The object of this construction is to render a small disc of flint-glass available to perform the office of compensation to a much larger one of crown-glass, and thus to render possible the construction of telescopes of much larger aperture than are now common, without hindrance from the difficulty at present experienced in procuring large discs of flint-glass. It is well known to those who are acquainted with telescopes, that in the construction of an ordinary achromatic object-glass, in which a single crown lens is compensated by a single one of flint, the two lenses admit of being separated only by an interval too small to afford any material advantage, _in diminishing the diameter of the flint lens_, by placing it in a narrower part of the cone of rays--the actual amount of their difference in point of dispersive power being such as to render the correction of the chromatic aberration impossible, when their mutual distance exceeds a certain limit. This inconvenience Mr. Rogers proposes to obviate, by employing, as a correcting lens--not a single lens of flint, but a compound one consisting of a convex crown and concave flint, whose foci are such as to cause their combination to act as a plain glass on the mean refrangible rays. Then it is evident, that by means of the greater dispersive power of flint than of crown glass, this will act as a concave on the violet, and as a convex on the red rays, and _that_ the more powerfully, according as the lenses separately have greater powers or curvature. If then, such a compound lens be interposed between the object-glass of a telescope--supposed to be a single lens of plate or crown-glass--and its focus, it will cause no alteration in the focus for mean rays, while it will lengthen the focus for violet, and shorten it for red rays. Now this is precisely what is wanted to produce an achromatic union of all the rays in the focus; and as nothing in this construction limits the powers of the individual correcting lenses, they may therefore be applied any where that convenience may dictate; and thus, theoretically speaking, a disc of flint-glass, however small, may be made to correct the colour of one of crown however large.