Über die Achromasie optischer Systeme für mehr als zwei Wellenlängen

Achromatism for any number of k wavelengths in a system of k thin lenses is possible when the partial dispersions of the k glasses of these lenses have no linear dependency with another. Indeed this dependency is existent within the visible spektrum (Abbe). It is shown here that it is less actual with increasing distance of the considered wave length from visible lines, esp. in infrared. Thus achromatism for more than two wavelengths is possible with normal glasses provided that no more than two of them are in the visible. But technical possibilities for the realisation of such a multi-achromatic system are by far better when natural or artificial crystals for one lens at least or for two of them are used. Glasses with shortened dispersion in blue ("short flints") are useful too, but ask for special consideration.