of a piece of steel spring highly polished, or, better still, polished silver, which is to be bent into a concave figure and placed vertically on its edge upon a piece of card or white paper, and when exposed either to the rays of the sun or any good artificial light, the curves shown in Fig. 111 are well defined.

In the same way, passing from reflecting to refracting bodies, the spherical figure of a convex lens causes the rays which fall near the outer edge to come to a focus nearer the lens than the rays which are refracted from the centre. The result, as might be expected, is just the reverse of the concave mirror. The rays A B, A B, Fig. 112, falling on the margin of the double-convex lens are refracted to a focus at F, whilst those rays, D D, D D, which fall near the axis of the lens come together at a more remote point, viz., at C. Here again a screen or diaphragm cutting off the rays refracted from the outer edge of the lens gives a better image; the picture produced by such a lens, provided with a screen, can be focused more distinctly; hence telescopes, microscopes, cameras, oxy-hydrogen lanterns, &c., &c., are usually fitted with diaphragms, which reduce the light, but cause the images to become more distinct. The lens of the eye would, from this cause, project on to the retina a confused or double picture, which might render vision extremely imperfect; this, however, is prevented by the iris, which acts as a diaphragm, thus the aberration of sphericity is corrected.

THE DISPERSION OF LIGHT, OR CHROMATIC ABERRATION.

If light consisted of a series of coloured rays, every one of which possessed the same index of refraction when they fall upon a glass lens, they would all come together in the same spot, and white light only would be obtained; but this is not the case, and it is known in practice that lenses, and especially condensing lenses, project coloured rings, and give images with coloured edges. And this is not remarkable when it is remembered that a double-convex lens may be regarded as a series of prisms united at their bases, and therefore capable of decomposing or dispersing light. It is a singular fact that Sir Isaac Newton considered, from the experiments he had tried with various prisms, that dispersion was proportioned to refraction, and he believed that all substances had the same chromatic aberrations when formed into lenses, and that any combination of a concave with a convex glass would produce colour with refraction. Newton reasoned only from the facts he had acquired on the dispersive powers of bodies, and pronounced the construction of achromatic telescopes which should not project images with coloured edges to be impossible. The fallibility even of his great mind is shown by the fact that, a few years after his death, Hall in 1733, and Dolland, the famous optician, in 1757, demonstrated that by using two media, viz., crown and flint glass, of different refractive and dispersive powers, a lens may be formed which is achromatic.

The principle of the achromatic lens is not complicated or difficult to understand, provided the previous matter relating to compound and simple colours (p. 89) has been already studied. Given a lens made of a certain glass, and projecting, amongst other colours, a ring of red light, what colour, projected from another lens, is required to neutralize it? The answer is obvious: any colour which together with the red light would form white light. That colour must be green, because it contains yellow and blue; and, as already shown, red, yellow, and blue form white light. In the adjustment of the two lenses

forming the achromatic (Fig. 113), it is so arranged that the colours which would be separately produced by each lens shall, when combined, by their unequal dispersion fall together at the same spot and unite together. Any two colours which unite and form white light are said to be complementary, and there is a very conclusive experiment which may be performed with polarized light passed through a selenite slide placed behind a Nicol's prism composed of

double-refracting spar. The two discs of light projected on to the screen separately are green and red; but when caused to overlap each other by enlarging the aperture through which they pass, the two colours unite in the centre, forming white light, whilst red and green remain intact in those positions which do not overlap. (Fig. 114.)

Other complementary colours would be yellow and indigo, blue and orange.

FIG. 115.--Arrangement of the Composite Lenses in an Achromatic Telescope.

Flint glass has a greater dispersive power than crown glass; it will spread or disperse the spectrum over a larger space. The dispersive power of the prism used in decomposing light for showing the spectra of incandescent metal is increased by filling them with carbonic disulphide (bisulphide of carbon), and the composition and dispersive powers of the three bodies is as follows:

THE INTERFERENCE OF LIGHT.

COLOURS OF THIN PLATES.

About the year 1672, Dr. Hook, a very clever mechanician, and learned in all the science of his day, discovered that by splitting mica, which is free from colour, and sometimes used instead of glass, into very thin films, they exhibited the most beautiful colours. But as they were less than the twelvethousandth part of an inch in thickness, Dr. Hook could not measure them, and was therefore unable to determine the law that regulated the production of any particular colour, according to the thickness of the film of mica. In due course of time the experiments engaged the attention of Sir Isaac Newton, and directly he touched the subject it was truly, so far as intellect was concerned, with the hand of a giant, and he soon discovered a method of measuring the films. He did not begin with mica, because it would have been very troublesome, if not impossible, to split it into a graduated series of films of the extreme thinness required to produce colour. Newton therefore commenced with air, and having once determined the law, it was easy, knowing the index of refraction of all other transparent bodies, to work out by calculation the respective thicknesses required to produce the same colours. He took a planoconvex lens, the radius of whose convexity was 14 ft., and placed it on a double-convex lens, the radius of whose convexity was 50 ft., and by means of proper clamps and screws the surfaces of the two lenses could be brought closely together. The convexity of the lower lens being so extremely slight, it might indeed be almost regarded as a flat surface, like any moderate area on the surface of the globe, because the sphere of glass (of which the lens would be a slice) had a theoretical diameter of 100 ft. (Fig. 116.)

I

FIG. 116.-Instrument used by Newton to obtain the Rings of Colour from Thin Plates of Air.

LL, upper lens pressed on the lower one, 77, by the thumb-screws p p p.

When the two lenses were pressed together, concentric rays of colour maae their appearance; indeed the same kind of effect is often produced accidentally when a number of flat plates of window-glass are piled one above the other, the enclosed air being then pressed by the weight of the superincumbent glass into a film sufficiently thin to show coloured rings.

The Hon. Robert Boyle first discovered that thin bubbles of the essential oils, spirit of wine, turpentine, soap and water, produce the colours, and he

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succeeded in blowing glass so thin that, like the mica, it displayed varieties of colour.

Lord Brereton observed the colour of thin oxidized or decomposed films, such as are produced by the action of the weather during a prolonged period on the ancient glass in church windows, or on glass which has been buried in the earth. When steel is tempered, the regular gradations of colour produced by the oxidation of a very thin outer film are a guide to the skilled workman who tempers the metal.

Mr. De la Rue, by floating a very thin film of a quick-drying varnish on the surface of hot water, and then receiving this on a sheet of paper, was enabled to secure in the most perfect manner those lovely tints, which are sometimes associated with the surface of ponds into which greasy matter or oil may pass, or in the puddles after rain in the yard of a gas-works where liquor containing coal oil has been spilt.

The variety of colours which Newton describes in his important "Table of the Colours of thin Plates in Air, Water, and Glass,” are given by him in the succession of spectra or order of colours, where he enumerates seven spectra or orders of colours; these are different from reflected and transmitted rays, and are produced by thicknesses of air, water, or glass, estimated from a scale of an inch divided into one-million parts.

FIG. 117.-Woodward's Model of Waves, with movable Rods.

Newton measured the diameter of every colourea ring; he did not depend merely upon calculation, but tried a number of experiments with the colours of the spectra, allowing each to fall separately on his apparatus, and discovered that under these circumstances he no longer obtained a variety of coloured rings, but observed that the central dark spot was surrounded by rings of the same colour as the light incident on the lenses alternating with dark rings.

Thus, supposing Newton to have placed the apparatus for producing the rings into the yellow part of the spectrum, there would be a dark spot in the centre, then a yellow ring, now a dark, again a yellow ring, and so on; he then squared the diameters of the reflected coloured rays, and obtained the odd numbers, 1, 3, 5, 7, 9, &c., while the square of the diameters of the dark rings were as 2, 4, 6, 8, 10, &c. When the rings were observed by transmitted light, the order was reversed-the coloured rings being at the even numbers, and the dark ones at odd integers.

These effects Newton called fits of transmission and fits of reflection; they could not be reconciled or explained by his own favourite theory, and, to the honour of this great philosopher, he did not attempt to press the corpuscular theory, and compel it to his own use, but simply left behind him a record of facts, only naming that which he had proved to exist, and giving the relative thicknesses of the plates of air by which each colour is reflected.

The undulatory theory of light alone is adopted to explain these phenomena, and by what is termed the interference of the waves the effects are supposed to be produced. Ingenious models have been made to explain the law of

FIG. 118.-A Model of Fixed Waves.

interference; but those of Mr. Charles Woodward, the President of the Islington Scientific Society, are the most simple, and are thus described by him in his admirable little work on the "Polarization of Light :"

A B (Fig. 117) represents a model with rods freely moving in a perpendicular direction through the frame A B, and furnished with pins resting upon the

FIG. 119.-Intensity of Waves doubled by the Superposition and Coincidence of two equal Systems.

upper part of the frame, so that when at rest the whole may assume the appearance of waves, as in the diagram.

CD (Fig. 118) represents a fixed model with waves of similar size and intensity, and numbered so as to distinguish each half-undulation.

FIG. 120.—Waves neutralized by the Superposition and Interference of two

equal Systems.

It will be seen that when the stars indicating the highest point of the waves, as A B, correspond with the odd numbers of half-undulations on CD, each system of waves will be in the same state of vibration; and, if so superposed, a series of waves of doubled intensity will be the result, as in Fig. 119.