and by means of the rays AI, the object will ap- particles of light. 2dly, It is not reflected at the pear alfo in its proper fituation A.

SECT. IV. Of the REFLECTION of Light. 359. WHEN a ray of light falls upon any body, however tranfparent, the whole of it never paffes through the body, but some part is always driven back or reflected from it; and it is by this reflected light that all bodies which have no light of their own become vifible to us. Of that part of the ray which enters, another part is alfo reflected from the second surface, or that which is fartheft from the luminous body. When this part arrives again at the first furface, part of it is reflected back from that surface; and thus it continues to be reflected between the two furfaces, and to pass backwards and forwards within the fubftance of the medium, till fome part is totally extinguished and lot. Befides this inconfiderable quantity, however, which is loft in this manner, the fecond furface often reflects much more than the firft; infomuch, that, in certain pofitions, fcarce any rays will pafs through both fides of the medium. A very confide: able quantity is alfo unaccountably loft or extinguished at each reflecting furface; info much, that no body, however tranfparent, can tranfmit all the rays which fall upon it; neither, though it be ever so well fitted for reflection, will it reflect them all.

$1. Of the CAUSE of REFLECTION. 360. THE reflection of light is by no means fo eafily accounted for as the refraction of the fame fluid. This laft may be accounted for in a fatisfactory manner, by the fuppofition of an attractive power diffufed throughout the medium, and extending a very little way beyond it; but with regard to the reflection of light, there feems to be no fatisfactory hypothefis hitherto invented. Of the principal opinions on this fubject, Mr RowNING hath given the following account.

361. I. It was the opinion of philofophers, before Sir Ifaac Newton difcovered the contrary, that light is reflected by impinging upon the folid parts of bodies. But that it is not fo, is clear for the following reafons: 1ft, It is not reflected at the firft furface of a body by impinging against it; for, in order to the due and regular reflection of light, that is, that the reflected rays should not be difperfed and scattered one from another; there ought to be no rafures or unevennefs in the reflecting furface large enough to bear a fenfible proportion to the magnitude of a ray of light; becaufe, if the furface abounds with fuch, the reflected rays will rather be scattered like a parcel of pebbles thrown upon a rough pavement, than reflected with that regularity with which light is obferved to be from a well-polifhed furface. Now thofe furfaces, which to our fenfes appear perfectly fmooth and well polifhed, are far from being fo; for to polish is no other than to grind off the larger eminences and protuberances of the metal with the rough and sharp particles of fand, emery, or putty, which muft of neceffity leave behind them an infinity of rafures and fcratches, which, though inconfiderable with regard to the former roughneffes, and too minute to be difcerned by us, must nevertheless bear a large proportion to, if not vaftly exceed, the magnitude of the

fecond furface by impinging against any folid particles. That it is not reflected by impinging upon the folid particles which constitute this fecond fu face, is fufficiently clear from the foregoing argument; the fecond furfaces of bodies being as incapable of a perfect polish as the first ; and it is farther confirmed from hence, viz. that the quantity of light reflected differs according to the different denfity of the medium behind the body; and that it is not reflected by impinging upon the particles which conftitute the turface of the medium behind it, is evident, because the strongest reflection of all, at the second surface of a body, is when there is a vacuum behind it.

362. II. It has been thought, that it is reflected at the firft furface of a body, by a repulfive force equally diffused over it; and at the fecond, by an attractive force. 1. If there be a repulfive force diffused over the furface of bodies that repels rays of light at all times, then, fince by increafing the obliquity of a ray we diminish its perpendicular force (which is that only whereby it must make its way through this repulfive force), however weakly that force may be supposed to act, rays of light may be made to fall with fo great a degree of obliquity on the reflecting surface, that there fhall be a total reflection of them there, and not one particle of light be able to make its way through, which is contrary to observation; the reflection of light at the first surface of a tranfparent body being never total to any obliquity whatever. The hypothefis therefore in this particular muft be falfe. 2. As to the reflection at the ad furface by the attractive force of the body, this may be confidered in two respects: ift, When it is total; ad, When it is partial. Ift, In cafes where the reflection is total, the caufe is undoubtedly that fame attractive force by which light would be refracted in paffing out of the fame body. This is manifeft from that analogy which is obfervable between the reflection of light at this fecond furface, and its refraction there. For otherwife, what can be the reason that the total reflection fhould begin just when the obliquity of the incident ray, at its arrival at the 20 furface, is fuch that the refracted angle ought to be a right one; or when the ray, were it not to return in reflection, ought to pass on parallel to the surface, without going from it? For in this cafe it is evident, that it ought to be returned by this very power, and in fuch manner, that the angle of reflection shall be equal to the angle of incidence. But, 2dly, as to the reflection at the fecond furface, when it is partial, an attractive force, uniformly fpread over it, can never be the cause thereof. Because it is inconceivable that the fame force, acting in the fame circumftances in every respect, can fometimes reflect the violet coloured rays, and tranfmit the red, and at other times reflect the red, and tranfmit the violet. But this objection is not valid; for in each colour, the reflection takes place at that angle, and no other, where the refraction of that ray would make it parallel to the pofterior furface.

363. This partial reflection and refraction is a great difficulty in all the attempts which have been made to give a mechanical explanation of

the

the phenomena of optics. It is equally a defide ratum in that explanation which was propofed y HUYGENS, and, fince his time revived by EULER, by means of the undulations of an elaftic fluid, although a vague confideration of undulatory motions feems to offer a very specious analogy. But a rigid application of such knowledge as we have acquired of fuch motions, will convince any unprejudiced mathematician, that the phenomena of undulation are effentially diffimilar to the phenomena of light. The inflection of light, and its refraction, equally demonftrate that light is acted on by moving forces in a direction perpendicular to the furface; and it is equally demonftrable that fuch forces muft, in proper circumftances, produce reflections precifely fuch as we obferve. The only difficulty is to show how there can be forces which produce both reflection and refraction, in circumftances which are fimilar. The fact is, that fuch effects are produced; the firft logical inference, is, that, with refpect to the light which is reflected, and that which is refracted, the circumstances are not fimilar; and our attention should be directed to the discovery of that diffimilarity. All the phenomena of combined reflection and refraction should be examined and claffed according to their generality, not doubting but that thefe points of refemblance will lead to the discovery of their causes. Now the experiments of Mr Bouguer show, that bodies differ extremely in their powers of thus feparating light by reflection and refraction, fome of them reflecting much more at a given angle than others. It is not therefore a general property of light to be partly reflected and partly retracted, but a distinctive property of different bodies: and fince we fee that they pofLeis it in different degrees, we are authorised to conclude that fome bodies may want it altogether. We may therefore expect fome fuccefs by confidering how bodies are affected by light, as well as how light is affected by bodies. Now, in ail the phenomena of the material world we find bodies connected by mutual forces. We know no cafe where a body A tends towards a body B, or, in common language, is attracted by it, without, at the fame time, the body B tending towards A. This is obferved in the phenomena of magnetitm, electricity, gravitation, corpuscular attraction, impuife, &c. We fhould therefore conclude from analogy, that as bodies change the motion of light, light alfo changes the motion of bodies; and that the particles near the furface are put into vibration by the paffage of light through among them.

364. It is clearly understood, that in all motions of vibration, such as the motions of pendulums, there is a moment when the body is in its natural fituation, as when the pendulum is in the vertical line. This may happen in the fame inftant in each atom of the tranfparent body. The particles of light which then come within the fphere of action may be wholly reflected; in the next moment, particles of light in the very fituation of the firft may be refracted. Then will arife a feparation of light; and as this will depend on the manner in which the particles of bodies are agitated by it during its paffage, and as this again will depend on the nature of the body, that is on the law of VOL. XVI. PART II.

action of thofe forces which connect the particles with each other, and with the particles of light, it will be different in different bodies. But in all bodies there will be this general resemblance, that the feparation will be moft copious in great obliquities of incidence, which gives the repulfive forces more time for action, while it diminishes the perpendicular force of the light. Such a refemblance between the phenomena and the legiti mate confequences of the affumption, (the agitation of the parts of the body), gives us fome authority for affigning this as the caufe; nor can the affumption be called gratuitous. To fuppofe that the particles of the tranfparent body are not thus agitated, would be a moft gratuitous contradiction of a law of nature to which we know no other exception. Thus the objection raised in § 255. is obviated, because the reflect on and refraction are not here conceived as fimultaneous, but as exceffive.

365. III. Some, being apprehenfive of the infufficiency of a repulfive and attractive force diffused over the furfaces of bodies, and acting uniformly, have fuppofed, that, by the action of light upon the furface of bodies, the matter of these bodies is put into an undulatory motion; and that where the furface of it is fubfiding, light is tranfmitted, and in those places where it is rifing, light is reflected. But to overlook the objections which we have just made to this theory of undulation, we have only to obferve, that, were it admitted, it seems not to advance us one jot farther; for in thofe cafes, fuppofe where red is reflected, and violet tranfmitted, how comes it to pass that the red impinges only on those parts when the waves are riling, and the violet when they are fubfiding?

366. IV. The next hypothefis to be taken notice of, is that remarkable one of Sir Ifaac Newton's, fits of eafy refl Aion and tranfmiffion, which we shall now explain and examine That author is of opinion, that light, in its paffage from the luminous body, is difpofed to be alternately reflected by and tranfmitted through any refracting furface it may meet with; that thefe difpofitions (which he calls fits of eafy reflection and easy transmission) return fucceffively at equal intervals; and that they are communicated to it at its first emiffion out of the luminous body it proceeds from, probably by some very fubtile and elastic substance diffused through the univerfe, in the following manner: As bodies falling into water, or paffing through the air, caufe undulations in each, fo the rays of light may excite vibrations in this elastic fubftance; the quickness of which vibrations depending on the elafticity of the medium, (as the quickness of the vibrations in the air, which propagate found, depend folely on the elafticity of the air, and not upon the quickness of thofe in the founding body), the motion of the particles of it may be quicker than that of the rays; and therefore, when a ray, at the inftant it impinges upon any furface, is in that part of a vibration of this elastic fubftance which confpires with its motion, it may be eafily tranfmitted; and when it is in that part of a vibration which is contrary to its motion, it may be reflected. He farther luppoles, that when light falls upon the furface of a body, Gcc

if

fituated in the fame plane; confequently the reflected rays will have the fame degree of inclination to each other that their incident ones have, from whatever part of the furface they are reflected.

370. II. Parallel rays reflected from a concave furface are rendered converging.-To illuftrate this, let AF. CD, EB, (fig. 6. Pl. CCLV.) reprefent 3 parallel rays falling upon the concave furface FB, whose centre is C. To the points F and B draw the lines CF, CB; thefe, being drawn from the centre, will be perpendicular to the furface at those points. The incident ray CD, alfo paffing through the centre, will be per peadicular to the surface, and therefore will return after reflection in the fame line; but the oblique rays AF and EB will be reflected into the lines FM and BM, fituated on the contrary fide of their respective perpendiculars CF and CB. They will therefore proceed converging, after reflection towards fome point, as M, in the line CD.

if it be not in a fit of eafy tranfmiffion, every ray is there put into one, fo that when they come at the other fide, (for this elaftic fubftance, easily pervading the pores of bodies, is capable of the fame vibrations within the body as without it), the rays of one colour fhall be in a fit of easy tranfmiffion, and thofe of another in a fit of eafy reflection, according to the thickness of the body, the intervals of the fits being different in rays of a different kind. This feems to account for the different colours of the bubble and thin plate of air and water, as is obvious, and likewife for the reflection of light at the fecond surface of a thick er body; for the light reflected from thence is alfo obferved to be coloured, and to form rings according to the different thickness of the body, when not intermixed and confounded with other light, as will appear from the following experiment. If a piece of glafs be ground concave on, one fide, and convex on the other, both its concavity and convexity having one common centre; and if a ray of light be made to pass through a fmall hole in a piece of paper held in that common centre, and be permitted to fall on the glafs; befides those rays which are regularly reflected back to the hole again, there will be others reflect ed to the paper, and form coloured rings furrounding the hole, not unlike thofe occafioned by the reflection of light from thin plates.

367. It is with reluctance, that we venture to call in queftion any doctrine of Newton; but to his theory of reflection there is this infuperable objection, that it explains nothing, unless the cause of the fits of more eafy reflection and tranfmiffion be held as legitimate; namely, that they are produced by the undulations of another elaftic fluid, incomparably more fubtile than light, acting upon it in the way of impulfe. The fits themselves are matters of fact, and no way different from what we have endeavoured to account for; but to admit this theory of them, would be to tranfgrefs every rule of philofophizing, as we have shown them to be fufceptible of explanation from acknowledged optical laws.

$2. Of the Laws of REFLECTION. 368. THE fundamental law of the reflection of light, is, that in all cafes the angle of reflection is equal to the angle of incidence. This is found by experiment to be the cafe, and, befides, may be demonftrated mathematically from the laws of percuffion in bodies perfectly elaftic. The axiom therefore holds good in every cafe of reflection, whether it be from plane furfaces or fpherical ones, and whether they are convex or concave; and hence the 7 following propofitions, relating to the reflection of light from plane and fpherical furfaces, may be deduced:

369. I. Rays of light reflected from a plane furface have the fame degree of inclination to one another that their refpective incident ones have.For the angle of reflection of each ray being equal to that of its refpective incident one, it is evident, that each reflected ray will have the fame degree of inclination to that portion of the furface from whence it is reflected, that its incident one has: but it is here fuppofed, that all those portions of fatface from whence the rays are reflected, are

571. III. Converging rays, falling on the like furface, are made to converge more.-For, every thing remaining as above, let GF, HB, be the incident rays. Now, because these rays have larger angles of incidence than the parallel ones AF and EB in the foregoing cafe, their angles of reflection will alfo be larger than thofe of the others; they will therefore couverge after reflection, suppofe in the lines FN and BN, having their point of concourse N farther from the point C than M, that to which the parallel rays AF and EB converged in the foregoing cafe; and their precise degree of convergency will be greater than that wherein they converged before reflection.

furface, are, after reflection, parallel, diverging, 372. IV. Diverging rays falling upon the like of parallel rays, they then become parallel; if or converging. If they diverge from the focus from a point nearer to the furface than that, they will diverge, but in a lefs degree than before reflection; if from a point between that and the centre, they will converge after reflection, and that to fome point on the contrary fide of the centre, but fituated farther from it than the point from which they diverged. If the incident rays diverge from a point beyond the centre, the reflected ones will converge to one on the other fide of it, but nearer to it than the point they diverged from; and if they diverge from the centre, they will be reflected thither again. 1. Let them diverge in the lines MF, MB, proceeding from M, the focus of parallel rays; then, as the parallel rays AF and EB were reflected into the lines FM and BM (by Prop. II.), these rays will now on the contrary be reflected into them. 2. furface than the focus of parallel rays, they will Let them diverge from N, a point nearer to the then be reflected into the diverging lines FG and BH, which the incident rays GF and HB defcrib ed, that were fhewn to be reflected into them in the foregoing propofition; but the degree wherein they diverge will be lefs than that wherein they diverged before reflection. 3. Let them proceed diverging from X, a point between the focus of parallel rays and the centre; they then make less angles of incidence than the rays MF and MB,