metre is subdivided into ten spaces of ten microns each. There are thirteen of these lines at the beginning of the centimetre, the first tenth of a millimetre being measured from the mean of the first three to the mean of the eleventh, twelfth, and thirteenth. The scale is engraved on a piece of platin-iridium made by Matthey, and containing 20 per cent. of iridium.

Professor W. A. Rogers gives the results of a very elaborate "study" of the scale, which is now in the custody of the American Society of Microscopists, and available, under regulations, to "parties of eminent ability" for the comparison and verification of their standards. Three copies are to be made on glass, which will be lent out.

Microscopic Test-Objects.*-The correspondence on this subject between "Monachus" and Mr. E. M. Nelson has been further continued, the former finally accepting (as "that which was to be demonstrated") Mr. Nelson's admission that when he wrote that he had by particular means made the discovery of the "true structure' of Surirella gemma he did not mean the "ultimate true structure."

There is one point however in the correspondence left untouched, which we refer to because the misapprehension which Mr. Nelson was under on the subject has at one time or another been widely shared and we have no doubt is so still.

If we have a grating (fig. 38) it will, as we know, give rise to

diffraction spectra as in fig. 39. But if we stop off all the spectra except two nearest the central dioptric beam (say at the top and side) we shall still see the grating. Hence it has been supposed that only those spectra were really necessary for the image, or as Mr. Nelson puts it," the true structure can be seen without taking up all the diffraction spectra."

It cannot be too clearly borne in mind that this is an erroneous notion and that it is a fundamental point of the diffraction theory that if we are to see a true image of the object, all the diffraction spectra into which the original pencils were separated must be again gathered up and brought to the eye, so that wherever any of the diffraction spectra (up to the limit of vanishing intensity) are wanting, the image is incomplete. The absence of the spectra shut off may produce very considerable variations in the image, not only in the breadth of the lines and spaces, but otherwise.

*See Bibliography, infra.

Aperture and Resolution.-L. Wright, while agreeing in the utter impossibility of ever knowing by absolute observation the "true structure" of minute objects, yet thinks there is something in the objections to overmuch dependence upon the results of very oblique light.

Let us suppose we have an object whose true structure is something like fig. 40, explained or described as follows:

Let the black lines A A A denote strong ribs, or striations, or ridges 20,000 to the inch; B B lesser ridges midway between them, and CCC either valleys or fainter markings midway between these. A low-angled lens would show the black lines only; a good glass would bring out B B as well; a good immersion the faint dotted lines C C C. But even in this simple case these latter would certainly appear as lines; for the distances represented by the dots are far too minute for their spectra (transverse to the others) being included in any lens yet made. Let us, however, now suppose the real structure to be modified as in fig. 41, the second strongest markings B B being next

FIG. 41.

A B C CABC CA

AAA, but CCC altogether absent, and not as here shown. The second lens would, in this case, show only a slight thickening or blurring of the coarser striation A A A; but the immersion objective might show nearly the same image as that given by the previous structure, since the narrow intervals A B, A B, A B, would give the same spectra as if the gaps CCC were filled up. It is true the wider distances BA, BA, BA would, by their own spectra, strengthen the BB lines; but the dotted lines CCC would be created, and appear to show structure which did not exist.

But no microscopic structure really consists of absolute lines, and hence this is a very small part of the complicated problem. If, as we have supposed, AÃA are ridges, they will have some absolute breadth,

Engl. Mech., xxxviii. (1884) pp. 470-1 (2 figs.).

and these dimensions really constitute a still more minute set of lines, whose spectra are far beyond the collecting power of our lenses. Hence the reason why real lines, like Nobert's test-bands, can be truly "resolved" or photographed, though microscopic objects cannot. Supposing the objective can resolve lines of 100,000 to the inch, all it is capable of showing in an object is, that something-some variation of structure-occurs at regular intervals of 100,000 to the inch. If this is so, it will be shown as lines; but it is perfectly obvious that very rarely can it really be mere lines. It will have form of some kind; and every minute variation in light and shade due to that form, constitutes an infinitely minute set of distances, which will all cause their own spectra, too distant, if not too faint, to be gathered in.

Error may arise in yet another way. Lord Rayleigh has shown mathematically, and partially proved experimentally (by gratings eaten out in gelatine) that if an optical grating be composed (instead of white and black lines) of equally transparent narrow stripes, whereof each alternate one retards light half a wave-length more than its neighbours, the spectra are fourfold in brightness. Now these also would image lines, though falsely. The application to transparent microscopic objects need not be pointed out.

Yet the more we understand the true relations of these spectra, and their optical effects, the truer will our interpretations become, within, at least, the limits of microscopic vision, and the more certainly shall we be directed to methods of manipulation which may truly interpret the phenomena. Taking merely the theory of the matter, let us consider the case of fig. 41 where only the lines A A and B B really exist, but C C are apparent by the illusory spectra of the narrow spaces between A B, A B. It is plain we have means, if our suspicion as to the existence of C C C is awakened, of clearing it up. For we can stop off not only the central pencil, but those inner spectra which give us the coarsest intervals A A A. This will bring into stronger relief the spectra representing the next widest spaces, B A, B A, and thus we may correct the former result. Also it is obvious that any skilful manipulator with a knowledge of physical optics, by stopping off central pencils, and, when necessary, inner spectra, might bring into stronger relief the much fainter spectra caused by fainter and finer striations, which were before "drowned," as it were, in the coarser phenomena. Mr. Stephenson proved this in the case of P. angulatum, bringing out minute patterns, when the central pencil was stopped off, which had never before been seen.

It is also evident why so much is learnt from various incidence of the light; but it will also appear that this should be studied more gradually than most mirror arrangements permit. As a rule, microscopists adjust for one obliquity, and make their observation; then try another. It would rather appear that continuous observation under a steadily increased obliquity must be necessary to good interpretation; and that even then a competent knowledge of the physical phenomena of optical gratings is necessary, as well as a careful collation and comparison of the appearances with those presented

under similar treatment by coarser objects, of which true dioptric images can be obtained. But even then it will be only a matter of interpretation more or less correct. All we know of A. pellucida is, that there are striæ, or ridges, or something occurring at intervals of so many to the inch. It is obvious they cannot be mere lines, as they appear to us; but as any "form" must involve another set of lines of at least double the minuteness, and probably far more, what is there can never be known, except from analogy and comparison with larger diatoms. As a rule, we must get lines only in minute structures, and as a rule, that appearance is certainly false. Nevertheless, the variations in distance between the spectra under gradually increased obliquity, and their consequent image-results, appears the most likely general method of ascertaining the true proportions of distances between striæ not all equidistant, while the successive stopping out of the inmost and brightest spectra appears the most promising general method of revealing those fainter spectra which may lie hidden behind, and which reveal some periodic variation in structure at the distances of the apparent lines.

The Future of the Microscope. - Amongst the reports on the South Kensington Loan Collection of Scientific Apparatus is one by Prof. Abbe on the "Optical Aids to Microscopy," * the earlier part of which (pp. 383-91) is occupied with a general description of the stands, objectives, and other apparatus exhibited, with critical comments. The succeeding thirty pages are devoted to a consideration of "the facts which throw a light on the conditions of optical performance, and furnish hints in regard to further progress."

The author commences with expressing the opinion that no epochmaking advance in the way of an extension of the domain of microscopical perception is now possible, although there is still great room for improvement in other, and in a relative sense minor, respects. The curve of progress, after having risen abruptly for several decades,

* Hoffmann, A. W., 'Bericht über die wissenschaftlichen Apparate auf der Londoner Internationalen Ausstellung im Jahre 1876.' 8vo, Braunschweig, 1878. Cf. pp. 383-420, Abbe, E., Die optischen Hülfsmittel der Mikroskopie.'

It appeared to us, on a perusal of Professor Abbe's paper, that he had not given sufficient weight to the increase in aperture and resolving power obtained by the use of homogeneous immersion, but to our objections on that point he writes as follows:-"Your objection leaves out of sight the general point of view from which the question of further perfection of the Microscope is discussed here. When the article was written, the opinion was generally spread, still-even among microscopists-that it was only a question of time that the Microscope should display the molecules themselves. This opinion I had always in view during the whole discussion. Hence results the large standard applied by me in estimating and measuring progress. The increase of delineating power from 1.1 to 14 or 1.5 is an exceedingly small increase compared with the supposed increase from 1.1 to co. That half the wave-length in air is the approximate limit,' and that this will not be overcome in a considerable' extent is true, notwithstanding homogeneous immersion, having regard to the said standard of estimation. The important point is that the wave-length does constitute a limit; that the value of the wave-length may be reduced in some degree by media of higher refraction is the subordinate feature under the point of view of the paper."

appears to have a tendency towards an asymptote parallel to the base line.

A condensed and summarized statement is given of the theoretical principles on which the compound Microscope is based, including the author's now well-known views on the formation of the images of minute objects in microscopical vision, together with observations on the important function of aperture in the Microscope, and the increase of aperture obtained by immersion lenses as compared with dry.

The remainder of the paper is devoted to a consideration of the possible ways and means by which, in the future, new successes may be hoped for, "the most important practical advantage of a rational theory of the Microscope being that, destroying mere vague hopes, it enables a proper direction to be given to the aims of the inventor."

With regard to a still further extension of aperture beyond 1.5 (the refractive index of crown glass), the author suggests that it may be thought that in process of time transparent substances, available for the construction of objectives, will be discovered, whose refractive index will far exceed that of our existing kinds of glass, together with immersion fluids of similarly high refractive power, so as to give new scope to the immersion principle. What, however, he asks, will be gained by all this? We shall perhaps, with certain objects, such as diatoms, discover further indications of structure where we now see bare surfaces; in other objects, which now show only the typical striations, we shall see something more of the details of the actual structure by means of more strongly diffracted rays; but we should get on the whole little deeper insight into the real nature and composition of the minuter natural forms, even should the resolving power of the Microscope be increased to twice its present amount; for, whatever part of the structure cannot at present be correctly represented on account of its small size, will then also give an imperfect image, although presenting a somewhat higher degree of similarity than before. If, therefore, we are not to rest upon conjectures which surpass the horizon of our present knowledge (as, for instance, would be the expectation of the discovery of substances of considerably higher refractive power than has hitherto been found in any transparent substance), our progress in this direction in the future will be small, and the domain of microscopy will only be very slightly enlarged, the more so because every such advance, however great, will be but of limited utility to science, on account of very inconvenient conditions. For a given extension of the aperture can only render possible a correspondingly enhanced performance of the Microscope when the object is surrounded by a medium whose refractive index at least equals that aperture. If the Microscopes of the future should utilize the high refractive power of the diamond, all the objects would have to be imbedded in diamond, without any intervening substance. The result of this consideration is, therefore, that as long as aperture serves that specific function, which experiment and theory compel us to ascribe to it at present, there is a limit to the further improvement of the Microscope, which, according to the present condition of our knowledge, must be considered as insurmountable. The optics of the day have already so