Christiani Hugenii Const. F. Astroscopia Compendiaria, Tubi Optici molimine liberata

HUGENII ASTROSCOPIA, &c. 14

For first, in preparing lenses, I know how much the difficulty of shaping increases with size; and the difficulty of finding the glass itself that lacks those defects which are most harmful to this work. For the further the rays are collected, the more these defects must necessarily reveal themselves. It is further certain, even if those things pose no obstacle, that things seen are not magnified except in proportion to the diameters of the aperture of the outer lens. These diameters do not increase with the length of the telescopes; but, as far as I see, they follow a sub-duplicate ratio of the lengths. So that given an aperture of three inches in a telescope thirty feet long, which experience grants as the limit, another, at three hundred feet, will be no more than nine and a half inches, and for that reason all things will appear only about three times larger with this very large telescope than with that of thirty feet. But if the same must be surpassed by a tenfold excess, a length of three thousand feet will now be needed, which it is manifest can be reached by no human aid, if only for the sake of the height.

Indeed, those apertures we have mentioned would be much larger, and would increase by a greater proportion, if nothing else stood in the way than the curvature, which is little suited for collecting rays due to the spherical figure. But now a certain other aberration of rays arises from the very nature of refraction, which Newton proved a few years ago by certain excellent experiments and the colors of glass prisms. This, however, has its own laws, by which, if I perceive them correctly, that sub-duplicate ratio of apertures to lengths, which I mentioned, is gathered.

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