A series of experiments ultimately brought to light a mineral substance, _Fluorite_, which, when combined in the proper proportion, one part to two of German crown and flint glass, was found to have the qualities looked for, and to possess different relations of a dispersive and refractive power. From Professor Abbe’s researches, begun in 1876, we have had the aperture of the objective greatly enlarged, and the homogeneous system brought into general use. Previous to this date the best made objective merely approximated to colour correction. Undoubtedly the chief object to be obtained was the removal or diminution of the secondary colour aberration. This, together with other residual errors Abbe pointed out in 1880, led to the improvement of the optical quality of the glass used in the manufacture of all optical instruments, the chief difficulties being surmounted in the Jena glass factory, whereby a complete revolution was effected in the microscopic objective. The apochromatic glasses of Zeiss, Powell, Beck, Ross, Watson, Swift, and other makers, in which the secondary spectrum has been totally eliminated, or only a negligible tertiary spectrum remains--that is to say, the objectives of these makers--are now corrected for three spectrum rays, and not two, as in the older objectives; and only those who look forward for making further discoveries in the intimate structure of bacilli or for resolving the finest diatom markings can be said to fully appreciate the importance and value of the investigations of the late Professor Abbe, and which have, so to speak, entirely changed old empirical views as to the value of high aperture, and demonstrated that high amplification, unless associated by proportionally high aperture, necessarily produces untrue images of minute structures. It was he also who introduced a practically perfect system of estimating apertures, known as the “numerical aperture notation,” by which not only can an accurate comparison be made of the relative apertures of any series of objectives, whether dry or immersion, but their resolving power under the various conditions of the kind of light employed. Their penetrating power and their illuminating power can now be estimated with mathematical exactness. [Illustration: Fig. 117.--Diagram of an Apochromatic Combination.]