The last six columns of the table of optical glasses given above contain figures which define the manner in which each of the glasses named distributes the various sections of the spectrum. The columns C-D, D-F, and F to G′ give as already indicated the differences between the refractive indices for the C, D, F and G′ lines respectively; the smaller figures in the intermediate columns indicate the ratio of each of these differences to the mean dispersion of the glass. If all kinds of glass distributed the various portions of the spectrum in the same proportionate manner, merely differing in the total amount of dispersion produced, these figures would be identically the same for all glasses. In actual fact it will be seen that the figures differ very widely from one type of glass to another. A moment’s consideration will show that when two glasses are used in a lens for the purpose of achromatising one another, _i.e._, when one is used to neutralise the dispersion of the other, such achromatisation can only be perfect if these ratios (the relative partial dispersions) are the same for both glasses. To put the same statement in more concrete terms, if the spectrum produced by one glass is comparatively long-drawn out at the red end, relatively compressed at the blue end, while in the other glass the opposite relation holds between the two ends of the dispersion spectrum, it is evident that the two spectra can never be superposed in such a way as to entirely neutralise one another--the spectrum produced by the one glass will predominate and leave a residual colour at the blue end, while the other will predominate at the other end. In the case of lenses achromatised by the use of such glasses, there will always be a slight fringe of colour around the borders of the images which they produce. One of the aims which Abbé and Schott set themselves in the production of new varieties of optical glass was to obtain one or more pairs of glasses in which the relative partial dispersions should be as nearly alike as possible while the actual values of ν should differ as widely as possible. Some success in this direction was at first claimed by the Jena workers, but unfortunately some of the most promising glasses in this respect were found to be too unstable for practical use and had ultimately to be abandoned. At the present time the only pair of really perfectly achromatic glasses offered by the Jena firm is that tabulated below, and it will be seen that although the relative partial dispersions are very closely alike, the ν values of the two glasses only differ by 10, and at least one of these glasses is not readily obtainable in really satisfactory optical quality. On the other hand, practically perfectly achromatised lenses (generally known as “apochromatic”) have been produced, especially by Zeiss of Jena, for microscopic purposes, by the careful selection of glasses suited to each other in this respect.