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This stronger inclination φ₂ o v e r c o r r e c t s the astigma- tism of the incoming beam of light end we get therefore a residual astigmatism 7)

We get another parameter for this residual astigmatism: a difference between the cutting-lengths of meridional and sagittal rays p′_m and p′_s , called 'astigmatical cutting-lengths difference', which will be 8) wherein F_m is the meridional equivalent focal-length of the system, calculated after the well known formula in fig.1.

To get, the numerical value of astigmatism in seconds of arc, we have to multiply ξ by the factor 206265. Counting with the slide rule is of sufficient accuracy. f₂ has to be introduced with negative sign. At above mentioned fundamental system the numerical value of the overcorrected astigmatism results with -30 seconds of arc.

The astigmatical cutting-length-difference k goes together with an astigmatical focus-length-difference' , that is a difference between the meridional and sagittal equivalent focal-lengths of the system. While the equivalent meridional focal- and cutting-lengths can be com- puted with aid of the formulae 9) 10)

(note: f2 is negative) the sagittal values of these dimensions must be computed by aid of the following analytical formulae ( accuracy wanted 5 -6 places)

11) sagittal focal length of primary 12) sagittal residual cone 13) sagittal cutting length

14) sagittal radius of the beam of rays on the secondary
15) convergence of sagittal rays in the second focus

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