It is not suggested that prayer could not exist without sacrifice. But where sacrifice did take place, the act of worship did not lie in the sacrifice alone, or in the propitiatory allocution that accompanied it, but in the two together. Footnote 12: Cf. Apollo Soter, Soph. O. T. 149, Dionysus Soter, Lycophr. 206, Zeus Soter, Aristoph. Plut. 1186, etc. Footnote 13: Max Müller, Lectures on the Science of Language, _passim_. The term is rarely used by recent investigators. Footnote 14: For the sacrificial act when addressed to gods, the word was θύειν; addressed to heroes, ἐναγίζειν. Herod, ii. 44. The color of the sacrificial animal for heroes was usually black, and no part of the flesh was eaten. Cf. Sch. Hom. Il. i. 459. Footnote 15: For heroes whose position in the state was as high as that of gods, we have only to refer to the eponyms of the Cleisthenic tribes at Athens, Theseus, Cecrops, Erechtheus, etc. Footnote 16: Local deities, such as Pelops at Olympia (Sch. Pind. Ol. i. 149), Archemorus at Nemea (Arg. Pind. Nem. i), Tlepolemus at Rhodes (Sch. Pind. Ol. vii. 146). Footnote 17: Cf. Suidas. s. v. Ἀναγυράσιος, Alciphro, iii. 58. Footnote 18: The doctrine of Socrates cited by Xenophon, Memor. iv. 7, represents popular Greek feeling on the subject of theological speculation. Footnote 19: Xenophanes of Colophon (sixth cent. B.C.E.) cited in Sex. Emp. adv. Math. ix. 193. The lines are frequently quoted, and are to be found in any history of philosophy. Footnote 20: A monotheistic or pantheistic tendency showed itself in the attempt on the part of poets like Aeschylus and Pindar to absorb the divine world into the personality of Zeno. Cf. Aesch. Heliades, 71: Ζεύς ἐστιν αὶθήρ, Ζεὺς δὲ γῆ Ζεὺς δ’ οὐρανός, Ζεύς τοι τὰ πάντα χ ὥτι τῶνδ’ ὑπέρτερον. Footnote 21: The solar myth theory was especially advocated by Max Müller in his various books and articles. Most of the older writers on mythology, _e.g._ in the earlier articles of Roscher’s Lexikon, accept it as an established dogma. There can be no reasonable doubt that the celestial phenomena of sun, moon, and stars exercised a powerful influence on popular imagination. Footnote 22: Dionysus came into Greece probably from Thrace and Macedon about the tenth century B.C.E. By the sixth century there was no Greek city in which he was not worshiped. As far as any center of his worship existed, it may be placed in Boeotia. Cf. Farnell, Cults of the Greek States, chs. iv. and v. Footnote 23: We find Aphrodite firmly established among Greek gods from the earliest times. It may be that the Semitic or Oriental connections which have been found for her (cf. Roscher, s. v. Aphrodite, Roscher’s Lex. i. 390-406) are due to the readiness with which she was associated with Oriental female deities. That fact, however, is itself significant. Footnote 24: