The apertometer is an auxiliary piece of apparatus invented by Abbe, for testing the fundamental properties of objectives and determining their numerical and angular apertures. This accessory of the microscope involves the same principles as that of Tolles, which the late Mr. J. Mayall and myself brought to the notice of the Royal Microscopical Society of London in 1876. Abbe’s apertometer (Fig. 39) consists of a flat cylinder of glass, about three inches in diameter, and half an inch thick, with a large chord cut off, so that the portion left is somewhat more than a semicircle; the part where the segment is cut is bevelled from above downwards, to an angle of 45°, and it will be seen that there is a small disc with an aperture in it denoting the centre of the semicircle. To use this instrument the microscope is placed in a vertical position, and the apertometer is placed upon the stage with its circular part to the front and the chord to the back. Diffused light, either from the sun or lamp, is assumed to be in front and on both sides. Suppose the lens to be measured is a dry one-quarter inch; then with a one-inch eye-piece having a large field, the centre disc, with its aperture on the apertometer, is brought into focus. The eye-piece and the draw-tube are now removed, leaving the focal arrangement undisturbed, and a lens supplied with the apertometer is screwed into the end of the draw-tube. This lens, with the eye-piece in the draw-tube, forms a low-power compound microscope. This is now inserted into the body-tube, and the back lens of the objective whose aperture we desire to measure is brought into focus. In the image of the back lens will be seen stretched across, as it were, the image of the circular part of the apertometer. It will appear as a bright band, because the light which enters normally at the surface is reflected by the bevelled part of the chord in a vertical direction, so that in reality a fan of 180° in air is formed. There are two sliding screens seen on either side of the figure of the apertometer; they slide on the vertical circular portion of the instrument. The images of these screens can be seen in the image of the bright bands. _These screens should now be moved so that their edges just touch the periphery of the back lens._ They act, as it were, as a diaphragm to cut the fan and reduce it, so that its angle just equals the aperture of the objective and no more.