266 MICKOSCOPE however, to have been now fully ascertained by Pro fessor Abbe that it is only through such diffraction-spectra that the microscope can make us acquainted with the minutest structural features of objects, since, according to the calculations of Professor Helmholtz and himself (based on the constants of the undulatory theory), no amount of magnifying power can separate dioptrically two lines, apertures, or markings of any kind, not more than TsVo" f an mc h a P ar t. The visual differentiation or "resolution" of lines or other markings whose distance lies FIG. 13. Scale of Gnat, showing Beaded Markings produced by Diffraction from a Photograph by Colonel Dr Woodward. within that limit is entirely the result of " interference, "- the objective receiving and transmitting, not only dioptric rays, but the inflected rays whose course has been altered in their passage through the object by the peculiar disposi tion of its particles, and combining these rays injto a series of diffraction-spectra, the number and relative position of which bear a relation to the structural arrangement on which their production depends. If the objective be per fectly corrected, and all the diffraction-spectra lie within its field, these will be recombined by the eye-piece so as to form a secondary or " diffraction " image, lying in the same plane with the dioptric image, and coinciding with it, while filling up its outlines by supplying intermediate details. But where the markings (of whatever nature) are so closely approximated as to produce a wide dispersion of the inter ference-spectra, only a part of them may fall within the range of the objective ; and the recombination of these by the eye-piece may produce a diffraction-image differing more or less completely (perhaps even totally) from the real structure; while, if they should lie entirely outside the field of the objective, no secondary or diffraction image will be produced. And thus, while the general form of such an object as a diatom -valve may be correctly given in a dioptric image, its surface may appear quite unmarked under an objective of small aperture, however great its magnifying power, though covered with regularly disposed markings when seen through an objective of wider aperture with perhaps only half the magnifying power. It is obvious, however, that, while the dioptric image represents the actual object, the diffraction-image thus formed by the reunion of a portion of the interference pencils is only an optical expression of the result of their partial recombination, which may represent something entirely different from the real structure. For it has been proved experimentally, by placing finely-ruled gratings in the position of objects, and by limiting the apertures of objectives by diaphragms with variously disposed perfora tions, that the same arrangement of lines shall be presented to the eye by differently lined surfaces, and different arrangements by similarly lined surfaces, according to the numbers and relative positions of the reunited spectra. Hence it is clear that there must be an essential difference in character and trustworthiness between the their diffraction-spectra, 1 and that the confidence to be placed in the latter class of representations will be greater in proportion to the completeness of the recombination of the separated interference-spectra, which, again, will be proportional (accurate correction of the aberrations being assumed) to the aperture of the objective. 2 The combined advance of scientific theory and of practical skill in the application of it have now brought up the compound achromatic microscope to an optical per fection that renders it capable of actually doing almost everything of which, in the present state of optical theory, it can be regarded as capable. The resolution of Nobert s nineteenth band, having 112,595 lines to an inch, which was long regarded as the crux of microscopists, is now found so easy as to leave little room for doubt that, if a new test were obtainable having the minimum visibile of 118,000 lines to the inch, an oil-immersion objective would be found to resolve it. But the experience of the past makes it evident that, as no limit can be set to the advance of optical theory, results yet more remarkable may be still expected to arise, every such advance being turned to account by the practical skill which experience has now enabled the best constructors of achromatic ob- images dioptrically formed of the general outlines and larger details of microscopic objects and those representations of their finer details which are given by the recombination of jectives to attain. 3 The progressive improvements thus effected in the construction of microscopic objectives have been accompanied by other improve ments, alike in the optical and in the mechanical arrangements by which the best performance of these objectives can be secured; and it will be desirable now to describe in succession the most approved forms of the eye-piece, the objective, and the illuminating apparatus respectively, and then those of the instrument as a whole, point ing out the special adaptiveness of each to the requirements of different classes of scientific investigators. EYE-PIECES. It very early became obvious to those who were engaged is the achromatization of microscopic objectives that their best performance was obtained when the image given by them was further enlarged by the eye-piece known as the Huygenian, as having been devised by Huygens for his telescopes. It consists of two plano-convex lenses (EE and FF, fig. 4), with their plane sides towards the eye ; these are placed at a distance equal to half the sum of their focal lengths, or, to speak with more precision, at half the sum of the focal length of the eye-glass, and of the dis tance from the field-glass at which an image of the object-glass would be formed by it. A "stop" or diaphragm BB must be placed between the two lenses, in the visual focus of the eye-glass, which is, of course, the position wherein the image of the object will be formed by the rays brought into convergence by their passage through the field-glass. Huygens devised this arrange ment merely to diminish the spherical aberration ; but it was subse quently shown by Boscovich that the chromatic dispersion was also in great part corrected by it. Since the introduction of achromatic object-glasses for compound microscopes, it has been further shown that nearly all error may be avoided by a slight over-correction of these, so that the blue and red rays may be caused to enter the eye in a parallel direction (though not actually coincident), and thus to produce a colourless image. Thus let N, M, N (fig. 14) repre sent the two extreme rays of three pencils, which without the field-glass would form a blue image convex to the eye-glass at BB, and a red one at RR ; then, by the intervention of the field-glass, a blue image concave to the eye-glass is formed at B B , and a red 1 Thus it is still a moot point whether the microscopic appear ances seen in the siliceous valves of diatoms (figs. 8-11) are the optical representations of elevations, depressions, or perforations, or of internal molecular arrangements not involving any inequality of surface.
- This doctrine was first fully developed by Professor Abbe in the
Archiv fur Microsk. Anatomic, vol. ix. (1874), and is more fully ex pounded in his subsequent contributions to Jour. Roy. Micros. Soc. See also the papers of Mr Stephenson and Mr Crisp in that journal, and in the preceding Monthly Microscopical Journal. 3 Any good workman can now make by the dozen such small-angled J inch objectives as Mr A. Ross produced with much pains and labour fifty years ago. It was not until 1844 that, with the honourable emulation of surpassing what Professor Amici had then accomplished, he produced a T V inch of 135, which, by taking advantage of some
very heavy flint-glass he had, he afterwards increased to 170.