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 a be a real positive quantity and ω a root of unity, then a is the amplitude of the product aω. In elliptic integrals, the amplitude is the limit of integration when the integral is expressed in the form $\int _{0}^{\phi }{\sqrt {1-{\mbox{N}}^{2}\sin ^{2}\phi \,d\phi }}$. 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.)