In the process of manufacture of doubly aspheric Schwarzschild-aplanat reflecting microscopes, the calculation (Burch 1947, see Abstr. A855 of 1947) of the offence against the sine condition of the simpler singly aspheric semi-aplanat design, was invalidated by an algebraic mistake. This letter corrects the algebra and gives computer-tabulated plots of the offence against the sine contition (OSC) for some semi-aplanats of infinite tube length.