scholiast defines the _lemures_ as “the wandering shades of men who died before their normal time and are hence redoubtable.”[305] Even today popular belief in many countries attributes a maleficent power to the spirits of those who have died a violent death. These disquieting superstitions acquired new force through the teachings of astrology, which by incorporating them in its system gave them a doctrinal foundation. Astrology spread the belief, which was and is common to all ancient and modern peoples of the East, that each soul has a predetermined number of years to spend on earth. The _mathematici_ multiplied calculations and methods in order to be able to predict the instant of death predetermined by the horoscope. “This is the great work of astrology, held by its adepts to be its most difficult and by its enemies to be its most dangerous and blameworthy operation.”[306] But by an internal contradiction this pseudo-science admitted that the natural end could be hastened by the intervention of a murderous star (ἀναιρέτης): Saturn and Mars can in certain positions call forth sudden death by accident, killing, execution. A fragment attributed to Aristotle asserts that a Syrian mage predicted to Socrates that he would meet such a fate.[307] Sometimes the maleficent planets tear a nursing child from its mother’s breast before a single revolution of the sun has been accomplished. All astrological treatises devote chapters to these “unfed” children (ἄτροφοι) and also to the _biothanati_ whose life has been interrupted by misfortunes of any kind. Petosiris was even concerned to discover—Ptolemy declared such preoccupation to be ridiculous[308]—what the stars reserved until the end of their life for those who had gone through only a portion of it. The texts which have been preserved—and often expurgated—by the Byzantines give no more than a bare indication of astral influences on the lot of men. In antiquity other more religious and more mystical works doubtless existed in which the inauspicious action of the murderous star, still affecting after death the souls torn from their mortal wrappings, was shown. Pythagorism, which was closely connected with astrology, took possession of these ideas and adapted them to its speculations. According to this philosophy one and the same harmony presided over all physical phenomena and was, like music, subject to laws of number. These laws therefore were at work during pregnancy, and a complicated arithmetic was employed to show by a multiplication of days that a child might be born after seven or nine months with power to live, but not after eight, for such was the strange doctrine of the sect. Thus gestation became a melody in which abortion was a false note.