_Aberration of lenses._--In connection with the above descriptions, the following statements respecting the spherical aberration of lenses may not be inappropriate. Mr. John Dollond, in a letter to Mr. Short, remarks, that ‘the aberration in a single lens is as the cube of the refracted angle; but if the refraction be caused by two lenses, the sum of the cubes of each half will be 1/4 of the refracted angle, twice the cube of 1 being 1/4 the cube of 2. So three times the cube of 1 is only _one ninth_ of the cube of 3.’ &c. Hence the indistinctness of the borders of the field of view of a telescope is diminished by increasing the number of lenses in an eye piece. Sir J. Herschel has shown that if two plano-convex lenses are put together as in fig. 75, the aberration will be only 0.2481, or _one fourth_ of that of a single lens in its best form. The focal length of the first of these lenses, must be to that of the second as 1 to 2.3. If their focal lengths are equal, the aberration will be 0.603, or nearly one half. The spherical aberration, however, may be _entirely_ destroyed by combining a meniscus and double convex lens, as shown in fig. 76, the convex sides being turned to the eye when they are used as lenses, and to parallel rays, when they are used as burning glasses. Sir J. Herschel has computed the following curvatures for such lenses. _Focal length of the convex lens_ +10.000 Radius of its first surface +5.833 Radius of its second surface -35.000 _Focal length of the meniscus_ +17.829 Radius of its first surface +3.688 Radius of its second surface +6.294 Focal length of the compound lens +6.407 On the general principles above stated, a good astronomical eye-piece may be easily constructed with two proper lenses, either according to the plan of Huygens or that of Ramsden; and, from what has been now stated it is demonstrably certain, that, in all cases where two glasses are properly combined, such an eye-piece is superior to a single lens, both in point of distinctness, and of the enlargement of the field of view. I lately fitted up an eye-piece, on Ramsden’s principle, with two lenses, each about 3 inches focal length, and 1-3/8 inch diameter, placed at half an inch distant, with their convex surfaces facing each other as in fig. 74, which forms an excellent eye-piece for an achromatic telescope, 6 feet 8 inches focal distance, and 4 inches aperture, particularly for viewing clusters of stars, the Milky Way, and the large nebulæ. The field of view is large, the magnifying power is only between 50 and 60 times, and the quantity of light being so great, every celestial object appears with great brilliancy, and it is in general much preferable, when applied to the stars than any of the higher powers. When applied to _Presepe_ in Cancer, it exhibits that group at one view, as consisting of nearly a 100 stars which exhibit a beautiful and most striking appearance.