  The techniques used in this paper are based on the exterior calculus of
Maurer-Cartan forms, and Weingarten surfaces are used to illustrate the methods
that apply to quadratic exterior equations with constant coefficients.
Isothermic {\it surfaces of constant astigmatism} (non-linear Weingarten
surfaces whose difference of principal curvatures is a constant) are shown to
represent dual surfaces of isothermic surfaces which satisfy the relation $H +
\alpha K = 0$.
