incident light? Why does not the reflected beam, in fuch circumftances, begin to affume a blue and greenish tinge, while the tranfmitted beam is tinged with red and orange? Such ought undoubtedly to be the fact, if reflexibility was altogether unconnected with refrangibility; for the rays are here fuppofed to fall on a fubftance capable either of reflecting or tranfmitting them; and the anterior furface of the glafs always reflects a great portion of the incident light, while the reft paffes through; but all the constituent parts of those portions, their red rays as well as their violet rays, are uniformly affected in the very fame manner at all angles of incidence. Thus then we fee that reflexion alone is not fufficient to produce the phenomenon in queftion. Is every kind of refraction, when coupled with reflexion, fufficient for this purpofe? Certainly not. Let a beam of white light fall on a glafs paralellipiped, and be tranfmitted, as it will be without feparation, to the oppofite fide: Let the paralellipiped be inclined to the incident light until the angle of incidence is as great as poffible. Through all the ftages of this inclination white light alone will be reflected-no decompofition takes place-no prevalence of reflexibility is perceived in the violet or blue rays; they are all equally reflected-all equally tranfmitted. It remains, therefore, to explain what is the fpecific nature of this different reflexibility, which only makes its appearance in company with refraction, and not in conjunction with every fort of refraction, but only with that kind which of itself separates the heterogeneous rays. Until this very fufpicious circumstance can be fatisfactorily accounted for, we should difobey thofe rules of inductive reasoning which our great mafter himself has taught us, both by his precept and his example, were we to give our unqualified affent to his doctrine of various reflexibility.

Profeffor Venturi concludes this part of his fpeculations with an attempt to fhow that there is nothing inconfiftent in these rays being leaft reflexible which he admits are most deflexible. That there is any thing inconfiftent in this, it would be absurd to affert; but he attempts to demonftrate fome connexion between the greater deflexibility and the lefs reflexibility of the red rays, and fo forth, in order to conclude that nature is confiftent in her operations. We think his failure is as complete as his attempt was unneceffary; and inftead of troubling our readers to follow his very vague reafonings on this matter, the only exceptionable thing which we find in his work, we shall content ourfelves with obferving that he has entirely overlooked the greater inflexibility of the lefs refrangible rays; a property proved to belong to them by the very fame experiments whereby the

greater deflexibility was difcovered. This property at once deftroys every part of Profeffor Venturi's argument.

We shall conclude this branch of the fubject by laying before our readers a theory, which we think warranted by the phenomena, and fufficient to explain the different appearances exhibited by thofe fingular experiments on thin plates, which compose the fecond book of the Optics. It is recommended by its fimplicity, and is in fome degree authorised by the ideas partially unfolded in that immortal work. Various incidental obfervations, fcattered over the concluding fpeculations of Sir Ifaac Newton, fuggeft the remark, that one experiment only upon the phenomena of Flexion was wanting to have made him draw the inferences which we are now about to fubmit.

When light falls upon thin plates, whofe thicknefs gradually increases within certain narrow limits, and is tranfmitted through them, it is formed into fringes or rings with dark intervals and of regularly increafing fizes. When the light is homogeneous, the fringes are of the fingle colour that falls on the plates, but larger in proportion as that light is of a lefs refrangible colour. When the light is heterogeneous, it is feparated into its component parts in the act of forming the fringes, and the fringes are coloured variously accordingly. To the dark intervals, feen by this tranfmiffion, correfpond fringes, when the plates are viewed by reflected light; and to the fringes feen by tranfmiffion, correfpond dark intervals by reflexion. It is clear, therefore, that the incident light is alternately reflected and tranfmitted; reflected at certain thickneffes of the plate, tranfmitted at others; and always decompounded, if heterogeneous, both by the reflexion and the tranfmiflion.

When light paffes by the edge of a body, at distances gradu- · ally increafing, within certain narrow limits, it is formed into fringes exactly refembling thofe above defcribed. They are parallel to the edge of the body; uniformly coloured, if the light was homogeneous, and larger in proportion as the colour is of a lefs refrangible kind. They are of different colours if the light was heterogeneous, and the colours are difpofed in the fame order of fuccellion as in the former cafe. Thefe fringes are of two kinds; they are either formed by inflexion or by deflexion. The former have their colours arranged like the rings formed by tranfmiffion in thin plates; the latter have their colours arranged like the rings produced by the reflexion of thin plates. Moreover, the dark intervals, and their fucceflion, as well as the fucceffion of the fringes, correfpond exactly in both cafes. As the thinneft plate makes the broadeft ring, fo the largest fringe is that

which

which is formed by light paffing nearest the body, and the largest of the dark intervals is the one neareft the largeft fringe. It only remains to remark, that the two cafes refemble each other in the circumstance of number. It was long imagined that the fringes, by flexion were only threefold, becaufe three only are difcoverable by the naked eye. This appearance thus got the name of the three fringes from the time of Grimaldi, the first obferver of it. But it is now well known that they are as numerous as the fringes or rings of thin plates; that, by fimple experiments with the prifm, they may be feen extending one after another to a great diftance, with their dark intervals; and that they always decrease as the distance from the bending body increases. This one obfervation only feems to have been wanting to make Sir Ifaac Newton admit the following pofitions. He uniformly calls the colours by flexion the three fringes' in the Optics; and the tres fimbria" in the Principia.'

When the rays of light fall on the inferior furface of the lens or other convex glafs which forms the thin plate, they come within the fphere of action of the fuperior furface of the other glafs or body which forms the plate. That body muft, therefore, exert upon the rays at fuch fmall diftances, the fame force which it would exert upon the rays were they to pafs by it at equal diftances. If the rays paffed at a certain diftance, we have feen that they would be deflected; if at another distance, inflected, and fo on in fucceffion alternatively; or, which is the fame thing, at one fet of diftances they would be repelled, at another fet of diftances they would be attracted by the bending body. But it can make no difference either on the power of the body to attract and repel, or upon the capacity of the rays to be acted upon, whether the line of their direction paffes by the body without touching it, or falls upon the body, and if produced, paffes through it. The fame power of flexion must equally be exerted in both cafes, and produce the fame effects. When, therefore, the light falls on the inferior furface of the upper glafs, and is about to emerge, it is either attracted or repelled by the other glafs, which exerts a force in lines perpendicular to its furface. If the light is incident at certain parts of the upper glafs, that is, at certain diftances from the inferior glafs, it will be repelled; if at certain other parts or diftances, it will be attracted. In either cafe, it will be formed into fringes or rings, of different colours if the incident beam was heterogeneous,

* Phil. Tranf. 1797, Part II. Prof. Venturi, who frequently quotes Mr Brougham's paper in Phil. Tranf. 1796, Part I. does not appear to have feen his fecond paper.

heterogeneous, and of the fame colour if it was homogeneous. To the spaces where the light was repelled, or deflected and reflected, will correfpond, below the glaffes, dark intervals; to the fpaces where the light was attracted, or inflected and tranfmitted, will correfpond dark intervals above the glaffes, and rings below. The thickness of the plate of air between the glaffes, or of the plate of water in the cafe of the foap bubble, is only another expreffion for the diftance of the bending body from the rays on which it acts. At alternate diftances its action is oppofite; and as the diftances increase, that action, whether attractive or repulfive, diminishes. At alternate thicknesses of the plates, the distances of the rays from the bending body are alternate, and the action of the body confequently oppofite; and as the thickness of the plate increases, the diftance augments, and the action, of whatever kind, is weakened. It is now very generally admitted, that the rays differ in flexibility, and that this quality difpofes them in fringes, which, when accurately examined, are found to be fpectra of the radiant body, dilated by flexion. It is alfo allowed that they differ in another quality, viz. in their capacity of being acted upon by the bending body at the fame diftance; and that this quality difpofes them in fringes or spectra of various fizes or degrees of dilatation. Hence all the phenomena of thin plates are easily refolv able into thofe of flexion, and the whole claffified according to one fimple and general law.

*

It is worth while here to remark, that if the action of bodies upon light regularly decreafes as the diftance increafes, or inverfely according to any power whatever of that distance; and if this action is at the fame time alternate at different definite intervals of the distance, and if we attempt to exhibit this action by a curve, whofe ordinates exprefs the force, alternately attractive and repulfive, while its abfciffe reprefent the diftances, we fhall find one of those paradoxes which frequently occur in the higher geometry, and which feem like interruptions in the great law of continuity. The curve will not be regularly progreffive and continuous; it will confift of feparate portions, going on diminishing in convexity, but following each other per faltum, on the oppofite fides of the axis; and this, whether the force diminishes as the fquare or cube, or whatever power of the diftance. Such a result in the theory of curve lines always leads us to conclude, that we have found an arch or portion of a line poffeffed of properties that do not belong to the rest of it, (a circumftance, by the way, not remarked by writers on this fub

*Phil. Tranf. 1796. pt. 1.

ject.)

† Phil. Trans. 1797. pt. 2.

ject.) But it is not altogether fo evident how we are to account for this interruption in the prefent cafe. Poffibly the law of continuity is not broken, and our data are erroneous; that is, we ought not to affume that the force exerted by bodies on light decreases regularly as any power of the distance, but that, in fucceffive intervals, this force becomes, on the whole, lefs and lefs, and alternately acts in oppofite directions, but, during each particular space of action, it first increases and then diminishes. This is the only way in which it is poffible to conceive the law of continuity preferved, and the action of bodies on light at the fame time alternate. The force will then be expreffed by a curve whofe axis is perpendicular to the bending body, and which cuts the axis repeatedly, receding from it alternately on oppofite fides, and always receding lefs and lefs as the axis increases, till it tends at laft to unite with the axis itself. Such a curve has not yet, we believe, been confidered: it is evidently not algebraical; it has an infinite number of arches conftantly diminishing in convexity, but not neceffarily decreasing in the length of their greatest diameters; and it approaches to its axis, not as to an affymptote, for it conftantly croffes it, but in another way not hitherto defcribed: it tends to coincide with the axis, and comes nearer to it than any affignable distance; yet, ftill, it cuts and croffes it again; fo that its oppofite arches are conftantly approaching nearer and nearer the axis, without ever meeting it.

If any one fhould think that fuch inferences are proofs that the theory above sketched is defective, it may be proper for him to reflect, that the explanation of the colours of lenfes and foap bubbles by the theory of thin plates is liable to fimilar objections. If we attempt to exprefs that theory by a curve, whofe abfciffe denotes the thickneis of the plate, and whofe ordinates denote the reflective and tranfmiffive powers alternately, we have a curve of the fame kind. It is fcarce neceflary to add, that, according to whatever power of the diftance (or thickness) thofe actions (whether of flexion or of reflexion and tranfmiflion) decrease, the curves in question approach a line drawn at right angles to the axis as an affymptote; a conclufion fupported by the theory, now univerfally received, which denies the existence of any perfect contact.

These confiderations deferve at least to be difcuffed. We offer them as approximations to the knowledge of the general law. The propofition now enunciated is not unauthorised by the facts already established, and farther induction may confirm it as the legitimate mode of claffifying all these curious and obfcure phenomena. Our purpofe will be ferved if they excite this invefti

gation,