O. Let W be a closed Riemann surface. A conformal self map of W will be called an automorphism. If G is a finite group of automorphisms of W, then the orbit space WIG is naturally a Riemann surface. In [1], [2] R. D. M. Accola proved certain formulas which relate the genera of W, WIG and W/H where H ranges over certain subgroups of G. He proved them using the Riemann-Hurwitz formula for the coverings WW/G and WW/H. The purpose of this note is to extend his results. In 1 we shall prove formulas

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... n the case of the Euler-characteristic of compact Hausdorff spaces on which a finite group G acts as the group of homeomorphisms. In 2 we shall prove a formula in the case of the signature of closed connected oriented generalized 4k-dimensional manifolds over the field of real numbers on which a finite group G acts effectively and orientation preservingly as the group of homeomorphisms.