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 o a root of unity, then a is the amplitude of the product ao. 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.)