Previous to grinding a diamond into a spherical figure, it is absolutely necessary that it should be ground flat, and parallel on both sides (if not a Laske or plate diamond), so that we may be enabled to see through it, and try it as opticians try a piece of flint glass: without this preparatory step, it will be extremely dangerous to commence the process of grinding, for many diamonds give a double, or even a species of triple refraction, forming two or three images of an object; this polarization of the light, arising from the primitive form of the crystal, of course totally unfits them for making lenses[5]. I need not observe, that it must be chosen of the finest water, and free from all visible flaws when examined by a deep magnifier. It was extremely fortunate for diamond lenses that the first made was free from the defect of double vision, otherwise diamonds en masse might at once have been abandoned as unfit for optical purposes. The cause why some stones give single vision, and others several peculiar refractions, may also arise from different degrees of density or hardness occurring in the same stone. Diamond-cutters are in the habit of designating stones male and female, sometimes a he and she (as they have it) are united in the same gem,—their he means merely a hard stone, and their she a soft one. When a diamond which will give several refractions is ground into a spherical figure and partially polished, it is seen by the microscope to exhibit a [p019] peculiar appearance of an aggregation of minute shivery cristallized flaws, sometimes radiated and sometimes in one direction, which can never be polished out: I believe I could disstinguish with certainty a bad lens from a good one by this phenomenon without looking through it[6]. Precious stones, from their crystalized texture, are liable to the same defects for optical purposes as diamonds.
Having ascertained the goodness of a stone it must next be prepared for grinding; it will in many cases be advisable to make diamond lenses plano-convex, both because this figure gives a very low aberration, and because it saves the trouble of grinding one side of the stone. It must never be forgotten, that it may be possible to neutralize the naturally low spherical aberration of a diamond lens by giving it an improper figure, or by the injudicious position of its sides in relation to the radiant. When the lens is to be plano-convex, cause the flat side to be polished as truly plane as possible, without ribs or scratches; for this purpose the diamond should be so set as to possess the capability of being turned round, that the proper direction with respect to the laminæ may be obtained: when the flat side is completed, let the other side be worked against another diamond, so as to be brought into a spherical figure by the abrasion of its surface. When this is accomplished, a concave tool of cast iron must be formed of the required curve in a lathe, having a small mandril of about 210ths of an inch in diameter, and a velocity of about 60 revolutions per second! The diamond must now be fixed by a strong hard cement (made of equal parts of the best shell lac and pumice-stone powder, carefully melted together without burning) to a short handle, and held by the fingers against the concave tool while revolving. This tool must be paved by diamond powder, hammered into it by an hardened steel convex punch: when the lens is uniformly ground all over, very fine sifted diamond-dust carefully washed in oil must be applied to another iron concave tool (I may here remark, that of all the metals which I have used for this purpose soft cast iron is decidedly to be preferred): this tool must [p020] be supplied with the finest washed powder till the lens is completely polished. During the process of grinding, the stone should be examined by a magnifying lens, to ascertain whether the figure is truly spherical; for it sometimes will occur that the edges are ground quicker than the centre, and hence it will assume the form of a colloid, and thus be rendered unfit for microscopic purposes.
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 180th of an inch, while that of a diamond, worked in the same tools, would be only the 1200 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 120th 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.
[3] It seems generally admitted that, within a certain range of power not exceeding that of a lens of 120th of an inch focus, the beauty and truth of the vision given by the new compound microscopes cannot be equalled by that of any single instrument, at least of glass. It is no less true, however, that the picture of the compounds, however perfect, is not like a real object, will not admit of amplification beyond a certain point with advantage. Under the action of very deep eye-glasses, the image of opaque objects especially, first loses its strong, well-determined outline—then grows soft and nebulous, and finally melts away in shadowy confusion. Let the experiment be made of raising the power of a compound up to that of a 160 inch lens—then try it against the single microscope of that power (having, of course, the utmost opening the nature of the object viewed will permit). The observer, if open to conviction, will soon be taught the superior efficacy of the latter—for it will show the lines on the dust of Menelaus with such force and vivacity, that they will always be apparent without any particular management of the light—nor can their image be extinguished by causing the illumination to be directed truly through the axis of the lens (as it always may in the compounds). A due consideration of the teeth and inequalities on the surface of a human hair, together with the transverse connecting fibres between the lines on the scales of the curculio imperialis, viewed as opaque objects, will suffice to complete the illustration of the subject; though the last object is not to be well seen by that kind of light which is given by silver cups—and a single lens of 160 inch focus can of course have no other. The effectiveness and penetrating faculties of simple magnifiers are invariably increased by an accession of power however great—that of compounds seems to be deteriorated beyond certain limits. An opinion may be hazarded that the achromatics and reflectors yet made do not really surpass the efficacy of equivalent single lenses, even of glass, when their power exceeds that of a 120 lens, from 120 to 140 the vision may be about equal—but from 140 upwards infinitely inferior.
The superior light of the single refraction can need no comment—and it is evident that there must be a degree of power at which that of the compounds will become too dim and feeble for vision,—while that of the single instrument will still retain a due intensity. For these reasons it is conceived that the close and penetrating scrutiny of lenses of diamond of perhaps only the 1200 inch focus, and an equal aperture (which their very low aberration would easily admit of,) must enable us to see further into the arcana of nature than we have yet been empowered to do. Glass globules of 1200 inch focus and indeed much deeper have been executed; but the testimony of lenses of diamond would certainly be far more respectable, and is at least worthy of trial and examination.—C.R.G.
[4] In Dr. Brewster’s treatise on new Philosophical instruments, Book 5, chap. 2, Page 403—Account of a new compound Microscope for objects of Natural History—is the following passage: “We cannot therefore expect any essential improvement in the single microscope, unless from the discovery of some transparent substance, which like the diamond combines a high refractive with a low dispersive power.” From which it seems certain that the Doctor never contemplated the possibility of working upon the substance of the diamond, though he must have been aware of its valuable properties.