PART IV.
Observations concerning the Reflexions and Colours of thick transparent polish'd Plates.
There is no Glass or Speculum how well soever polished, but, besides the Light which it refracts or reflects regularly, scatters every way irregularly a faint Light, by means of which the polish'd Surface, when illuminated in a dark room by a beam of the Sun's Light, may be easily seen in all positions of the Eye. There are certain Phænomena of this scatter'd Light, which when I first observed them, seem'd very strange and surprizing to me. My Observations were as follows.
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.