# 1911 Encyclopædia Britannica/Amplitude

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 $\int_0^\phi \sqrt{1-N^2 sin^2 \phi \,d\phi}$. 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.)