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Inserting the above parameters in Eqs. (3.317) to (3.323) gives the result of Table 3.18 for the complete data of the system. The Schwarzschild constants v for the three mirrors show that all three are hyperbolic with eccentricities not excessive compared with normal 2-mirror solutions. The above data give exact correction for Case 9 in Table 3.3 of all four third order aberrations S/ , S//, Sm, S/V.

The complexity of the Eqs. (3.317) is instructive. We saw in ยง 3.2.4 that the third order theory of a 1-mirror telescope is trivially simple; that of a 2-mirror telescope considerably more complex. The 3-mirror formulation

Fig. 3.73. 3-mirror system due to Paul (1935), see also footnote on p. 324 concerning Mersenne

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