from the inverted order of the colours. For, faid he, when we look into the water, all the images that we fee reflected by it are inverted with refpect to the objects themselves; the tops of the trees, for inftance, that stand near the brink, appearing lower than the roots. That the rainbow is oppofite to the fun, had always been obferved. It was, therefore, natural to imagine, that the colours of it were produced by fome kind of refection of the rays of light from drops of rain, or vapour. The regular order of the colours was another circumftance that could not cfcape notice. But, notwithstanding mere reflection had in no oth been obferved to produce colours, and it could not but have been oblerved that refraction is írequently attended with that phenomenon, yet no perfon feems to have thought of having recourse to a proper refraction in this cafe, before one FLE.CHER of Breslau, who, in a treatite publish. cd01571, deavoured to account for the colours of trembow by a double retraction and one reflection. But he imagined that a ray of light, af

cafe

ter

ter entering a drop of rain, and suffering, a refrac tion both at its entrance and exit, was afterwards refl ted from another drop before it reached the eye of the fpectator. He feems to have overlooked the reflection at the farther fide of the drop, or to have imagined that all the bendings of the light within the drop would not make a fufficient curvature to bring the ray of the fun to the eye of the fpectator. That he fhould think of two refractions, was the neceffary confequence of his fuppofing that the ray entered the drop at all. This fuppofition, therefore, was all the light he threw upon the fubject. B. PORTA fuppofed that the rainbow is produced by the refraction of light in the whole body of rain or vapour, but not in the feparate drops.

426. After all, a man who had no pretenfion to philofophy, hit upon this curious difcovery. This was ANTHONY DE DOMINIS, Bp. of Spalatro, whofe treatise De Radiis Vifus et Lucis, was publifhed by J. Bartolus in 1611. He firft advanced, that the double refraction of Fletcher, with an intervening reflection, was fufficient to produce the colours of the bow, and alfo to bring the rays that formed them to the eye of the fpectator, without any fubfequent reflection. He diftinctly defcribes the progrefs of a ray of light entering the upper part of the drop, where it fuffers one refraction, and after being thereby thrown upon the back part of the inner furface, is from thence reflected to the lower part of the drop; at which place undergoing a fecond refraction, it is thereby bent fo as to come directly to the eye. To verify this hypothefis, the bifhop proceeded in a very fenfible and philofophical manner. For he procured a fmall globe of folid glass, and viewing it when it was expofed to the rays of the fun, in the fame manner in which he had fuppofed that the drops of rain were fituated with refpect to them, he actually obferved the fame colours which he had feen in the true rainbow, and in the fame order.

427. Thus the circumftances in which the colours of the rainbow were formed, and the progrefs of a ray of light through a drop of water, were clearly underflood; but philofophers were long at a lofs to affign reafons for all the particular colours and for the order of them. Indeed nothing but the doctrine of the different refrangibility of the rays of light, a difcovery reserved for the great Sir Ifaac Newton, could furnish a complete folution of this difficulty. De Dominis fuppofed that the red rays were thofe which had traversed the least space in the infide of a drop of water, and therefore retained more of their native force, and confequently, ftriking the eye more brifkly, gave it a stronger fenfation; that the green and blue colours were produced by thofe rays, the force of which had been, in some meafure, obtunded in paffing through a greater body of water; and that all the intermediate colours were compofed (according to the hypothefis which prevailed at that time) of a mixture of thefe three primary on s. That the different colours were caused by some difference in the impalfe of light upon eye, and the greater or lefs impreffion that was thereby made upon it,

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was an opinion which had been adopted by many perfons who had ventured to depart from the authority of Aristotle.

428. Afterwards De Dominis obferved, that all the rays of the fame colour muft leave the drop of water in a part fimilarly fituated with respect to the eye, in order that each of the colours may appear in a circle, the centre of which is a point of the heavens, in a line drawn from the fun through the eye of the fpectator. The red rays, he obferved, muft iffue from the drops nearest to the bottom of it, that the circle of red may be the outermoft, and therefore the most elevated in the bow. But though he conceived fo justly of the manner in which the inner rainbow is formed, he was far from having as just an idea of the cause of the exterior bow. This he endeavoured to explain in the fame manner in which he had done the interior.

429. When Sir Ifaac Newton discovered the different refrangibility of the rays of light, he immediately applied his new theory of light and colours to the phenomena of the rainbow, taking this remarkable object of philofophical inquiry, where De Dominis and Defcartes were obliged to leave their investigations imperfect. For they could give no good reason why the bow should be coloured, and much lefs could they give any fatisfactory account of the order in which the colours appear. If different particles of light had not different degrees of refrangibility, on which the colours depend, the rainbow, befides being much narrower than it is, would be colourless; both the different refrangibility of differently coloured rays being admitted, the reafon is obvious, both why the bow fhould be coloured, and alfo why the colours fhould appear in the order in which they are obferved. Let a (Pl. CCLVI. fig. 17.) be a drop of water, and S a ray of light; which, on its leaving the drop of water, reaches the eye of the fpectator; this ray, at its entrance into the drop, begins to be decompofed into its proper colours; and upon leaving the drop, after one reflection and a fecond refraction, it is farther decompofed into as many small differently coloured pencils as there are primitive colours in the light. Three of them only are drawn in this figure, of which the blue is the moft, and the red the leaft refracted.

430. The doctrine of the different refrangibility of light enables us to give a reafon for the fize of a bow of each particular colour. Newton, having found that the fines of refraction of the most refrangible and leaft refrangible rays, in paffing from rain-water into air, are in the proportion of 185 to 182, when the fine of incidence is 138, calculated the fize of the bow; and he found, that if the fun was only a phyfical point, without fenfi. ble magnitude, the breadth of the inner bow would be 2 degrees; and if to this 30' was added, for the apparent diameter of the fun, the whole breadth would be 24 degrees. But as the outermolt colours, efpecially the violet, are extremely faint, the breadth of the bow will not in reality appear to exceed two degrees. He finds, by the fame principles, that the breadth of the exterior bow, if it was everywhere equally vivid, would

be

drop of rain after one reflection, those will be effectual, which are reflected from the fame point, and which entered the drop near to one another."

be 4° 20. But in this cafe there is a greater de duction to be made on account of the faintnefs of the light of the exterior bow; so that, in fact, it will not appear to be more than 3° broad. 431. The principal phenomena of the rainbow are all explained, on Sir Ifaac Newton's principles, in the following propofitions:

432. I. "When the rays of the fun fall upon a drop of rain and enter into it, fome of them, after one reflection and two refractions, may come to the eye of a spectator who has his back to wards the fun, and his face towards the drop."

433. If XY (pl. CCLVII, fig. 1.) is a drop of rain, and the fun shines upon it in any lines sf, sd,'sa, &c. most of the rays will enter into the drops; fome few of them only will be reflected from the firft furface; thofe rays which are reflected from thence do not come under our present confideration, because they are never refracted at all. The greateft part of the rays then enter the drop, and those paffing on to the second furf ce, will moft of them be tranfmitted through the drop; but neither do thofe rays which are thus tranfmitted fall under our prefent confideration, fince they are not reflected. For the rays, which are described in the propofition, are fuch as are twice refracted and once reflected. However, at the 2d surface, or hinder part of the drop at pg, fome few rays will be reflected, while the reft are tranfmitted: thofe rays proceed in fome fuch lines as n r, nq; and coming out of the drop in the lines r v, qt, may fall upon the eye of a spectator, whois placed anywhere in thofe lines, with his face towards the drop, and confequently with his back towards the fun, which is fupposed to shine upon the drop in the lines sf, sd, sa, &c. These rays are twice refracted and once reflected; they are refracted when they pafs out of the air into the drop; they are reflected from the second furface, and are refracted again when they pass out of the drop into the air.

434 H. When rays of light reflected from a drop of rain come to the eye, thofe are called EFFECTUAL which are able to excite a sensation." 435. III. "When rays of light come out of a drop of rain, they will not be effectual, unless they are parallel and contiguous."

436. There are but few rays that can come to the eye at all; for fince the greatest part of thofe rays which enter the drop XY, (fig. 1. Pl. CCLVII.) between X and a, pass out of the drop through the hinder furface pg; only few are reflected from thence, and come out through the nearer furface between a and y. Now, fuch rays as emerge or come out of the drop, between a and Y, will be ineffectual, unless they are parallel to one another, as rv and qt are; because such rays as come out, diverging from one another, will be fo far afunder when they come to the eye, that all of them cannot enter the pupil; and the very few that can enter it will not be fufficient to excite any fenfation. But even rays which are parallel, as rv, qt, will not be effectual, unless there are feveral of them contiguous or very near to one another. The two rays rv, qt alone will not be perceived, though both of them enter the eye; for fo very few rays are not fufficient to excite a fenfation.

437. IV. "When the rays of light come out of a

438. Any rays, ass b and c d (fig. 2.) when they have paffed out of the air into a drop of water, will be refracted towards the perpendiculars bi, dl; and as the ray s b falls farther from the axis a than the ray cd, sb will be more refracted than cd; fo that these rays, though parallel to one another at their incidence, may defcribe the lines be and de after refraction, and be both of them reflected from one and the fame point e. Now all rays which are thus reflected from one and the fame point, when they have described the lines ef, eg, and after reflection emerge at ƒ and g, will be fo refracted, when they país out of the drop into the air, as to defcribe the lines fh, gi, parallel to one another. If these rays were to return from e in the lines eb, ed, and were to emerge at b and , they would be refrac ted into the lines of their incidence bs, dc. But if these rays, instead of being returned in the lines eb, ed, are reflected from the fame point e in the lines eg, ef, the lines of reflection eg and ef will be inclined both to one another, and to the surface of the drop; just as much as the lines e b and ed are. Firft eb and eg make juft the fame angle with the furface of the drop; for the angle ben, which eb makes with the furface of the drop, is the complement of incidence, and the angle gev, which eg makes with the furface, is the comple. ment of reflection; and these two are equal to one another. In the fame manner we might prove, that e d and ef make equal angles with the furface of the drop. 2dly, The angle bed is equal to the angle feg; or the reflected rays eg, ef, and the incident rays be, de, are equally inclined to each other. For the angle of incidence bel is equal to the angle of reflection gel, and the angle of incidence del is equal to the angle of reflection fel; confequently the difference between the angles of incidence is equal to the difference between the angles of reflection; or bel— del=gel-fel, or bed gef. Since therefore either the lines eg, ef, or the lines e b, ed, are equally inclined both to one another, and to the furface of the drop, the rays will be refracted in the fame manner, whether they were to return in the lines e b, ed, or are reflected in the lines egi ef. But if they were to return in the lines e b, ed, the refraction, when they emerge at b and d, would make them parallel. Therefore, if they are reflected from one and the fame point e in the lines eg, ef, the refraction, when they emerge at g and f, will likewife make them parallel.

439. But though fuch rays as are reflected from the fame point, in the hinder part of a drop of rain, are parallel to one another when they emerge, and fo have one condition that is requifite towards making them effectual, yet there is another con dition neceflary; for rays that are effectua cauft be contiguous as well as parallel. And though rays, which enter the drop in different places, may be parallel when they emerge, thofe only will be contiguous which enter it nearly at the fame place.

440. Let XY (fig. 1. Pl. CCLVII.) be a drop of