The spherical aberration of a diamond lens is extremely small, and when compared with that of a glass lens the difference is rendered strikingly apparent. This diminution of error in the diamond arises from the enormous refractive power possessed by this brilliant substance, and the consequent increase of amplification, with _very shallow curves_. The longitudinal aberration of a plano-convex diamond lens is only 0.955; while that of a glass one of the same figure is 1.166; both numbers being enumerated in terms of their thickness, and their convex surfaces exposed to parallel rays. But the indistinctness produced by lenses, arises chiefly from every mathematical point on the surface of an object being spread out into a small circle; these circles, intermixing with each other, occasion a confused view of the object. Now this error must necessarily be in the ratio of the areas of these small circles, which being respectively as the squares of their diameters, the lateral error produced by a diamond lens will be 0.912; while that of a glass lens of like curvature is 2.775; but the magnifying power of the diamond lens will be to that of the glass as 8 to 3, their curves being similar; (or, in other words, the superficial amplification of an object; with the perfect diamond lens before mentioned, is 22500 times, while a similar magnifier, made of glass, amplifies only 3136 times, reckoning 6 inches as the standard of distinct vision:) thus the diamond will enable us to gain more power than it is possible to procure by lenses of glass, for the focal distance of the smallest glass lens which can be well made is about the 1/80th of an inch, while that of a diamond, worked in the same tools, would be only the 1/200th of an inch. If we wish to compare the aberrations of the two lenses when of equal power, the curvature of the glass must be increased; and as it is well known the lateral aberration increases inversely as the square of the radius, (the aperture and position remaining [p021] the same,) the aberration of the diamond lens will only be about 1/20th of that produced by the glass one, even when their thickness is the same; but as the curvature of the diamond is less, the thickness may be greatly diminished. The chromatic dispersion of the adamant being nearly as low as that of water, its effects in small lenses can barely be appreciated by the eye, even in the examination of that valuable class of test objects, which require enormous angles of aperture to be rendered visible, which it is evident must be of easier attainment by diamond magnifiers than by any other sort of microscope. A mathematical investigation of the spherical aberration of the diamond when formed into lenses, I hope to lay before the public at a future opportunity. The comparative numbers here taken from the longitudinal aberration are, I believe, sufficiently accurate for practical purposes. _18, Picket-Street, Strand_. FOOTNOTES: