This is a supplement to the planetary, lunar and solar tables produced by Bryant Tuckerman (1962, 1964). These tables have proved an invaluable aid to historians of astronomy. An important usage is the dating of ancient and medieval astronomical observations, but the tables also have wide application in determining the accuracy of early measurements and calculations. This supplementary volume owes its origin to the discovery by the authors of significant errors in Tuckerman's tabular positions of Mars. They made a comparison between Tuckerman's positions for the Sun and planets and those computed from an integrated ephemeris. Only in the case of the longitude of Mars were errors found to be serious.