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be determined with sufficient accuracy for the use of practical petrologists, and they would then be able to study the microscopical structure of rocks in a more satisfactory manner than heretofore, and at once clear up a number of interesting questions, which, however, relate more to geological and mineralogical problems than to the construction and use of the microscope. I will not, therefore, further occupy your time in describing them, since I feel that I may have already made my address somewhat too special in my anxiety to point out a new direction in which the practical application of the microscope may be further developed.

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I must, however, not conclude without describing some applications of my method of study in the case of organic structures. There can be no doubt that it will enable us to decide several interesting questions connected with the constitution of shells. If sections were prepared specially for this purpose the measurements might be made with abundant accuracy. However, in order to test what may be done, I have merely used sections cut many years ago to show the organic structure. Though they are only about Too of an inch thick they enabled me to learn many interesting facts. Thus, for example, in the case of a shell of Pinna, cut nearly parallel to the prisms, it was easy to see that when they are cut somewhat obliquely only one system of the lines of the grating is divided, the separation being in the line of the axes of the prisms. It was also easy to see that one of the images is nearly, if not quite, unifocal, and the other very decidedly bifocal. I obtained for the index of the ordinary ray 1 63, and for that of the extraordinary 1.49. In the case of calcite these should be about 1.65 and 1.48.

In a section of the shell of Haliotis tuberculata occur in the outer layer certain transparent portions, which one might readily suppose were only calcite. This method of study, however, enabled me to prove that they are really aragonite, since certain portions give two well- marked bifocal images. Comparing together all the facts, they indicate that the substance has a powerful negative double refraction and two optic axes not much inclined to one another. The observed indices were 1.71, 1.69, and 1.55, the mean being 1.65. That for aragonite is 1.63, which is as close an agreement as could be expected from one single set of measurements with a section only of an inch in thickness.

These examples will, I trust, be sufficient to prove that it is possible even now to apply this method of study with success in the case of very thin sections. With improved apparatus and using sections specially prepared, there should be no difficulty in obtaining excellent results.

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II.—Description of Professor Abbe's Apertometer, with Instructions for its Use. By CARL ZEISS, of Jena.

(Read before the ROYAL MICROSCOPICAL SOCIETY, by JOHN E. Ingpen, Esq., December 5, 1877.)

PLATE II.

THE apparatus in question is intended to enable an exact measurement of angular aperture of any object-glass, dry or immersion, to be made, and to afford a definition of aperture, which is not limited by the maximum air-angle, which is independent of the medium in front of the lens, and which at the same time, by its theoretical signification, may afford a direct indication of the resolving power of an objective.

The principle of the method is stated by Professor Abbe in the following manner :-The lens is made to act as a telescopic objective by combining it either with the naked eye or with an auxiliary microscope equivalent to a terrestrial eye-piece, and by observing the images of external objects near the back focal plane of the lens. The angular field of the miniature telescope established in this way, is determined by observation, the real area of field in the microscopic action of the lens, or the central part of this area, being made to act as the area of aperture in telescopic vision. By this inversion the angular field in the telescopic action of the lens is made strictly identical with the angular aperture in its microscopic action. In order to get a determination of aperture not depending on the medium in which it is observed, the angular amount of the telescopic field is reduced, by a calculated scale, to a purely numerical value-the product of the sine of semi-aperture with the refractive index of the medium in which it is observed. This product is constant for different media (air, water, or balsam), and by its value in any objective indicates the limit of resolving power (the minimum distance of separable parts) in relation to the wavelength of light.

The apparatus consists of a semicircular disk of crown glass, 90 mm. (3.5 inches) in diameter, and 12 mm. (0.5 inch) in

DESCRIPTION OF PLATE II.

FIG. 1.-Plan of Apertometer, full size. a, silvered cover with transparent centre; b, b, blackened brass indices. The inner scale shows the air-angle, the outer scale the "numerical aperture," by which a direct comparison can be made between dry and immersion objectives.

FIG. 2.-Elevation, showing position of one of the indices b. The image of the point is made to coincide with the margin of the field of view.

FIG. 3.-Section of examining glass, showing the position of its achromatic lens and diaphragm.

FIG. 4.-Diaphragm of examining glass.

FIG. 5.-One of the indices shown in perspective.

thickness, polished on the cylindrical edge, and ground to an angle of 45° in the direction of the diameter. This disk being put on the stage of a microscope, the rays admitted by the cylindrical edge of the disk horizontally are directed into the axis of the microscope by total reflexion. The centre of the semicircle is formed by a little hole in a silvered cover cemented to the upper face of the disk.

Two indices of blackened brass with sharp edges, sliding on the periphery of the disk, afford visible marks for observing the limits of telescopic field, or microscopic aperture, of any objective.

On the upper face of the disk there are two engraved scales; one of them showing the angular semi-aperture for air, the other the numerical indication of aperture as stated above.

A 2-inch object-glass, with a specially adjusted diaphragm above the lens, is added to the apparatus. It is to be adapted to a drawtube applied within the microscope, in order to get the telescopic eye-piece necessary for measuring the higher power objectives.

The management of the apparatus is as follows:

The semicircular disk of crown glass is to be put on the stage of a microscope, and the objective, the aperture of which is to be measured (we will call it a), is roughly focussed to the little hole in the silvered cover-glass. In the case of an immersion lens a drop of water of course will be applied.

This done, the eye-piece of the microscope is taken off, without altering the position of the objective x. The naked eye, in looking down into the open tube, will now see above the objective a small air-image of the cylindrical edge of the glass disk and images of objects round the microscope, which are brought into the axis of the microscope by total reflexion.

If a is an objective of low power, from inch downwards, the naked eye is sufficient for observing the aperture. For this purpose the two indices of black brass are put to the edge of the glass disk, and moved to and fro until the points of them as seen in the image above a just touch the margin of the illuminated field; i. e. appear or disappear, the pupil of the eye being kept in a central position. The position of the indices is read by their straight edges on the innermost scale of the disk. The half sum of both readings will give the semi air-angle of the objective x. For systems of higher power the image above the objective is too small for observation with the naked eye. In this case an auxiliary microscope is necessary for this observation, which is got by means of the draw-tube. The lens belonging to the apparatus (we will call it B) is screwed to the draw-tube and combined with one of the ordinary eye-pieces. The auxiliary microscope thus obtained, is focussed to the image above named, by moving the draw-tube up and down until the edge of the disk is seen quite distinctly. Now

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