# Page:EB1911 - Volume 01.djvu/946

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AMPHITRITE—AMPTHILL

Pompeii, its Life and Art (2nd ed. 1904), chap. 30; for the Colosseum, Middleton, Remains of Ancient Rome, ii. pp. 78-110, and Huelsen's art. “Flavium Amphitheatrum” in Pauly-Wissowa, Realencyclopädie. (H. S. J.)

AMPHITRITE, in ancient Greek mythology, a sea-goddess, daughter of Nereus (or Oceanus) and wife of Poseidon. She was so entirely confined in her authority to the sea and the creatures in it, that she was never associated with her husband either for purposes of worship or in works of art, except when he was to be distinctly regarded as the god who controlled the sea. She was one of the Nereids, and distinguishable from the others only by her queenly attributes. It was said that Poseidon saw her first dancing at Naxos among the other Nereids, and carried her off (Schol. on Od. iii. 91). But in another version of the myth, she then fled from him to the farthest ends of the sea, where the dolphin of Poseidon found her, and was rewarded by being placed among the stars (Eratosthenes, Catast. 31). In works of art she is represented either enthroned beside him, or driving with him in a chariot drawn by sea-horses or other fabulous creatures of the deep, and attended by Tritons and Nereids. In poetry her name is often used for the sea.

AMPLITUDE (from Lat. amplus, large), in astronomy, the angular distance of the rising or setting sun, or other heavenly body, from the east or west point of the horizon; used mostly by navigators in finding the variation of the compass by the setting sun. In algebra, if α be a real positive quantity and ω a root of unity, then α is the amplitude of the product αω. In elliptic integrals, the amplitude is the limit of integration when the integral is expressed in the form ${\displaystyle \int _{0}^{\phi }{\sqrt {1-N^{2}sin^{2}\phi \,d\phi }}}$. The hyperbolic or Gudermannian amplitude of the quantity x is tan-1 (sinh x). In mechanics, the amplitude of a wave is the maximum ordinate. (See Wave.)