To Apollo

Title. Some manuscripts have the title (τοῦ αὐτοῦ) Ὁμήρου ὕμνοι ɛἰς Ἀπόλλωνα, others the singular ὕμνος. But the plural occurs at the head of some other hymns, and is simply a general title of this collection, not evidence that this hymn was regarded in antiquity as two separate poems.

Prelude. I shall sing of Apollo, whose entry to Zeus's house causes the gods to spring up in fear, as he draws his shining bow. Leto alone remains beside Zeus. She unstrings his bow, closes his quiver, and taking it from his shoulders she hangs bow and quiver against a pillar of Zeus's hall, and leads him to his seat. Zeus offers him nectar and greets him, and the other gods do likewise. Then they take their seats again. And Leto rejoices to have borne a son who is so mighty an archer. Greetings to you, blessed Leto, because you bore such glorious children as Apollo and Artemis! To her you gave birth in Ortygia, to him in Delos, as you leaned against Mount Cynthus, close to the palm tree, by Inopus' streams.

These lines form a self-contained prelude, and could easily stand on their own as a hymn to Apollo, complete with his parents Zeus and Leto, and his sister Artemis. They announce the subject of the hymn, and immediately continue with a relative clause describing Apollo's entry to Zeus's palace on Olympus and his reception by the other gods, especially his parents Leto and Zeus.

THE HOMERIC HYMNS

Nature and purpose

The three poems studied in this book belong to a collection of thirty-three hymns in hexameter verse, composed in honour of ancient Greek gods and goddesses. Their title in the manuscripts is Ὁμήρου ὕμνοι. They vary considerably in length. In the collection as we have it, the four longest hymns, to Demeter (495 lines), Apollo (546 lines), Hermes (580 lines), and Aphrodite (293 lines), are preceded by the last section of a hymn to Dionysus, which originally must also have been a longer one. (For a possible reconstruction of this hymn see West (2001b); cf. also Dihle (2002) for a contrary view.) Of the others, the longest (H. 7, also to Dionysus) is fifty-nine lines, the shortest (H. 13, to Demeter) only three. Several deities are the subject of more than one hymn, and a few are short pieces composed of extracts from longer poems (13, 17, and 18 from the longer hymns to Demeter, the Dioscuri, and Hermes, and 25 from Hesiod's Theogony).

Most of these poems probably belong to the ‘Archaic’ period, i.e. between c. 700 and 500 bc, but some appear to be later in date. An Attic vase painting of c. 470 bc shows a boy holding a papyrus-roll, on which are written what appear to be the opening two words of Hymn 18.

The Central Thrust of This Book

A large class of theories in continuum physics takes as its starting point the balance laws for mass, for linear and angular momenta, and for energy, together with an entropy imbalance that represents the second law of thermodynamics. Unfortunately, most engineering curricula teach the momentum balance laws for an array of materials, often without informing students that these laws are actually independent of those materials. Further, while courses do discuss balance of energy, they often fail to mention the second law of thermodynamics, even though its place as a basic law for continua was carefully set forth by Truesdell and Toupin almost half a century ago.

This book presents a unified treatment of continuum mechanics and thermodynamics that emphasizes the universal status of the basic balances and the entropy imbalance. These laws and an hypothesis – the principle of frame-indifference, which asserts that physical theories be independent of the observer (i.e., frame of reference) – are viewed as fundamental building blocks upon which to frame theories of material behavior.

The basic laws and the frame-indifference hypothesis – being independent of material – are common to all bodies that we discuss. On the other hand, particular materials are defined by additional equations in the form of constitutive relations (such as Fourier's law) and constraints (such as incompressibility). Trivially, such constitutive assumptions reflect the fact that two bodies, one made of steel and the other of wood, generally behave differently when subject to prescribed forces – even though the two bodies obey the same basic laws.

Throughout this book:

1. (i) Lightface Latin and Greek letters generally denote scalars.

2. (ii) Boldface lowercase Latin and Greek letters generally denote vectors, but the letters o, x, y, and z are reserved for points.

3. (iii) Boldface uppercase Latin and Greek letters generally denote tensors, but the letters X, Y, and Z are reserved for points.