It is demonstrated on the basis of the Dirac equation that quarks cannot be confined by a vector gluon potential of the form(r/r 0)a or[ln(r/r 0]a, a>0, if the quark-gluon interaction conserves parity. In order to confine quarks with the parity-conserving interaction, the effective gluon potential must be a pseudovector or a scalar. These are shown in a simple Yang-Mills field with theSU(2) group.

Abstract.Growing interest in the origin of life, the physical foundations of biological theory, and the evolution of animal social systems has led to increasing efforts to understand the processes by which elements or living systems at one level of organizational complexity combine to form stable systems of higher order. J. Bronowski saw the need to extend or reformulate evolutionary theory to deal with the hierarchy problem and to account for the evolution of systems of “stratified stability.” The hierarchy problem has (...) become a matter of great interest also in nonequilibrium thermodynamic theory.An effort is made here to develop an abstract, phenomenological model, based on the laws of thermodynamics, to account for the origin and hierarchical evolution of living systems. It is argued that the principle of minimum entropy production, developed by I. Prigogine, applies generally to all thermodynamic systems and processes and is implicit in an extended and more complete formulation of the second law of thermodynamics. From this are derived a thermodynamic criterion and a principle of thermodynamic selection governing the formation of stable systems of “elements” of various levels of organization. Thermodynamic selection gives rise to the creation of “elements” having increasingly “open” characteristic structures which may combine spontaneously to form “social” or crystalline systems capable of growing and reproducing themselves through processes of fissioning or budding. Such simple, self‐reproducing systems are capable of evolving by natural selection, which is seen to be a special case of the more general process of thermodynamic selection. The principle of natural selection, thus formulated, has the character of a fundamental physical law. Self‐reproducing systems with suitably open hereditary programs may combine to form stable social systems, which may grow and reproduce as a unit. In this way self‐reproducing systems of increasing hierarchical order, size, and organizational complexity may evolve through processes of thermodynamic (natural) selection. Some implications of this open‐ended model and opportunities for testing its empirical and theoretical utility are explored. (shrink)

So far as I am aware, the commentators on the above passageall say that it is imitated from Euripides, Bacchae 492 sqq., and the commentators on Euripides, loc. cit., agree. It seems to me, however, that there is reason to suppose them all wrong; not of course that there is no connexion between the two passages, for there most obviously is, but that Horace is not imitating the Greek directly, but an imitation or adaptation of it by Pacuvius.

Professor D'Arcy W. Thompson has recently revived a conjecture of Lauth on Geoponica, XIII, 8, 1, which runs as follows: εις οκ σονται ν χωρ ν νθιονἢ ρτεμσιον ἢ βρτονον περ τν πα$$υλιν υτεσς. τος δ ντας λσεις ν . The conjecture is that ντας is the Egyptian hontasu, ‘lizard.’ That this would make sense is obvious; but the usage of the Geop. itself, to say nothing of other authors, indicates that the word is simply what it appears to be, (...) namely the pres. part, of εμ. Thus we find in X, 46 τ ςκα σκληκας ¿ π¿ισειν μλλων φυτεειν μπξς σκλλ τν κλδ¿ν, τ¿ς δ ντας ναιρες ν κ.τ.λ. Here the explanation ‘lizards’ would hardly be reasonable; still more cogent, however, is XII, 8, 2–3, ¿κ σονται … τς δ οσας κμπας διαθερς, where no such conjecture is possible. Not dissimilar is XII, 19, 9, τς τε γρ οσας ψλλας θερεικα λλας οκ γενσθαι. All these extracts are taken from authors of the second and third centuries A.D., though we have no means of knowing how closely their actual wording is followed; it is therefore in point to cite a passage of Galen, the opening paragraph of the tractate περ αρσεων Medicine, he says, has for its aim health, and a physician must know how to bring about health if absent and preserve it if present . καλεται δ, he continues, τ μν ργαζμενα τν μ οσαν γειατν τε καβοηθματα, τ δ φυλττοντα τν οσαν γιειν διαιτματα. In other words, ὢν can be used in much the same sense as παρν. This is no novelty of Roman times, for we may compare, for instance, Soph. Ant. 1109, ο ' ντες ο τ'πντες, and El, 305 τς οσας … κα τς ποσας λπδας. (shrink)

The Gods and Typhon.—The story of how the gods took bestial shape to hide from the fury of Typhon is several times told in Hellenistic and Latin authors. There seems no room for doubt that it is an aetiological myth, intended to explain the cult of beasts in Egypt, and also, in one or two versions, the sacredness of fish in Syria. That in one form, that given by Antoninus Liberalis, it goes back to Nikandros is reasonably certain. The doubtful (...) point, to my mind, is whether it can be traced much further, and, in particular, whether it was known to Pindar, as is commonly assumed. The authority for supposing that he knew and referred to it is a single passage of Porphyry, de abstinentia III. 16 . It runs: Πίνδαρος δ ν προσοδίοις παντας τος θεος ποίησεν τε ύπ Τυνος διώκοντα οủκ νθρώποις όμοιωθέντας λλ τοις λοις ζοις έρασθέντα δ Πασιάης Δία γενέσθαι μν ταρον νν δ ετν και κύκνον. (shrink)

The purpose of this paper is to indicate the slightness of the foundation on which a commonly received doctrine about Roman funerals rests, and to discuss a point in connexion with the ritual of funera acerba.

Not a little speculation has been expended on the Genius in ancient and modern times. I propose very briefly to recapitulate the known facts about him, examine the chief explanations, and give what I consider the true one.

It is not without a certain feeling of surprise that I find the fragment preserved by Strabo VIII. 3, 20, and somewhat doubtfully ascribed by him to Stesichoros, still commonly attributed to that writer. As the purpose of this note is to give what seem to me cogent reasons for holding that no poem of such a metre and content could be by an author of any possible date earlier than Alexandrian times, I cite the passage of Strabo in full. (...) It runs as follows, and is part of an argument for the existence of an ancient city called Samos in Elis. (shrink)

The publication of Dr. Warren E. Blake's edition of the romance of Chariton has at last made it possible to know what the tradition of the text amounts to and form some opinion of its principal weaknesses. That these include lacunae will be obvious to anyone who even glances through his apparatus criticus; I think there are at least three which neither he nor any of the former editors has noted. The supplements I propose are of course mere examples of (...) how they might be filled; their existence seems pretty certain, but no more than the general sense of what is missing is likely to be got unless some new papyrus or other unexpected find puts us in possession of more evidence. (shrink)

To add without good reason to the already enormous literature surrounding the most fascinating and puzzling of all Vergil's works ought, nowadays, to be regarded as an offence against learning. My excuse for this article is that even the latest work on the subject, Ed. Norden's charming monograph, Die Geburt des Kindes , appears to me wrong on one important point, inadequate on another.

The following lines are a famous crux: τ μν τι βασιλες σσ μεγαλν πολων ει συγγενς φθαλμς αδοιτατον γρας τε τοτο μειγνμενον φρεν. The reading is that of all MSS., save for the necessary correction αδοιτατον for αδοιςτατον, which will not scan. I have purposely left it without punctuation. The core of the difficulty of course is the word φθαλμς Farnell, it seems to me, has made it abundantly clear that this cannot be literal, for, apart from the oddity of (...) the epithet συγγενς in such a context, to take it as meaning the actual physical eye of Arkesilas involves giving ει the impossible meaning ‘sees’. But the metaphorical meaning is not much easier. A person or group of persons can be the ‘eye’, that is to say the most precious part, of something, as the Emmenidai were the ‘eye of Sicily’, Ol. ii, 10, Amphiaraos the ‘eye’ of Adrastos' army, Ol. vi, 16, the eldest or only son, or even the presence of the master, the ‘eye’ of the house , a child the ‘eye’—we should perhaps say ‘light’—of his mother's life, Eurip. Andr., 406, and perhaps, for the interpretation is not too certain, a chosen band of Athenians the ‘eye’ of Theseus' land, Aesch., Eumen., 1025. In these instances we may I think acquiesce in Groeneboom's remark on Pers., loc. cit., that ‘eye’ is used to signify the most precious or noble part of something, its glory. (shrink)