Part 18

_Obs._ 1. The Sun shining into my darken'd Chamber through a hole one third of an Inch wide, I let the intromitted beam of Light fall perpendicularly upon a Glass Speculum ground concave on one side and convex on the other, to a Sphere of five Feet and eleven Inches Radius, and Quick-silver'd over on the convex side. And holding a white opake Chart, or a Quire of Paper at the center of the Spheres to which the Speculum was ground, that is, at the distance of about five Feet and eleven Inches from the Speculum, in such manner, that the beam of Light might pass through a little hole made in the middle of the Chart to the Speculum, and thence be reflected back to the same hole: I observed upon the Chart four or five concentric Irises or Rings of Colours, like Rain-bows, encompassing the hole much after the manner that those, which in the fourth and following Observations of the first part of this Book appear'd between the Object-glasses, encompassed the black Spot, but yet larger and fainter than those. These Rings as they grew larger and larger became diluter and fainter, so that the fifth was scarce visible. Yet sometimes, when the Sun shone very clear, there appear'd faint Lineaments of a sixth and seventh. If the distance of the Chart from the Speculum was much greater or much less than that of six Feet, the Rings became dilute and vanish'd. And if the distance of the Speculum from the Window was much greater than that of six Feet, the reflected beam of Light would be so broad at the distance of six Feet from the Speculum where the Rings appear'd, as to obscure one or two of the innermost Rings. And therefore I usually placed the Speculum at about six Feet from the Window; so that its Focus might there fall in with the center of its concavity at the Rings upon the Chart. And this Posture is always to be understood in the following Observations where no other is express'd.

_Obs._ 2. The Colours of these Rain-bows succeeded one another from the center outwards, in the same form and order with those which were made in the ninth Observation of the first Part of this Book by Light not reflected, but transmitted through the two Object-glasses. For, first, there was in their common center a white round Spot of faint Light, something broader than the reflected beam of Light, which beam sometimes fell upon the middle of the Spot, and sometimes by a little inclination of the Speculum receded from the middle, and left the Spot white to the center.

This white Spot was immediately encompassed with a dark grey or russet, and that dark grey with the Colours of the first Iris; which Colours on the inside next the dark grey were a little violet and indigo, and next to that a blue, which on the outside grew pale, and then succeeded a little greenish yellow, and after that a brighter yellow, and then on the outward edge of the Iris a red which on the outside inclined to purple.

This Iris was immediately encompassed with a second, whose Colours were in order from the inside outwards, purple, blue, green, yellow, light red, a red mix'd with purple.

Then immediately follow'd the Colours of the third Iris, which were in order outwards a green inclining to purple, a good green, and a red more bright than that of the former Iris.

The fourth and fifth Iris seem'd of a bluish green within, and red without, but so faintly that it was difficult to discern the Colours.

_Obs._ 3. Measuring the Diameters of these Rings upon the Chart as accurately as I could, I found them also in the same proportion to one another with the Rings made by Light transmitted through the two Object-glasses. For the Diameters of the four first of the bright Rings measured between the brightest parts of their Orbits, at the distance of six Feet from the Speculum were 1-11/16, 2-3/8, 2-11/12, 3-3/8 Inches, whose Squares are in arithmetical progression of the numbers 1, 2, 3, 4. If the white circular Spot in the middle be reckon'd amongst the Rings, and its central Light, where it seems to be most luminous, be put equipollent to an infinitely little Ring; the Squares of the Diameters of the Rings will be in the progression 0, 1, 2, 3, 4, &c. I measured also the Diameters of the dark Circles between these luminous ones, and found their Squares in the progression of the numbers 1/2, 1-1/2, 2-1/2, 3-1/2, &c. the Diameters of the first four at the distance of six Feet from the Speculum, being 1-3/16, 2-1/16, 2-2/3, 3-3/20 Inches. If the distance of the Chart from the Speculum was increased or diminished, the Diameters of the Circles were increased or diminished proportionally.

_Obs._ 4. By the analogy between these Rings and those described in the Observations of the first Part of this Book, I suspected that there were many more of them which spread into one another, and by interfering mix'd their Colours, and diluted one another so that they could not be seen apart. I viewed them therefore through a Prism, as I did those in the 24th Observation of the first Part of this Book. And when the Prism was so placed as by refracting the Light of their mix'd Colours to separate them, and distinguish the Rings from one another, as it did those in that Observation, I could then see them distincter than before, and easily number eight or nine of them, and sometimes twelve or thirteen. And had not their Light been so very faint, I question not but that I might have seen many more.

_Obs._ 5. Placing a Prism at the Window to refract the intromitted beam of Light, and cast the oblong Spectrum of Colours on the Speculum: I covered the Speculum with a black Paper which had in the middle of it a hole to let any one of the Colours pass through to the Speculum, whilst the rest were intercepted by the Paper. And now I found Rings of that Colour only which fell upon the Speculum. If the Speculum was illuminated with red, the Rings were totally red with dark Intervals, if with blue they were totally blue, and so of the other Colours. And when they were illuminated with any one Colour, the Squares of their Diameters measured between their most luminous Parts, were in the arithmetical Progression of the Numbers, 0, 1, 2, 3, 4 and the Squares of the Diameters of their dark Intervals in the Progression of the intermediate Numbers 1/2, 1-1/2, 2-1/2, 3-1/2. But if the Colour was varied, they varied their Magnitude. In the red they were largest, in the indigo and violet least, and in the intermediate Colours yellow, green, and blue, they were of several intermediate Bignesses answering to the Colour, that is, greater in yellow than in green, and greater in green than in blue. And hence I knew, that when the Speculum was illuminated with white Light, the red and yellow on the outside of the Rings were produced by the least refrangible Rays, and the blue and violet by the most refrangible, and that the Colours of each Ring spread into the Colours of the neighbouring Rings on either side, after the manner explain'd in the first and second Part of this Book, and by mixing diluted one another so that they could not be distinguish'd, unless near the Center where they were least mix'd. For in this Observation I could see the Rings more distinctly, and to a greater Number than before, being able in the yellow Light to number eight or nine of them, besides a faint shadow of a tenth. To satisfy my self how much the Colours of the several Rings spread into one another, I measured the Diameters of the second and third Rings, and found them when made by the Confine of the red and orange to be to the same Diameters when made by the Confine of blue and indigo, as 9 to 8, or thereabouts. For it was hard to determine this Proportion accurately. Also the Circles made successively by the red, yellow, and green, differ'd more from one another than those made successively by the green, blue, and indigo. For the Circle made by the violet was too dark to be seen. To carry on the Computation, let us therefore suppose that the Differences of the Diameters of the Circles made by the outmost red, the Confine of red and orange, the Confine of orange and yellow, the Confine of yellow and green, the Confine of green and blue, the Confine of blue and indigo, the Confine of indigo and violet, and outmost violet, are in proportion as the Differences of the Lengths of a Monochord which sound the Tones in an Eight; _sol_, _la_, _fa_, _sol_, _la_, _mi_, _fa_, _sol_, that is, as the Numbers 1/9, 1/18, 1/12, 1/12, 2/27, 1/27, 1/18. And if the Diameter of the Circle made by the Confine of red and orange be 9A, and that of the Circle made by the Confine of blue and indigo be 8A as above; their difference 9A-8A will be to the difference of the Diameters of the Circles made by the outmost red, and by the Confine of red and orange, as 1/18 + 1/12 + 1/12 + 2/27 to 1/9, that is as 8/27 to 1/9, or 8 to 3, and to the difference of the Circles made by the outmost violet, and by the Confine of blue and indigo, as 1/18 + 1/12 + 1/12 + 2/27 to 1/27 + 1/18, that is, as 8/27 to 5/54, or as 16 to 5. And therefore these differences will be 3/8A and 5/16A. Add the first to 9A and subduct the last from 8A, and you will have the Diameters of the Circles made by the least and most refrangible Rays 75/8A and ((61-1/2)/8)A. These diameters are therefore to one another as 75 to 61-1/2 or 50 to 41, and their Squares as 2500 to 1681, that is, as 3 to 2 very nearly. Which proportion differs not much from the proportion of the Diameters of the Circles made by the outmost red and outmost violet, in the 13th Observation of the first part of this Book.

_Obs._ 6. Placing my Eye where these Rings appear'd plainest, I saw the Speculum tinged all over with Waves of Colours, (red, yellow, green, blue;) like those which in the Observations of the first part of this Book appeared between the Object-glasses, and upon Bubbles of Water, but much larger. And after the manner of those, they were of various magnitudes in various Positions of the Eye, swelling and shrinking as I moved my Eye this way and that way. They were formed like Arcs of concentrick Circles, as those were; and when my Eye was over against the center of the concavity of the Speculum, (that is, 5 Feet and 10 Inches distant from the Speculum,) their common center was in a right Line with that center of concavity, and with the hole in the Window. But in other postures of my Eye their center had other positions. They appear'd by the Light of the Clouds propagated to the Speculum through the hole in the Window; and when the Sun shone through that hole upon the Speculum, his Light upon it was of the Colour of the Ring whereon it fell, but by its splendor obscured the Rings made by the Light of the Clouds, unless when the Speculum was removed to a great distance from the Window, so that his Light upon it might be broad and faint. By varying the position of my Eye, and moving it nearer to or farther from the direct beam of the Sun's Light, the Colour of the Sun's reflected Light constantly varied upon the Speculum, as it did upon my Eye, the same Colour always appearing to a Bystander upon my Eye which to me appear'd upon the Speculum. And thence I knew that the Rings of Colours upon the Chart were made by these reflected Colours, propagated thither from the Speculum in several Angles, and that their production depended not upon the termination of Light and Shadow.

_Obs._ 7. By the Analogy of all these Phaenomena with those of the like Rings of Colours described in the first part of this Book, it seemed to me that these Colours were produced by this thick Plate of Glass, much after the manner that those were produced by very thin Plates. For, upon trial, I found that if the Quick-silver were rubb'd off from the backside of the Speculum, the Glass alone would cause the same Rings of Colours, but much more faint than before; and therefore the Phaenomenon depends not upon the Quick-silver, unless so far as the Quick-silver by increasing the Reflexion of the backside of the Glass increases the Light of the Rings of Colours. I found also that a Speculum of Metal without Glass made some Years since for optical uses, and very well wrought, produced none of those Rings; and thence I understood that these Rings arise not from one specular Surface alone, but depend upon the two Surfaces of the Plate of Glass whereof the Speculum was made, and upon the thickness of the Glass between them. For as in the 7th and 19th Observations of the first part of this Book a thin Plate of Air, Water, or Glass of an even thickness appeared of one Colour when the Rays were perpendicular to it, of another when they were a little oblique, of another when more oblique, of another when still more oblique, and so on; so here, in the sixth Observation, the Light which emerged out of the Glass in several Obliquities, made the Glass appear of several Colours, and being propagated in those Obliquities to the Chart, there painted Rings of those Colours. And as the reason why a thin Plate appeared of several Colours in several Obliquities of the Rays, was, that the Rays of one and the same sort are reflected by the thin Plate at one obliquity and transmitted at another, and those of other sorts transmitted where these are reflected, and reflected where these are transmitted: So the reason why the thick Plate of Glass whereof the Speculum was made did appear of various Colours in various Obliquities, and in those Obliquities propagated those Colours to the Chart, was, that the Rays of one and the same sort did at one Obliquity emerge out of the Glass, at another did not emerge, but were reflected back towards the Quick-silver by the hither Surface of the Glass, and accordingly as the Obliquity became greater and greater, emerged and were reflected alternately for many Successions; and that in one and the same Obliquity the Rays of one sort were reflected, and those of another transmitted. This is manifest by the fifth Observation of this part of this Book. For in that Observation, when the Speculum was illuminated by any one of the prismatick Colours, that Light made many Rings of the same Colour upon the Chart with dark Intervals, and therefore at its emergence out of the Speculum was alternately transmitted and not transmitted from the Speculum to the Chart for many Successions, according to the various Obliquities of its Emergence. And when the Colour cast on the Speculum by the Prism was varied, the Rings became of the Colour cast on it, and varied their bigness with their Colour, and therefore the Light was now alternately transmitted and not transmitted from the Speculum to the Chart at other Obliquities than before. It seemed to me therefore that these Rings were of one and the same original with those of thin Plates, but yet with this difference, that those of thin Plates are made by the alternate Reflexions and Transmissions of the Rays at the second Surface of the Plate, after one passage through it; but here the Rays go twice through the Plate before they are alternately reflected and transmitted. First, they go through it from the first Surface to the Quick-silver, and then return through it from the Quick-silver to the first Surface, and there are either transmitted to the Chart or reflected back to the Quick-silver, accordingly as they are in their Fits of easy Reflexion or Transmission when they arrive at that Surface. For the Intervals of the Fits of the Rays which fall perpendicularly on the Speculum, and are reflected back in the same perpendicular Lines, by reason of the equality of these Angles and Lines, are of the same length and number within the Glass after Reflexion as before, by the 19th Proposition of the third part of this Book. And therefore since all the Rays that enter through the first Surface are in their Fits of easy Transmission at their entrance, and as many of these as are reflected by the second are in their Fits of easy Reflexion there, all these must be again in their Fits of easy Transmission at their return to the first, and by consequence there go out of the Glass to the Chart, and form upon it the white Spot of Light in the center of the Rings. For the reason holds good in all sorts of Rays, and therefore all sorts must go out promiscuously to that Spot, and by their mixture cause it to be white. But the Intervals of the Fits of those Rays which are reflected more obliquely than they enter, must be greater after Reflexion than before, by the 15th and 20th Propositions. And thence it may happen that the Rays at their return to the first Surface, may in certain Obliquities be in Fits of easy Reflexion, and return back to the Quick-silver, and in other intermediate Obliquities be again in Fits of easy Transmission, and so go out to the Chart, and paint on it the Rings of Colours about the white Spot. And because the Intervals of the Fits at equal obliquities are greater and fewer in the less refrangible Rays, and less and more numerous in the more refrangible, therefore the less refrangible at equal obliquities shall make fewer Rings than the more refrangible, and the Rings made by those shall be larger than the like number of Rings made by these; that is, the red Rings shall be larger than the yellow, the yellow than the green, the green than the blue, and the blue than the violet, as they were really found to be in the fifth Observation. And therefore the first Ring of all Colours encompassing the white Spot of Light shall be red without any violet within, and yellow, and green, and blue in the middle, as it was found in the second Observation; and these Colours in the second Ring, and those that follow, shall be more expanded, till they spread into one another, and blend one another by interfering.

These seem to be the reasons of these Rings in general; and this put me upon observing the thickness of the Glass, and considering whether the dimensions and proportions of the Rings may be truly derived from it by computation.