par-axial rays; consequently, spherical aberration must be eliminated for two colors, and if this be impossible, then it must be eliminated for those particular wavelengths which are most effectual for the instrument in question (a graphical representation of this error is given in m. von rohr, theorie und geschichte des photographischen objectivs). the condition for the reproduction of a surface element in the place of a sharply reproduced point — the constant of the sine relationship must also be fulfilled with large apertures for several colors. e. abbe succeeded in computing microscope objectives free from error of the axis point and satisfying the sine condition for several colors, which therefore, according to his definition, were aplanatic for several colors; such systems he termed apochromatic. while, however, the magnification of the individual zones is the same, it is not the same for red as for blue; and there is a chromatic difference of magnification. this is produced in the same amount, but in the opposite sense, by the oculars, which abbe used with these objectives (compensating oculars), so that it is eliminated in the image of the whole microscope. the best telescope objectives, and photographic objectives intended for three-color work, are also apochromatic, even if they do not possess quite the same quality of correction as microscope objectives do. the chromatic differences of other errors of reproduction seldom have practical importance.