fhould be the fame in this cafe needs little explication; for the middle of the object being in the centre, rays flowing from thence will fall perpendicularly upon the surface, and therefore neceffa rily return thither again; fo that the middle of the image will be coincident with the middle of the object. But that the image fhould be inverted, is perhaps not fo clear. To explain this, let AB (fig. 18. pl. CCLII.) be the object, having its middle point C in the centre of the reflecting furface SV; through the centre and the point R draw the line CR, which will be perpendicular to the reflecting furface; join the points AR and BR, and let AR reprefent a ray flowing from A; this will be reflected into RB; for C being the middle point between A and B, the angles ARC and CRB are equal; and a ray from B will likewife be reflected to A; and therefore the pofition of the image will be inverted with refpect to that of the object. In this propofition, it is to be supposed that the object AB is fo fituated with refpect to the reflecting furface, that the angle ACR may be right; for otherwise the angles ARC and BRC will not be equal, and part of the image will therefore fall upon the object and part off.

405. vi. If in any of the three laft cafes, in each of which the image is formed on the fame fide of the reflecting furface with the object, the eye be fituated farther from the furface than the place where the image falls, the rays of each pencil, croffing each other in the several points of the image, will enter the eye as from a real object fituated there; fo that the image will appear pendulous in the air between the eye and the reflecting furface, and in the pofition wherein it is formed, viz. inverted with refpect to the object, in the fame manner that an image formed by refracted light appears to an eye placed beyond it; which was fully explained under Prop. IV. (§ 356.) and therefore needs not be repeated. But as what relates to the appearance of the object when the eye is placed nearer to the furface than the image, was not there fully inquired into, that point fhall now be more ftrictly examined under the following cafe, which equally relates to refracted and reflected light.

406. vii. If the eye be fituated between the reflecting furface and the place of the image, the object is then feen beyond the furface; and the farther the eye recedes from the furface towards the place of the image, the more confused, larger, and nearer the object appears. To explain this, let AB (fig. 7. pl. 256) reprefent the object; IM its image, one of whole points M is formed by the concurrence of the reflected rays DM, EM, &c. which before reflection came from B; the other, I, by the concurrence of DI, EI, &c. which came from A; and let ab be the pupil of an eye, fituated between the furface DP and the image. This pupil will admit the rays Ha, Kb; which, becaufe they are tending towards I, are fuch as came from A, and therefore the point A will appear diffufed over the space RS. In like manner the pupil will alfo receive into it the reflected rays Ka and Lb, which, because they are tending towards M, by fuppofition came from B; and therefore the point B will be feen fpread as it were over the fpace TV, and the object will feem to fill the fpace RV; but the reprefentation of it will be confufed, becaufe VOL. XVI. PART II.

the intermediate points of the object being equal y enlarged in appearance, there will not be room for them between the points S and T, but they will coincide in part one with another; for inflance, the appearance of that point in the object whefe reprefentation falls upon c in the image, will fill the fpace mn; and fo of the reft. Now, if the fame pupil be removed into the fituation ef, the reflected rays Ee and Gf will then enter the eye, and therefore one extremity of the object will appear to cover the space XY; and because the rays Of and Le will alfo enter it in their progrefs towards M, the point B from whence they came will appear to cover ZV; the object therefore will appear larger and more confused than before. And when the eye recedes quite to the image, it fees but one fingle point of the object, and that appears diffused all over the reflecting furface. For inftance, if the eye recedes to the point M, then rays flowing from the point B enter it, upon whatever part of the furface they fall; and fo for the reft. The object alfo appears nearer to the furface, the farther the eye recedes from it towards the place of the image; probably because, as the appearance of the object becomes more and more confused, its place is not fo eafily diftinguished from that of the reflecting furface itfelf, till at last, when it is quite confufed (as it is when the eye is arrived at M) they both appear as one, the furface affuming the colour of the object. As to the precife apparent magnitude of an object seen after this manner, it is fuch that the angle it appears under fhall be equal to that which the image of the fame object would appear under, were we to fuppofe it feen from the fame place; that is, the apparent object (for fuch we must call it, to diftinguish it from the image of the fanie object) and the image fubtend equal angles at the eye.

407. DEM. Here we muft fuppofe the pupil of the eye to be a point only, because the magnitude of that caufes fmall alteration in the apparent magnitude of the object; as we fhall fee by and by. Let then the point a represent the pupil, then will the extreme rays that can enter it be Ha and Ka; the object therefore will appear under the angle Ha K, which is equal to its vertical one Mal, under which the image IM would appear were it to be feen from a. Again, if the eye be placed in f, the cbject appears under the angle GƒO equal to IfM, which the image fubtends at the fame place; and therefore the apparent object and image of it fubtend equal angles at the eye. Q. E. D. Now if we fuppofe the pupil to have any fenfible magnitude, fuch, fuppofe, that its diameter may be ab; then the object feen by the eye in that fituation will appear under the angle HXL, which is larger than the angle IIa K, under which it appeared before; becaufe the angle at X is nearer than the angle at a to the line IM, which is a fubtenfe common to them both. From this propofition it follows, that, were the eye close to the furface at K, the real and apparent object would be feen under equal angles (for the real object appears from that place under the fame angle that the image does, as will be shown at the end of this fection); therefore, when the eye is nearer to the image than that point, the image will fubtend a larger angle at it Ddd

8 inches; and ACB, the refracting angle of the prifm, whereby fo great a length was made, was 64°. With a lefs angle the length of the image was lefs, the breadth remaining the fame. It is farther to be obferved, that the rays went on in ftraight lines from the prifm to the image, and therefore, at their going out of the prifm, had all that inclination to one another from which the length of the image proceeded. This image PT was coloured, and the more eminent colours lay in this order from the bottom at T to the top at P; red, orange, yellow, green, blue, indigo, violet; together with all their intermediate degrees, in a continual fucceffion, perpetually varying."

411. Sir Ifaac concludes from this experiment, and many others, that the light of the fun confifts of a mixture of feveral forts of coloured rays, fome of which at equal incidences are more refracted than others, and therefore are called more refrangible. The red at T, being neareft to the place Y, where the rays of the fun would go direaly if the prifin was taken away, is the leaft refracted of all the rays; and the orange, yellow, green, blue, indigo, and violet, are continually more and more refracted, as they are more and more diverted from the course of the direct light. For by mathematical reafoning he has proved, that when the prifm is fixed in the pofture above mentioned, fo that the place of the image fhall be the loweft poffible, or at the limit between its defcent and afcent, the figure of the image ought then to be round like the fpot at Y, if all the rays that tended to it were equally refracted. Therefore, feeing by experience it is found that this image is not round, b, about five times longer than broad, it follows that all the rays are not equally refracted. And this conclufion is farther confirmed by the following experiments: "In the fan-beam SF (fig. 12. Plate CCLVI.), which was propagated into the room through the hole in the window-fhut EG, at the diftance of fome feet from the hole, I held the prifm ABC in fuch a posture, that its axis might be perpendicular to that beam; then I looked through the prifn upon the hole F, and turning the prifm to. and fro about its axis to make the image pt of the hole afcend and defcend, when between its two contrary motions it feemed ftationary, I flopped the prifm; in this fituation of the prifin, viewing through it the faid hole F, I obferved the length of its refracted image pt to be many times greater than its breadth; and that the most refracted part thereof appeared violet at p; the leaft retracted red, at t; and the middle parts indigo, blue, green, yellow, and orange, in order. The fame thing happened when I removed the prifm out of the fun's light, and looked through it upon the hole fhining by the light of the clouds beyond it. And yet if the refractions of all the rays were equal, according to one certain proportion of the fines of incidence and refraction, as is vulgarly fuppofed, the refracted image ought to have appeared round, by the mathematical demonftration above mentioned. So then, by thefe two experiments it appears, that in equal incidences there is a confiderable inequality of refractions.”

412. For the difcovery of this fundamental pro. perty of light, which has opened the whole myf

tery of colours, our author was not only beholden to the experiments themfelves which many others had made before him, but alfo to his skill in geometry; which was abfolutely neceflary to determine what the figure of the refracted image ought to be upon the old principle of an equal refraction of all the rays: but having thus made the difcovery, he contrived the following experiment to prove it at fight.

Then

413. "In the middle of two thin boards, DE, de, (fig. 13. Pl. CCLVI.) I made a round hole in each at G and g, a third part of an inch diameter; and in the window-fhut a much larger hole being made at. F, to let into my darkened chamber a large beam of the fun's light, I placed a prifm, ABC, behind the shut in that beam, to refract it towards the oppofite wall; and clofe behind this prifm I fixed one of the boards DE, in fuch a manner that the middle of the refracted light might pafs through the hole made in it at G, and the reft be intercepted by the board. Then at the distance of about 12 feet from the first board, I fixed the other board, de, in fuch a manner that the middle of the refracted light, which came through the hole in the first board, and fell upon the oppofite wall, might pass through the hole in this other board de, and the reft, being intercepted by the board, might paint upon it the coloured spectrum of the fun. And close behind this board fixed another prifm a bc, to refract the light which came through the hole I returned fpeedily to the firft prifm ABC, and by turning it flowly to and fro about its axis, I caufed the image which fell upon the 2d board de, to move up and down upon that board, that all its parts might pafs fucceffively through the hole in that board, and fall upon the prifm behind it. And in the mean time I noted the places, M, N, on the oppolite wall, to which that light, after its refraction in the 2d prifm, did país; and by the difference of the places at M and N, I found that the light, which, being moft refracted in the firft prifm ABC, did go to the blue end of the image, was again more refracted by the ad prifm a b c, than the light which went to the red end of that image. For when the lower part of the light which fell upon the 2d board de, was caft through the hole g, it went to a lower place M on the wall; and when the higher part of that light was caft through the fame hole g, it went to a higher place N on the wall; and when any intermediate part of the light was caft through that hole, it went to fome place in the wall between M and N. The unchanged pofition of the holes in the boards made the incidence of the rays upon the 2d prifm to be the fame in ail cafes. And yet in that common incidence fome of the rays were more refracted and others iets; and thofe were more refracted in this prim, which by a greater refraction in the firit prifin were more turned out of their way; and therefore, for their conftancy of being more refracted, are defervedly called more refrangible."

414. Our author thows alfo by experiments made with convex glafs, that lights (reflected from natural bodies) which differ in colour, differ alfo in degrees of refrangibility; and that they differ in the fame manner as the rays of the fun Ddd 2

do

do. The fun's light confifts of rays differing in reflexibility, and thofe rays are more reflexible than others which are more refrangible. A prifin, ABC, (g. 14. Pl. CCLVI.) whofe two angles, at its bafe BC, were equal to one another, and half right ones, and the third at A a right one, I placed in a beam FM of the fun's light, let into a dark chamber through a hole F, one third part of an inch broad. And turning the prifm flowly about its axis, until the light, which went through one of its angles ACB, and was refracted by it to G and H, began to be reflected into the line MN by its bafe BC, at which till then it went out of the glafs; I obferved that thofe rays, as MH, which had fuffered the greateft refraction, were fooner reflected than the reft. To make it evident that the rays which vanithed at H were reflected into the beam MN, I made this beam pafs through another prifm VXY, and being refracted by it, to fall afterwards upon a fheet of white paper pt placed at fome distance behind it, and there by that sefraction to paint the ufual colours at pt. Then caufing the firft prifm to be turned about its axis, according to the order of the letters ABC, I obferved, that when thofe rays MH, which in this prifm had fuffered the greateft refraction, and appeared blue and violet, began to be totally reflected, the blue and violet light on the paper which was most refracted in the fecond priim received a fenfible increase at p, above that of the red and yellow at ; and afterwards, when the reft of the light, which was green, yellow, and red, began to be totally reflected and vanifhed at G, the light of thofe colours at t, on the paper pt, received as great an increafe as the violet and blue had received before; which puts it paft difpute, that thofe rays became firft of all totally reflected at the bafe BC, which before, at equal incidences with the reft upon the bafe BC, had fuffered the greatest refraction. I do not here take notice of any refractions made in the fides AC, AB, of the first priim, becaufe the light enters almott perpendicularly at the first fide, and goes out almoft perpendicularly at the fecond; and therefore fufiers none, or fo little, that the angles of incidence at the bafe BC are not fenfibly altered by it; especially if the angles of the prifm at the bafe BC be each about 40°. For the rays FM begin to be totally reflected when the angle CMF is about 50°, and therefore they will then make a right angle of 90° with AC. It appears all from experiments, that the beam of light MN, reflected by the bafe of the prifm, being augmented, firft by the more refrangible rays, and afterwards by the lefs refrangible, is compofed of rays differently refrangible.

415."The light whofe rays are all alike refrangible, I call fimple, homogeneul and fimilar; and that whofe rays are fome more refrangible than others, I call compound, heterogeneal and diffimilar. The former light I call HOMOGENFAL, not because I would affirm it to in all refpects, but because the rays which agree in refrangibility agree at leaft in all their other properties which I confider in the following difcourfe. The colours of homogencal lights I call primary, homogensal, and fimple; and thofe of HETEROGENEAL lights, heterogeneal and compound. For these are always compounded of

And

homogeneal lights, as will appear in the following difcourfe. The homogeneal lights and rays which appear red, or rather make objects appear fo, I call rubrific or red making; those which make objects appear yellow, green, bine, and violet, I call yellow-making, green-making, bluemaking, violet-making; and fo of the reft. if at any time I fpeak of light and rays as coloured or endowed with colours, I would be understood to fpeak, not philofophically and properly, but grofsly, and according to fuch conceptions as vulgar people in fe ing all these experiments would be apt to frame. For the rays, to fpeak properly, are not coloured. In them there is nothing elfe than a certain power and difpofition to ftir up a fenfation of this or that colour. For as found, in a bell or musical ftring, or other founding body, is nothing but a trembling motion, and in the air nothing but that motion propagated from the object, and in the fenforium it is a ferfe of that motion under the form of found; fo co lours in the object are nothing but a difpofition to reflect this or that fort of rays more copiouliy than the reft: in rays the are nothing but their difpofitions to propagate this or that motion into the fenforium, and in the lenforium they are fenfations of thofe motions under the forms of colours." See CHROMATICS.

416. "By the mathematical propofition above mentioned, it is certain that the rays which are e qually refrangible do fall upon a circle anfwering to the fun's apparent difk,which will alfo be proved by experiment by and by. Now let AG (fig. 15. Pl. CCLVI.) reprefent the circle which all the most refrangible rays, propagated from the whole difk of the fun, would filuminate and paint upon the oppofite wall if they were alone; EL the circle, which all the leaft refrangible rays would in like manner illuminate if they were alone: BH, CI, DK, the circles which fo many intermediate forts would paint upon the wall, if they were fingly propagated from the fun in fucceffive order, the reft being intercepted; and conceive that their are other circles without number, which innume rable other intermediate forts of rays would fuc ceffively paint upon the wall, if the fun fould fucceffively emit every fort apart. And seeing the fun emits all thefe forts at once, they must all together illuminate and paint innumerable equal circles; of all which, being, according to their de grees of refrangibility, placed in order in a conti pual feries, that oblong fpectrum PT is compofed, which was defcribed in the firft experiment.

66

417. Now if thefe circles, whilft their centres keep their diftances and pofitions, could be made lets in diameter, their interfering one with another, and confequently the mixture of the be terogeneous rays, would be proportionably diminifhed. Let the circles AG, BH, CI, &c. remain as before; and let ag, bh, di, &c. be fo many lets circles lying in a like continual feries, between two parallel right lines a e and g 1, with the fame diftances between their centres, and illuminated with the fame forts of rays; that is, the circle a g with the fame fort by which the correfponding circle AG was illuminated; and the ref of the circ es bh, ci, dk, el, refpectively, with the famic forts of rays by which the correfponding circles