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235. The light which is transmitted through the plate of air also produces coloured rings, as may be easily ascertained by looking at the sky through the system of prisms placed at a little distance from the eye. This second set of rings, presents the same contours as the preceding, but their colours are different and their tints much more feeble. We shall examine them further, when we have attended to those which are given by reflection.

236. We can form coloured rings, by pressing together, in this manner, two prisms of whatever substance. We can form them also by placing a surface of glass on a plate of resin, metal, metallic glass, or any other polished body. The rings continue to be formed, likewise, in the most perfect vacuum that can be produced by the air-pump. They continue, too, when we heat the glasses to such a degree as to soften them and solder them together. If we could in this way exclude the air entirely, we should infer directly, that the rings were not produced by the proper action of the interposed plate of this fluid; but, although it is physically impossible to attain this limit, yet the permanence of the phenomena, after the nearest approaches to it, evidently indicates that they would remain, even when the air was entirely expelled from between the two surfaces. Indeed the laws established by Newton, show that in this extreme case, the dimensions of the rings would experience only a very small increase, almost inappreciable by the most delicate experiments.

It is not indeed necessary that the thin plate should be air, or that it should be contained between two solid bodies. A plate of water, of alcohol, of ether, or of any other evaporable liquid, being extended over a black glass, produces similar colours, when evaporation has rendered it sufficiently thin; only, the thickness of such a plate always varying in an irregular manner, the tints thus developed, will exhibit all the irregularity of its undulations. We obtain the same results also with sheets of mica and of glass when they are sufficiently thin.*

*Thin sheets of mica are obtained, by separating with a knife, the leaves of a thick sheet. In order to obtain thin sheets of glass, we melt with a lamp the extremity of a hollow tube of this substance; we then blow into it while the extremity is red hot, and force it to develope itself in a ball, which will expand until it bursts on account of its thinness.

237. In general, whatever be the substances of which the rings are formed, and in whatever manner we combine them, the colours which they present are always the same, and arranged in an order precisely similar, from the least to the greatest thicknesses. The only difference we find is in the absolute space which the colours of the several rings occupy, which changes with the nature of the substance and with the more or less rapid diminution of the thickness. Accordingly, the most natural method of examining these phenomena, seems to be, first, to determine the order and succession of the colours of the rings, in a lamina of any substance whatever, but whose thickness varies regularly according to some known law; secondly, to find, for this substance, the relation which the thickness bears to the colour; and lastly, to compare these relations in different substances, and see what they have in common or how they differ.

The order in which the colours are arranged in the different rings, may be conveniently investigated, by observing those which are formed between two prisms, especially if we select those cases in which the rings are large, and if we dilate them still more by looking through a magnifying glass. Nevertheless this process is not susceptible of very great precision; for the adhesion of the prisms being commonly effected by a violent and irregular pressure, the rings which result from it are likewise almost always irregular. Sometimes there are several points of pressure, and consequently, several black spots, from which the colours go on diminishing continually, and compose sets of rings which intermingle with each other. Thus, in order to extend our observations beyond what these first phenomena make known, it is necessary to employ some other apparatus, which will exhibit the same phenomena with more regularity. This we do by placing, one upon the other, two spherical glasses of unequal curvatures. If the surfaces of these glasses are well formed, they can have only one point of contact, from which the space comprehended between them, goes on constantly increasing in thickness, according to the laws of geometry resulting from the difference of their radii. Moreover, the small curvature generally given to these glasses, causes the light which traverses them to arrive at the plate of air, without being sensibly dispersed. This disposition is, therefore, eminently fitted for taking exact measurements of the dimensions of the rings, and

for comparing their tints with the corresponding thicknesses; and this is the disposition which Newton employed. Among all the possible combinations of curvature, he always had one of the glasses plane, and the other of the same convexity on both its surfaces, because this disposition afforded the greatest facility for determining the curvatures with exactness; for we can easily ascertain by reflection, when a glass is plane; and we can likewise determine the radius of a glass, equally convex, by measuring the distance at which it concentrates the simple rays, which fall parallel upon one of its surfaces.

238. When a convex glass of a large radius is thus placed upon a plane glass, and gently pressed against it in order to establish the contact more perfectly, the coloured rings present themselves immediately, and appear regular and distinct, with a black spot at their centre. Then each circular zone of the plate of air, reflects the colour which belongs to its thickness; and consequently, if we gradually augment this thickness, by gently raising the superior glass, the colours reflected at the same distance from the centre of the rings must change; and those which at first formed rings distant from the centre, must gradually approach it, until the thickness of the air, even at this point, becoming too great for them, they disappear and give place to others which were at first still farther removed. But since, at this last place where they disappear, the distance between the glasses can only vary by degrees almost insensible, on account of their being tangents respectively to each other, it follows that each colour, when brought there, must extend itself very widely and thus become easily distinguished. This succession, which can be rendered as gradual as we please, affords, therefore, a simple and exact method of determining the species and order of the colours which compose the series of rings.

Newton performed this experiment with a convex glass, the two surfaces of which were wrought upon the same sphere, the radius of which was 51 feet; and by means of the results thus obtained, as well as by observations which he had before made with the prisms, he fixed, in the following terms, the order and series of tints of which the circular rings were composed.

"Next the pellucid central spot, made by the contact of the glasses, succeeded blue, white, yellow, and red. The blue was so little in quantity that I could not discern it in the circles made Opt.

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by the prisms, nor could I well distinguish any violet in it, but the yellow and red were pretty copious, and seemed about as much in extent as the white, and four or five times more than the blue. The next circuit in order of colours, immediately encompassing these, were violet, blue, green, yellow, and red; and these were all of them copious and vivid, excepting the green, which was very little in quantity, and seemed much more faint and dilute than the other colours. Of the other four, the violet was the least in extent, and the blue less than the yellow or red. The third circuit or order was purple, blue, green, yellow, and red; in which the purple seemed more reddish than the violet in the former circuit, and the green was much more conspicuous, being as brisk and copious as any of the other colours, except the yellow; but the red began to be a little faded, inclining very much to purple. After this succeeded the fourth circuit of green and red. The green was very copious and lively, inclining on the one side to blue, and on the other side to yellow. But in this fourth circuit there was neither violet, blue, nor yellow, and the red was very imperfect and dirty. Also the succeeding colours became more and more imperfect and dilute, till after three or four revolutions they ended in perfect whiteness. Their form, when the glasses were most compressed so as to make the black spot appear in the centre, is delineated in figure 151, where a, b, c, d, e; f, g, h, i, k; l, m, n, o, p; q, r ; s, t ; v, x ; y, z, denote the colours reckoned in order from the centre, BLACK, blue, white, yellow, red; VIOLET, blue, green, yellow, red; purPLE, blue, green, yellow, red; GREEN, red; greenish blue, red; greenish blue, pale red; GREENISH BLUE, reddish white."*

239. Having made these observations, Newton proceeded to measure the diameters of the rings, still making use of the same glasses; but he took care now simply to put them one upon the other, without any pressure being exerted which might bend them or alter their natural curvature; then placing his eye above the rings, as nearly perpendicularly as he could, he measured the diameters of the six first in the brightest part of their breath,

* The colours whose names are in capital letters, are those which form the commencement of each ring, reckoning from the central spot; and the dimmest rings are those designated in figure 151 by the shaded portions.

which, for the first and nearest the centre, was found to be nearly in the confines of the white and yellow; for the second, between the orange and the yellow; for the third, at the yellow; for the fourth, between the yellowish green and red; and for the fifth and sixth, between the greenish blue and red, always nearly in the middle of the space occupied by each ring. Now it may be readily shown by geometry, that the interval between two spheres, or between a plane and a sphere, which touch each other, increases in the ratio of the square of the distances from Top.141. the point of contact. Newton took, therefore, the squares of all the diameters which he had measured, and by comparing these squares with each other, beginning with the smallest, he found that they proceeded according to the progression of odd numbers, 1, 3, 5, 7, 9,....; whence he inferred that the thicknesses of the air at the places where the rings appeared to be limited by the diameters, were also in the same progression.

In order to make these observations with accuracy, it is necessary to place the eye as nearly as possible in the direction of the vertical, which passes through the centre of all the rings, that we may avoid the dilatations which take place, when the rays are oblique to the surface of the glasses. For the same reason, it is necessary to measure the diameters, not in the plane. of incidence at which the light arrives, for this would give unequal obliquities to the rays which come to the eye from the extremities of the same diameter; but transversely to the direc tion of incidence and perpendicularly to its plane, as represented in figure 152. Finally, as the diameters are measured on the superior surface of the glass, while the rings are actually formed at the inferior surface, it is necessary to take account of the refractions which they experience in traversing it, and to apply a correction for this effect. Newton neglected none of these precautions; and we shall perceive that they were indispensable, when we consider how extremely small the thicknesses were which he was endeavouring to estimate.

240. Newton measured also the diameters of the rings in the dimmest parts; which, for the first, he found to correspond to the middle of the central spot; for the second, to the dark violet; for the third, to the deep blue; for the fourth, fifth, and sixth, to the commencement of the greenish blue. He likewise took the squares of these diameters, in order to ascertain the corresponding

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