# 1911 Encyclopædia Britannica/Amplitude

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**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 . 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.)