The second and most important imperfection of single lenses, when used for the object-glasses of telescopes, is, that the rays of compounded light being differently refrangible, come to their respective foci at different distances from the glass; the more refrangible rays, as the violet, converging sooner than those which are less refrangible, as the red. I have had occasion to illustrate this circumstance, when treating on the colours produced by the prism, (see p. 128, and figures 32 and 33,) and it is confirmed by the experiment of a paper painted red, throwing its image, by means of a lens, at a greater distance than another paper painted blue. From such facts and experiments, it appears, that the image of a white object consists of an indefinite number of coloured images, the violet being nearest, and the red farthest from the lens, and the images of intermediate colours at intermediate distances. The aggregate, or image itself, must therefore be in some degree confused; and this confusion being much increased by the magnifying power, it is found necessary to use an eye glass of a certain limited convexity to a given object glass. Thus, an object glass of 34 inches focal length will bear an eye-glass of only 1 inch focus, and will magnify the diameters of objects 34 times; one of 50 feet focal distance will require an eye-glass of 4½ inches focus, and will magnify only 142 times; whereas, could we apply to it an eye-glass of only 1 inch focus, as in the former case, it would magnify no less than 600 times. And were we to construct an object-glass of 100 feet focal length, we should require to apply an eye-glass, not less than 6 inches focus, which would produce a power of about 200 times; so that there is no possibility of producing a great power by single lenses, without extending the telescope to an immoderate length.

Sir Isaac Newton, after having made his discoveries respecting the colours of light, considered the circumstance we have now stated as an insuperable barrier to the improvement of refracting telescopes; and therefore turned his attention to the improvement of telescopes by reflection. In the telescopes which he constructed and partly invented, the images of objects are formed by reflection from speculums or mirrors; and being free from the irregular convergency of the various coloured rays of light, will admit of a much larger aperture and the application of a much greater degree of magnifying power. The reflector which Newton constructed was only 6 inches long, but it was capable of bearing a power equal to that of a 6 feet refractor. It was a long time, however, after the invention of these telescopes before they were made of a size fitted for making celestial observations. After reflecting telescopes had been some time in use, Dollond made his famous discovery of the principle which led him to the construction of the achromatic telescope. This invention consists of a compound object glass formed of two different kinds of glass, by which both the spherical aberration and the errors arising from the different refrangibility of the rays of light are, in a great measure corrected. For the explanation of the nature of this compound object glass and of the effects it produces; it may be expedient to offer the following remarks respecting the dispersion of light and its refraction by different substances.

The dispersion of light is estimated by the variable angle formed by the red and violet rays which bound the solar spectrum;—or rather, it is the excess of the refraction of the most refrangible ray above that of the least refrangible ray. The dispersion is not proportional to the refraction—that is, the substances which have an equal mean refraction, do not disperse light in the same ratio. For example, if we make a prism with plates of glass, and fill it with oil of Cassia, and adjust its refracting angle ACB, (fig. 31, p. 127,) so that the middle of the spectrum which it forms falls exactly at the same place where the green rays of a spectrum formed by a glass prism would fall—then we shall find that the spectrum formed by the oil of Cassia prism will be two or three times longer than that of the glass prism. The oil of Cassia, therefore, is said to disperse the rays of light more than the glass, that is, to separate the extreme red and violet rays at O and P more than the mean ray at green, and to have a greater dispersive power. Sir I. Newton appears to have made use of prisms composed of different substances, yet, strange to tell, he never observed that they formed spectrums, whose lengths were different, when the refraction of the green ray was the same; but thought that the dispersion was proportional to the refraction. This error continued to be overlooked by philosophers for a considerable time, and was the cause of retarding the invention of the achromatic telescope for more than 50 years.

Dollond was among the first who detected this error. By his experiments it appears, that the different kinds of glass differ extremely with respect to the divergency of colours produced by equal refractions. He found that two prisms, one of white flint glass, whose refracting angle was about 25 degrees, and another of crown glass whose refracting angle was about 29 degrees, refracted the beam of light nearly alike; but that the divergency of colour in the white flint was considerably more than in the crown glass; so that when they were applied together, to refract contrary ways, and a beam of light transmitted through them, though the emergent continued parallel to the incident part, it was, notwithstanding, separated into component colours. From this he inferred, that, in order to render the emergent beam white, it is necessary that the refracting angle of the prism of crown glass should be increased, and by repeated experiments he discovered the exact quantity. By these means he obtained a theory in which refraction was performed without any separation or divergency of colour; and thus the way was prepared for applying the principle he had ascertained to the construction of the object glasses of refracting telescopes. For the edges of a convex and concave lens, when placed in contact with each other, may be considered as two prisms which refract contrary ways; and if the excess of refraction in the one be such as precisely to destroy the divergency of colour in the other, a colourless image will be formed. Thus, if two lenses are made of the same focal length, the one of flint glass and the other of crown, the length or diameter of the coloured image in the first will be to that produced by the crown glass, as 3 to 2 nearly. Now, if we make the focal lengths of the lenses in this proportion, that is, as 3 to 2, the coloured spectrum produced by each will be equal. But if the flint lens be concave, and the crown convex—when placed in contact—they will mutually correct each other, and a pencil of white light refracted by the compound lens will remain colourless.

figure 53.

The following figure may perhaps illustrate what has been now stated. Let LL (fig. 53.) represent a convex lens of crown glass, and ll a concave lens of flint glass. A ray of the sun S, falls at F on the convex lens which will refract it exactly as the prism ABC, whose faces touch the two surfaces of the lens at the points where the ray enters and quits it. The solar ray, SF, thus refracted by the lens LL, or prism ABC, would have formed a spectrum PT on the wall, had there been no other lens, the violet ray F crossing the axis of the lens at V, and going to the upper end P of the spectrum; and the red ray FR, going to the lower end T. But as the flint-glass lens ll, or the prism AaC which receives the rays FV, FR, at the same points, is interposed, these rays will be united at f, and form a small circle of white light; the ray SF of the sun being now refracted without colour from its primitive direction SFY into the new direction Ff. In like manner the corresponding ray SM will be refracted to f, and a white and colourless image of the sun will be there formed by the two lenses. In this combination of lenses it is obvious that the spherical aberration of the flint lens corrects to a considerable degree that of the crown-glass, and by a proper adjustment of the radii of the surfaces, it may be almost wholly removed. This error is still more completely corrected in the triple achromatic object-glass, which consists of three lenses—a concave flint lens placed between convexes of crown glass. Fig. 54 shows the double achromatic lens, and fig. 55, the triple object-glass, as they are fitted up in their cells, and placed at the object end of the telescope. In consequence of their producing a focal image free of colour they will bear a much larger aperture and a much greater magnifying power than common refracting telescopes of the same length. While a common telescope whose object-glass is 3½ feet focal distance will bear an aperture of scarcely 1 inch, the 3½ feet Achromatic will bear an aperture of 3¼ inches, and consequently transmits 10½ times the quantity of light. While the one can bear a magnifying power of only about 36 times, the other will bear a magnifying power for celestial objects of more than 200 times.

figure 54.figure 55.

The theory of the achromatic telescope is somewhat complicated and abstruse, and would require a more lengthened investigation than my limits will permit. But what has been already stated may serve to give the reader a general idea of the principle on which it is constructed, which is all I intended. The term achromatic by which such instruments are now distinguished was first given to them by Dr. Bevis. It is compounded of two Greek words which signify, ‘free of colour.’ And, were it not that even philosophers are not altogether free of that pedantry which induces us to select Greek words which are unintelligible to the mass of mankind, they might have been contented with selecting the plain English word colourless, which is as significant and expressive as the Greek word achromatic. The crown-glass, of which the convex lenses of this telescope are made, is the same as good common window-glass; and the flint-glass is that species of glass of which wine-glasses, tumblers, decanters and similar articles are formed, and is sometimes distinguished by the name of crystal-glass. Some opticians have occasionally formed the concave lens of an achromatic object-glass from the bottom of a broken tumbler.

This telescope was invented and constructed by Mr. John Dollond, about the year 1758. When he began his researches into this subject, he was a silk weaver in Spitalfields, London. The attempt of the celebrated Euler to form a colourless telescope, by including water between two meniscus glasses, attracted his attention, and, in the year 1753, he addressed a letter to Mr. Short, the optician, which was published in the Philosophical Transactions of London, ‘concerning a mistake in Euler’s theorem for correcting the aberrations in the object glasses of refracting telescopes.’ After a great variety of experiments on the refractive and dispersive powers of different substances, he at last constructed a telescope in which an exact balance of the opposite dispersive powers of the crown and flint lenses made the colours disappear, while the predominating refraction of the crown lens disposed the achromatic rays to meet at a distant focus. In constructing such object glasses, however, he had several difficulties to encounter. In the first place, the focal distance as well as the particular surfaces must be very nicely proportioned to the densities or refractive powers of the glasses, which are very apt to vary in the same sort of glass made at different times. In the next place, the centers of the two glasses must be placed truly in the common axis of the telescope, otherwise the desired effect will be in a great measure destroyed. To these difficulties is to be added—that there are four surfaces (even in double achromatic object glasses) to be wrought perfectly spherical; and every person practised in optical operations will allow, that there must be the greatest accuracy throughout the whole work. But these and other difficulties were at length overcome by the judgment and perseverance of this ingenious artist.