This telescope constitutes the most important and useful improvement ever made upon telescopic instruments; and, it is probable, it will, ere long, supersede the use of all other telescopes. Its importance and utility will at once appear when we consider, that a good achromatic telescope of only 4 or 5 feet in length will bear a magnifying power as great, as that of a common astronomical telescope 100 feet long, and even with a greater degree of distinctness, so that they are now come into general use both for terrestrial and celestial observations. There are, indeed, certain obstructions which prevent their being made of a very large size; but from the improvement in the manufacture of achromatic glass which is now going forward, it is to be hoped that the difficulties which have hitherto impeded the progress of opticians will soon be removed. In order to understand the nature of this telescope, it will be necessary to advert a little to the _imperfections_ connected with common refracting telescopes.
The first imperfection to which I allude is this, that _spherical surfaces do not refract the rays of light accurately to a point_; and hence the image formed by a single convex lens is not perfectly accurate and distinct. The rays which pass near the extremities of such a lens meet in foci nearer to the lens than those which pass nearly through the centre, which may be illustrated by the following figure. Let PP (fig. 52) be a convex lens and E_e_ an object, the point E of which corresponds with the axis, and sends forth the rays EM, EN, EA, &c., all of which reach the surface of the glass, but in different parts. It is manifest that the ray EA which passes through the middle of the glass, suffers no refraction. The rays EM, EM, likewise, which pass through near to EA, will be converged to a focus at F, which we generally consider as the focus of the lens. But the rays EN, EN, which are nearer to the edge of the glass will be differently refracted, and will meet about G, nearer to the lens, where they will form another image G_g_. Hence, it is evident, that the first image F_f_, is formed only by the union of those rays which pass very near the centre of the lens; but as the rays of light proceeding from every point of an object are very numerous, there is a succession of images formed, according to the parts of the lens where they penetrate, which necessarily produces indistinctness and confusion. This is the imperfection which is distinguished by the name of _spherical aberration_, or the error arising from the spherical form of lenses.