A system fulfilling this condition and free from spherical aberration is called " aplanatic " (Greek a-, privative, irXavrl, a wandering).
Abbe succeeded in computing microscope objectives free from error of the axis point and satisfying the sine condition for several colours, which therefore, according to his definition, were " aplanatic for several colours "; such systems he termed " apochromatic."
According to Abbe, a system can only be regarded as aplanatic if it is spherically corrected for not only one axial point, but when it also fulfils the sine-condition and thus magnifies equally in all zones a surface-element situated vertically on the axis at this point.
30.-0' is the virtual image on the notion of aplanatic points.
By experiment Abbe proved that old, good microscope objectives, which by mere testing had become so corrected that they produced usable images, were not only free from spherical aberrations, but also fulfilled the sine-condition, and were therefore really aplanatic systems.
This system will always be aplanatic. These objectives permitted a much larger aperture than a simple achromatic system.