--18--

If we shorten the second axis-distance Δ' computed for the coma-free device multiplying with the factor t = 0,8 we get an undercorrected coma β about one half of that of the anastig- matic device and an overcorrected astigmatism ξ and k approximately one half of that of the coma-free device. Both residuals are so brought to values, which can be eliminated at the same step by a simple plano-cornvex spherical lens, inclined for a certain angle φ3 along its sagittal diameter. The power of the lens can be chosen freely but a very convenient value will be f3 = 18 f1.

Its distance from the meridional focus, a1m, must be computed under supposing the new values after the formulae 7 -17. For the material of the lens we choose a light Boro Silicat-Crown with a medium refrac- tion index of about nd = 1,516 and a medium dispersion of about vd = 64.

The exact mathematical condition-formulae for the inclination φ3 of the spherical lens are very inconvenient for not-mathematicians because they lead to a solution of square equations. But such a com- putation is really unnecessary, because the exact value of φ3 can be get by adjusting likewise the exact inclinations φ1 and φ2 of the mirrors. At the end of this account the formulae will be given. Supposing our above mentioned fundamental system, we will get the inclination φ3 of a plano-convex lens with f3 = 18 f1, which elimi- nates the residual coma and the overcorrected astigmatism of our mirror-system, about 28°

This respectively strong inclination is admissible if the two surfaces of the lens are coated to avoid the loss of light owing to reflection ( the spherical corrector in the authors 'big one' is not coated and causes little trouble). The theoretical chromatical aberration of the very weak lens has proved negligible and injures neither visual nor photographic work. To avoid comatical spectrum, caused by the incli- nation of the lens, the lens will not be exactly centered but gets a little wedge of about 1.5 - 2 minutes of arc. To eliminate the last residual spectrum colors (over-or undercorrected) the lens will be re- moved perpendicularly to the secondary's beam of rays up or down. This displacement, got by adjusting, will be in any case very small. An adjusting way of ± 2/8″ will be sufficient.