Corrections have to be applied to the readings of protected and unprotected reversing thermometers because they are read at a temperature that differs from that at the time of reversal. In deriving these corrections it is generally assumed that Feruglio's (1912) equation [(5) below] is exact. It is shown here that Feruglio's equation is not quite exact, but a close approximation. From this equation practical formulae, equations (6) and (8) below, can be derived very simply without further sacrifice of accuracy.