A more speculative work was his _Tripoliticus_, arguing that the best constitution ought to be compounded of the three species, monarchic, aristocratic, and democratic, as in Sparta. Only then would it be sure to last. Polybius accepted the principle of the Mixed Constitution, but found his ideal in the constitution of Rome, which later history was to prove so violently unstable. Cicero, _De Republica_, takes the same line (Polyb. vi. 2-10; Cic. _De Rep._ i. 45; ii. 65). Dicaearchus treated of similar political subjects in his public addresses at Olympia and at the Panathenaea. We hear more about his work on the history of literature, though his generation was almost the first to realize that such a subject had any existence. He wrote _Lives of Philosophers_--a subject hitherto not considered worth recording--giving the biographical facts followed by philosophic and aesthetic criticism. We hear, for example, of his life of Plato; of Pythagoras (in which he laid emphasis on the philosopher's practical work), of Xenophanes, and of the Seven Wise Men. He also wrote _Lives of Poets_. We hear of books on Alcaeus and on Homer, in which latter he is said to have made the startling remark that the poems 'should be pronounced in the Aeolic dialect'. Whatever this remark exactly meant, and we cannot tell without the context, it seems an extraordinary anticipation of modern philological discoveries. He wrote on the _Hypotheses_--i. e. the subject matter--_of Sophocles and Euripides_; also on _Musical Contests_, περὶ Μουσικῶν ἀγώνων, carrying further Aristotle's own collection of the _Didascaliae_, or official notices of the production of Tragedies in Athens. The book dealt both with dates and with customs; it told how Skolia were sung, with a laurel or myrtle twig in the hand, how Sophocles introduced a third actor, and the like. In philosophy proper he wrote On the Soul, περὶ ψυχῆς. His first book, the _Corinthiacus_, proved that the Soul was a 'harmony' or 'right blending' of the four elements, and was identical with the force of the living body. The second, the _Lesbiacus_, drew the conclusion that, if a compound, it was destructible. (Hence a great controversy with his master.) He wrote περὶ φθορᾶς ἀνθρώπων, on the _Perishing of Mankind_; i. e. on the way in which large masses of men have perished off the earth, through famine, pestilence, wild beasts, war, and the like. He decides that man's most destructive enemy is Man. (The subject may have been suggested to him by a fine imaginative passage in Aristotle's _Meteorology_ (i. 14, 7) dealing with the vast changes that have taken place on the earth's surface and the unrecorded perishings of races and communities.) He wrote a treatise against _Divination_, and a (satirical?) _Descent to the Cave of Trophonius_. He seems, however, to have allowed some importance to dreams and to the phenomena of 'possession'.