unlefs when the light fell very obliquely upon a fmooth paper, or some other smooth white body, fo as to make them appear much broader than they would otherwife have done; but in these circumftances, the colours were plainly vifible, and in the following order. The first or innermoft fringe was violet, and deep blue next the shadow, light-blue, green, and yellow in the middle, and red without. The 2d fringe was almoft contiguous to the firft, and the 3d to the 2d; and both were blue within, and yellow and red without; but their colours were very faint, especially thofe of the 3d. The colours, therefore, proceed ed in the following order from the fhadow; violet, indigo, pale blue, green, yellow, red; blue, yellow, red; pale blue, pale yellow, and red. The fhadows made by fcratches and bubbles in polished plates of glass, were bordered with the like fringes of coloured light. By looking on the fun through a feather, or black ribbon, held close to the eye, feveral rainbows will appear, the fhadows which the fibres or threads caft on the retina being bordered with the like fringes of colours. Measuring thefe fringes and their intervals with the greatest accuracy, he found the former to be in the progreffion of the numbers, 1, √},√}, and their intervals to be in the fame progreffion with them, that is, the fringes and their intervals together to be in continual progreffion of the numbers 1,3},√√√}, or thereabouts. And these proportions held the fame very nearly at all diftances from the hair, the dark intervals of the fringes being as broad in proportion to the breadth of the fringes at their firft appearance as afterwards, at great diftances from the hair, though not fo dark and distinct.

131. In Sir Ifaac's next obfervation, we find a very remarkable and curious appearance, pretty fimilar to the one noticed by Dr HOOKE, 121, 122. The fun fhining into his darkened chamber, through a hole of an inch broad, he placed, at the distance of 2 or 3 feet from the hole, a fheet of pafteboard, black on both fides; in the middle of it, he made a hole about of an inch fquare, for the light to pass through; behind the hole, he faftened to the pafteboard the blade of a fharp knife, to intercept some part of the light which paffed through the hole. The planes of the pafteboard and blade of the knife were parallel to one another, and perpendicular to the rays; and when they were fo placed that none of the light fell on the pafteboard, but all of it paffed through the hole to the knife, and there part of it fell upon the blade of the knife, and part of it paffed by its edge, he let that part of the light which paffed by, fall on a white paper, 2 or 3 feet beyond the knife, and there faw two ftreams of faint light fhoot out both ways from the beam of light into the fhadow, like the tails of comets. But because the fun's direct light, by its brightnefs upon the paper, obfcured thefe faint ftreams, fo that he could fearce fee them, he made a little hole in the midft of the paper for that light to pass through and fall on a black cloth behind it; and then he faw the two ftreams plainly. They were like one another, and pretty nearly equal in length, breadth, and quantity of light. Their light, at that end which was next to the fun's direct light, was pretty

ftrong for the space of about of an inch, or of an inch, and decreased gradually till it became. infenfible. The whole length of each of thefe streams, measured upon the paper, at 3 feet from the knife, was about 6 or 8 inches; fo that it fubtended an angle, at the edge of the knife, of about 10° or 12°, or at moft 14°. Yet fometimes he thought he faw it fhoot 3° or 4° farther; but with a light fo very faint, that he could hardly perceive it. This light he fufpected might, in part, arife from fome other caufe than the two ftreams. For, placing his eye in that light, beyond the end of that ftream which was behind the knife, and looking towards the knife, he could fee a line of light upon its edge; and that not only when his eye was in the line of the ftreams, but alfo when it was out of that line, either towards the point of the knife, or towards the handle. This line of light appeared contiguous to the edge of the knife, and was narrower than the light of the innermoft fringe, and narroweft when his eye was fartheft from the direct light; and therefore feemed to pafs between the light of that fringe and the edge of the knife; and that which paffed nearest the edge feemed to be moft bent, though not all of it. He then placed another knife by the former, so that their edges might be parallel, and look towards one another, and that the beam of light might fall upon both the knives, and fome part of it pafs between their edges. In this fituation he observed, that when the diftance of their edges was about the 400th part of an inch, the ftream divided in the middle, and left a fhadow between the two parts. This fhadow was fo black and dark, that all the light which paffed between the knives feemed to be bent and turned afide to the one hand or the other; and as the knives ftill approached one another, the fhadow grew broader, and the streams fhorter next to it, till upon the contact of the knives, all the light vanifhed.

132. From this experiment he concludes, that the light which is leaft bent, and which goes to the inward ends of the ftreams, paffes by the edges of the knives at the greatest distance; and this distance, when the fhadow began to appear between the ftreams, was about the 800th part of an inch; and the light which passed by the edges of the knives, at diftances ftill lefs and lefs, was more and more faint, and went to thofe parts of the ftreams which were farther from the direct light; becaufe, when the knives approached one another till they touched, thofe parts of the streams vanished laft which were fartheft from the direct light. In the experiment of one knife only, the coloured fringes did not appear; but, on account of the breadth of the hole in the window, became fo broad as to run into one another, and, by joining, to make one continued light in the beginning of the ftreams; but in the laft experiment, as the knives approached one another, a little before the fhadow appeared between the two freams, the fringes began to appear on the inner ends of the ftreams, on either fide of the direct light; 3 one fide, made by the edge of one knite, and 3 on the other fide, made by the edge of the other knife. They were moft diftin&t when the khospą were placed at the greateft diftance from 5hXle in the window, and became ftill more to by ma

on

way the ray fhould be bent, but that the other knife increased the bending.

king the hole lefs; fo that he could fometimes fee a faint trace of a 4th fringe beyond the 3 abovementioned: and as the knives approached one another, the fringes grew more diftinct and larger, till they vanished; the outermoft vanishing firft, and the innermoft laft. After they were all vanished, and the line of light which was in the middle between them was grown very broad, extending itself on both fides into the ftreams of light defcribed before, the above-mentioned fhadow began to appear in the middle of this light, and to divide it along the middle into two lines of light, and increased till all the light vanished. This enlargement of the fringes was fo great, that the rays which went to the innermoft fringe feemed to be bent about 20 times more when the fringe was ready to vanish, than when one of the knives was taken away.

133. From both thefe experiments compared together, Sir Ifaac concludes, that the light of the firft fringe paffed by the edge of the knife at a diftance greater than the 800th part of an inch; that the light of the 2d paffed by the edge of the knife at a greater distance than the light of the firft fringe, and that of the 3d at a greater diftance than that of the 2d; and that the light, of which the ftreams above-mentioned confifted, paffed by the edges of the knives at less distances than that of any of the fringes.

134. He then got the edges of two knives ground truly ftraight, and pricking their points into a board, fo that their edges might look towards one another, and, meeting near their points, contain a rectilinear angle, he fastened their handles toge ther, to make the angle invariable. The distance of the edges of the knives from one another, 4 inches from the angular point, where the edges of the knives met, was the 8th part of an inch; fo that the angle contained by their edges was about 1° 54'. The knives being thus fixed together, he placed them in a beam of the fun's light let into his darkened chamber, through a hole the 42d part of an inch wide, 10 or 13 feet from the hole; and he let the light which paffed between their edges fall very obliquely on a smooth white ruler, 4inch, or an inch, from the knives; and there he faw the fringes made by the two edges of the knives run along the edges of the fhadows of the knives, in lines parallel to thofe edges, without growing fenfibly broader, till they met in angles equal to the angle contained by the edges of the knives; and where they met and joined, they ended, without croffing one another. But if the ruler was held at a much greater diftance from the knives, the fringes, where they were farther from the place of their meeting, were a little parrower, and they became fomething broader as they approached nearer to one another, and after they met, they croffed one another, and then became much broader than before. From thefe obfervations he concluded, that the diftances at which the light compofing the fringes paffed by the knives, were not increafed or altered by the approach of the knives, but that the angles, in which the rays were there bent, were much increafed by that approach; and that the knife which was nearest to any ray, determined which

135. When the rays fell very obliquely upon the ruler, at the distance of a 3d part of an inch from the knives, the dark line between the first and 2d fringe of the shadow of one knife, and the dark line between the firft and ad fringe of the fhadow of the other knife, met one another, at the distance of the 5th part of an inch from the end of the light which paffed between the knives, where their edges met one another; so that the diftance of the edges of the knives, at the meeting of the dark lines, was the 160th part of an inch; and one half of that light paffed by the edge of one knife, at a diftance not greater than the 320th part of an inch, and, falling upon the paper, made the fringes or the fhadow of that knife; while the other half paffed by the edge of the other knife, at a distance not greater than the 320th part of an inch, and, falling upon the paper, made the fringes of the fhadow of the other knife. But if the paper was held at a distance from the knives greater than the 3d part of an inch, the dark lines above mentioned met at a greater distance than the 5th part of an inch from the end of the light which paffed between the knives, at the meeting of their edges; fo that the light which fell upon the paper where thofe dark lines met paffed between the knives, where their edges were farther diftant than the 60th part of an inch. For at another time, when the two knives were 8 feet and 5 inches from the little hole in the window, the light which fell upon the paper where the above-mentioned dark lines met paffed between the knives, where the distance between their edges was, as in the following table, at the distances from the paper there noted: 136. Diftances of the paper from the knives in inches.

Distances between the edges of the knives in millefimal parts of an inch.

0,012

0,020

0,034

0,057

0,081

0,087

138. From thefe obfervations he concluded, that the light which makes the fringes upon the paper is not the fame light at all diftances of the paper from the knives; but that, when the paper is held near the knives, the fringes are made by light which pafles by the edges of the knives at a less distance, and is more bent than when the paper is held at a greater diftance from the knives.

138. When the fringes of the fhadows of the knives fell perpendicularly upon the paper, at a great diftance from the knives, they were in the form of hyperbolas, their dimenfions being as follows. Let CA, CB, (fig. 2, pl. 250.) reprefent lines drawn upon the paper, parallel to the edges of the knives; and between which all the light would fall if it fuffered no inflection. DE is a right line drawn through C, making the angles ACD, BCE, equal to one another, and terminating all the light which falls upon the paper, from the point where the edges of the knives meet.

Then