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glass produced different degrees of separation of the red and violet rays, or gave spectra of different lengths when the refraction of the middle ray of the spectrum was the same.
In order to explain how such a property led him to the construction of a telescope without colour, or an achromatic telescope, let us take a lens LL of crown or plate glass, whose focal length LY is about twelve inches. When the sun's rays SL,
SL fall upon it, the red will be refracted to R, the yellow to Y, and the violet to V. If we now place behind it a concave lens ll of the same glass, and of the same focus or curvature, it will be found, both by experiment and by drawing the refracted rays, according to the rules given in elementary works, that the concave glass ll will refract the rays LR, LR into LS, LS', and the rays LV, LV into LS', LS' free of all colour; but as these rays will be parallel, the two lenses will not have a focus, and consequently cannot form an image so as to be used as the object-glass of a telescope. This is obvious from another consideration; for since the curvatures of the convex and concave lenses are the same, the two put together will be exactly the same as if they were formed out of a single piece of glass, having parallel surfaces like a watch-glass, so that the parallel rays of light SL,
SL will pass on in the same direction LS, LS' affected by equal and opposite refractions as in a piece of plane glass.
Now, since the convex lens LL separated the white light SL, SL into its component coloured rays, LV, LV being the extreme violet, and LR LR the extreme red; it follows that a similar concave lens of the same glass is capable of uniting into white light LS', LS' rays, as much separated as LV, LR are. Consequently, if we take a concave lens ll of the same, or of a greater refractive power than the convex one, and having the power of uniting rays farther separated than LV, LR are, a less concavity in the lens ll will be sufficient to unite the rays LV, LR into a white ray LS'; but as the lens li is now less concave than the lens LL is convex, the concavity will predominate, and the uncoloured rays LS', LS' will no longer be parallel, but will converge to some point 0, where they will form a colourless or achromatic image of the sun.
The effect now described may be obtained by making the convex lens LL of crown or of plate glass, and the concave one of flint glass, or that of which wineglasses are made. If the concave lens ll has a greater refractive power than LL, which is always the case, the only effect of it will be to make the rays converge to a focus more remote than 0, or to render a less curvature necessary in ll, if O is fixed for the focus of the combined lenses.
Such is the principle of the achromatic telescope as constructed by Mr. Hall. This ingenious individual employed working opticians to grind his lenses, and he furnished them with the radii of the surfaces, which were adjusted to correct the aberration of figure as well as of colour. His invention, therefore, was not an accidental combination of a convex and a concave lens of different kinds of glass, which might have been made merely for experiment; but it was a complete achromatic tele
scope, founded on a thorough knowledge of the different dispersive powers of crown and flint glass. It is a curious circumstance, however, in the history of the telescope, that this invention was actually lost. Mr. Hall never published any account of his labours, and it is probable that he kept them secret till he should be able to present his instrument to the public in a more perfect form; and it was not till John Dollond had discovered the property of light upon which the instrument depends, and had actually constructed many fine telescopes, that the previous labours of Mr. Hall were laid before the public.* From this period the achromatic telescope underwent gradual improvement, and by the successive labours of Dollond, Ramsden, Blair, Tulley, Guinand, Lerebours, and Fraunhofer, it has become one of the most valuable instruments in physical science.
Although the achromatic telescope, as constructed by Dollond, was founded on the principle that the spectra formed by crown and flint glass differed only in their relative lengths, when the refraction of the mean ray was the same, yet by a more minute examination of the best instruments, it was found that they exhibited white or luminous objects tinged on one side with a green fringe, and on the other with one of a claret colour. These colours, which did not arise from any defect of skill in the artist, were found to arise from a difference in the extent of the coloured spaces in two equal spectra formed by crown and by flint glass. This property was called the irrationality of the coloured spaces, and the uncorrected colours which remained when the primary spectrum of the crown glass was corrected by the primary spectrum of the flint glass were called the secondary or residual spectrum. By
a happy contrivance, which it would be out of place here to describe, Dr. Blair succeeded in correcting this secondary spectrum, or in removing the green and claret-coloured fringes which appeared in the best telescopes, and to this contrivance he gave the name of the Aplanatic Telescope.
But while Newton thus overlooked these remarkable properties of the prismatic spectrum, as formed by different bodies, he committed some considerable mistakes in his examination of the spectrum which was under his own immediate examination. It does not seem to have occurred to him that the relations of the coloured spaces must be greatly modified by the angular magnitude of the sun or the luminous body, or aperture from which the spectrum is obtained; and misled by an apparent analogy between the length of the coloured spaces and the divisions of a musical chord,* he adopted the latter, as representing the proportion of the coloured spaces in every beam of white light. Had two other observers, one situated in Mercury, and the other in Jupiter, studied the prismatic spectrum of the sun by the same instruments, and with the same sagacity as Newton, it is demonstrable that they would have obtained very different results. On account of the apparent magnitude of the sun in Mercury, the observer there would obtain a spectrum entirely without green, having red, orange, and yellow at one end, the white in the middle, and terminated at the other end with blue and violet. The observer in Jupiter would, on the contrary, have obtained a spectrum in which the colours were much more condensed. On the planet Saturn a spectrum exactly similar would have been obtained,
* « This result was obtained,” as Newton says, “by an assistant whose eyes were more critical than mine, and who, by right lines drawn across the spectrum, noted the confines of the colours. And this operavjon being divers times repeated both on the same and on several papers, I found that the observations agreed well enough with one another." OPTICS, Part II. Book III.
notwithstanding the greater diminution of the sun's apparent diameter. It may now be asked, which of all these spectra are we to consider as exhibiting the number, and arrangement, and extent of the coloured spaces proper to be adopted as the true analysis of a solar ray.
The spectrum observed by Newton has surely no claim to our notice, merely because it was observed upon the surface of the earth. The spectrum obtained in Mercury affords no analysis at all of the incident beam, the colours being almost all compound, and not homogeneous, and that of Newton is liable to the same objection. Had Newton examined his spectrum under the very same circumstances in winter and in summer, he would have found the analysis of the beam more complete in summer, on account of the diminution of the sun's diameter; and, therefore, we are entitled to say that neither the number nor the extent of the coloured spaces, as given by Newton, are those which belong to homogeneous and uncompounded light.
The spectrum obtained in Jupiter and Saturn is the only one where the analysis is complete, as it is incapable of having its character altered by any farther diminution of the sun's diameter. Hence we are forced to conclude, not only that the number and extent of the primitive homogeneous colours, as given by Newton, are incorrect; but that if he had attempted to analyze some of the primitive tints in the spectrum, he would have found them decidedly composed of heterogeneous rays. There is one consequence of these observations which is somewhat interesting. A rainbow formed in summer, when the sun's diameter is least, must have its colours more condensed and homogeneous than in winter, when the size of its disk is a maximum, and when the upper or the under limb of the sun is eclipsed, a rainbow formed at that time will lose entirely the yellow rays, and have the green and the