at Cambridge, and to my former pupil, Mr H. P. Richards, now Fellow and Tutor of Wadham College, Oxford; but above all to Mr J. S. Reid, whose name is well known to scholars from his excellent editions of the Academica and other works of Cicero, and to my old and valued friend Mr H. J. Roby. The help which I have received from the two latter is only imperfectly represented by the additions and corrections marked with the signature R., in the case of those supplied by Mr Roby, and J. S. R., in the case of those supplied by Mr Reid. Many of my own notes have been modified, and perhaps more should have been, in deference to their candid and searching criticism.

The remaining volume will, I hope, be completed for publication during the course of next year.

April, 1880.

The elementary contraries, hot, cold, moist, dry, are separated from this first matter by virtue of the eternal movement belonging to it; thus are produced the four elements; the earth was in the form of a cylinder, self-poised, in the centre of the universe; round it was air, and round that again a fiery sphere which was broken up so as to form the heavenly bodies. As all substances are produced out of the Infinite so they are resolved into it, thus 'atoning for their injustice' in arrogating to themselves a separate individual existence. The Infinite is divine, containing and directing all things: divine too are the innumerable worlds which it is ever generating and re-absorbing into its own bosom. (N. D. 1 25.)

After Anaximander comes Anaximenes, also of Miletus, who is supposed to have flourished about 520 B. C. While his doctrine approaches in many respects to that of Anaximander, he nevertheless returned to the principle of Thales in so far that he assumed as the apxý, a definite substance, Air, in contradistinction to the indefinite άπeɩрoν of his immediate predecessor. Air is infinite in extent and eternal in duration. It is in continual motion, and produces all things out of itself by condensation and rarefaction, passing through successive stages from fire downwards to wind, cloud, water, earth and stone. As man's life is supported by breathing, so the universe subsists by the air which encompasses it. We are told that Anaximenes gave the name of God both to his first principle Air, and to certain of its products, probably the stars. (N. D. I 26.)

The greatest of the Pre-Socratic philosophers, Heraclitus of Ephesus, known among the ancients as the obscure and the weeping philosopher, was a little junior to Anaximenes. Following in the steps of his predecessor, he held that it was one and the selfsame substance which by processes of condensation and rarefaction changed itself into all the elements known by us, but he preferred to name this from its highest potency fire, rather than to stop at the intermediate stage of air. But the point of main interest with him was not the original substance, but the process, the everlasting movement upwards and downwards, fire (including air), water, earth; earth, water, fire. All death is birth into a new form, all birth the death of the previous form. There is properly no existence but only 'becoming,' i. e. a continual passing from one existence into another. Each moment is the union of opposites, being and notbeing: the life of the world is maintained by conflict, Tóλeμos aτp

πάντων. Every particle of matter is in continual movement. All things are in flux like the waters of a river. One thing alone is permanent, the universal law which reveals itself in this movement. This is Zeus, the all-pervading reason of the world. It is only the illusion of the senses which makes us fancy that there are such things as permanent substances. Fire exhibits most clearly the incessant movement and activity of the world: confined in the body it constitutes the human soul, in the universe at large it is God (the substance and the process being thus identified).

Heraclitus is the first philosopher of whom we read that he referred to the doctrines of other philosophers. He is said to have spoken highly of some of the seven Wise Men, but condemned severely Pythagoras and Xenophanes as well as the poets Hesiod, Homer and Archilochus. Though I agree with Ueberweg in classing him with the older Ionics, yet his philosophy was no doubt largely developed with a reference to the rival schools of Italy.

In the N. D. allusion is twice made to the obscurity of Heraclitus (174, III 35), but he does not appear in the catalogue of philosophers criticized by Velleius, and this though Philodemus had certainly treated of him, as we may see from the allusions in the Fragments (Gompertz, pp. 70, 81). The reason for this omission is probably that, his philosophy having been incorporated into the Stoic system, it was unnecessary to discuss it separately. See Hirzel, p. 7 foll., and N. D. 111 35, 1 74.

We must now cross the water with Pythagoras of Samos, born 582 B.C., who settled at Crotona in Italy, 529 B.C., and there founded what is known as the Italic school. He seems to have found in the mysteries and in the Orphic hymns the starting point which Thales had discovered in Homer; and there can be little doubt that his doctrine and system were also in part suggested by his travels in Egypt. He established a sort of religious brotherhood with strict rules and a severe initiation, insisted on training in gymnastics, mathematics and music, and taught the doctrines of immortality and of the transmigration of souls, and the duty of abstaining from animal food. He is said to have committed nothing to writing himself, but his doctrines were religiously guarded by his disciples (cf. N. D. 1 10), and recorded by Archytas and Philolaus, the latter a contemporary of Socrates.

The new and startling feature in the Pythagorean philosophy

as opposed to the Ionic systems, was that it found its apxý, its key of the universe, not in any known substance, but in number and proportion. This might naturally have occurred to one who had listened to the teaching of Thales and Anaximander. After all it makes no difference, he might say, what we take as our original matter, it is the law of development, the measure of condensation which determines the nature of each thing. Number rules the harmonies of music, the proportions of sculpture and architecture, the movements of the heavenly bodies. It is Number which makes the universe into a κóσμos, and is the secret of a virtuous and orderly life. Then by a confusion similar to that which led Heraclitus to identify the law of movement with Fire, the Pythagoreans went on to identify number with substance. One, the Monad, evolved out of itself Limit (order) and the Unlimited (freedom, expansiveness), the Dyad; out of the harmonious mixture of these contraries all particular substances were produced. Again, One was the point, Two the line, Three the plane, Four the concrete solid (but from another point of view, as being the first square number, equal into equal, it was conceived to be Justice). Yet once more, One was the central fire, the hearth of the universe, the throne of Zeus, round which revolved not only the heavenly bodies, but the earth itself. The Decad is the ordered universe surrounded by its fiery envelope. The Pythagorean doctrine of the soul and of God is variously reported. Zeller thinks that Cicero's representation belongs to the later teachers, and not to Pythagoras himself, as it is not supported by Plato and Aristotle. If we may trust the oldest accounts, there does not seem to have been any close connexion between the religious and philosophical opinions of Pythagoras. We are told that he believed in One God eternal, unchangeable, ruling and upholding all things, that the soul was a 'harmony,' that the body was its prison, in which it was punished for past sin and disciplined for a divine life after death, that those who failed to profit by this discipline would pass into lower forms of life, or suffer severer penalties in Hades (N. D. 1 27, 74, III 27, 88).

The second of the Italic schools was the Eleatic, founded by Xenophanes of Colophon in Asia Minor (b. 569 B.C.), who migrated to Elea in Italy about 540 B.C. While the Pythagoreans strove to explain nature mathematically and symbolically, the Eleatics in their later developments did the same by their metaphysical abstractions. Xenophanes himself seems to have received his first philosophical

impulse in the revulsion from the popular mythology. He condemned anthropomorphism and polytheism altogether, and said that Homer and Hesiod had attributed to the Gods conduct which would

have been disgraceful in men. God is one, all eye, all ear, all understanding; he is for ever unmoved, unchangeable, a vast allembracing sphere. See N. D. 1 28. It is disputed whether the last expression is to be taken literally, implying that the universe is God, or whether it is a metaphor to express God's perfection and omnipresence. The chief representative of the Eleatic School is Parmenides (b. 515 B.C.). He disengaged the doctrine of Xenophanes from its theological form, and ascribed to Being what his predecessor had ascribed to God. His philosophy is the antithesis of that of Heraclitus. While Heraclitus said all is motion and change, the appearance of fixity is merely illusion of the senses; Parmenides asserted, with distinct reference to him, that all that exists has existed and will exist the same for ever, that it is change and multiplicity which is illusory. It is only by thought we can become conscious of the really existent; being and thought are the same, sense can only give rise to uncertain opinion. In such language we see partly a protest against the vagueness of the conception of development or becoming,' by which the Ionic philosophers endeavoured to explain the origin of things, 'You say fire becomes water, but each thing is what it is, and can never be otherwise;' partly an idea of the indestructibility of matter; partly an anticipation of the later distinction between necessary and contingent truth; thus one point dwelt upon by him was the impossibility of any separation of parts of space.

But though truth only belonged to the world of real existence, Parmenides condescended to give his romance of nature for the benefit of those who could not penetrate beyond the world of phenomena. He begins with two principles, light and darkness, also called fire and earth, or male and female; and supposes all things to proceed from their mixture. The existing universe consists of a central fire, the seat of the presiding Deity, and of several concentric rings of mingled light and darkness, bounded on the outside by a wall of flame. The first-born of Gods was Love, by whom the union of opposites is brought about. In this we may trace a reminiscence of the Hesiodic "Epws (N. D. 1 28).

Zeno of Elea (b. 490 B.C.) is chiefly known from his arguments showing the absurd consequences of the ordinary belief in the