This construction, likewise, possesses other and very remarkable advantages. For, first, when the correcting lens is approximately constructed on a calculation founded on its intended aperture, and on the refractive and dispersive indices of its materials, the final and complete dispersion of colour may be effected, not by altering the lenses by grinding them anew, but by shifting the combination nearer to, or farther from, the object-glass, as occasion may require, along the tube of a telescope, by a screw motion, till the condition of achromaticity is satisfied in the best manner possible. And secondly, the spherical aberration may in like manner be finally corrected, by slightly separating the lenses of the correcting glass, whose surfaces should for this purpose be figured to curvatures previously determined by calculation, to admit of this mode of correction--a condition which Mr. Rogers finds to be always possible. The following is the rule he lays down for the determination of the foci of the lenses of the correcting glass:--‘The focal length of either lens of the correcting lens is to that of the object-glass, in a ratio compounded of the ratio of the square of the aperture of the correcting lens to that of the object-glass, and of the ratio of the difference of the dispersive indices of the crown and flint glass, to the dispersive index of crown.’ For example, to correct the colour of a lens of crown or plate glass of 9 inches aperture, and 14 feet focal length (the dimensions of the telescope of Fraunhofer at Dorpat) by a disc of flint glass 3 inches in diameter, the focus of either lens of the correcting lens will require to be about 9 inches. To correct it by a 4 inch disc will require a focus of about 16 inches each. Mr. Rogers remarks, that it is not indispensable to make the correcting glass act as a plane lens. It is sufficient if it be so adjusted as to have a shorter focus for red rays than for violet. If, preserving this condition, it be made to act as a concave lens, the advantage procured by Mr. Barlow’s construction of reducing the length of the telescope with the same focal power, is secured, and he considers, moreover, that by a proper adaptation of the distances, foci, &c., of the lenses, we might hope to combine with all these advantages that of the destruction of the secondary spectrum, and thus obtain a perfect telescope. The above is an abstract of a paper read to the ‘Astronomical Society of London’ in April 1828, by A. Rogers, Esq.