We find the relationships among optical dielectric constant epsilon(infinity), activation energy E-ac, averaged atomic mass per a formula unit, Sigma(j)m(j)/N, volume V and transition temperature T-c for various type ion conductors with forms of E-ac=alpha/(epsilon(infinity)-beta), E-ac=A(o) + delta/[(Sigma(j)m(j)/N)-d], E-ac=A(v)/V-2/3, and In(T-c)=g-hIn(Sigma(j)m(j)), where alpha, beta, delta, A(o), d, A(v), g and h are constants depending on the kinds of conduction elements. We derive those proportional forms from a simple equation of motion under the assumption of ion hopping assisted by enhanced vibration displacement of host lattice. The enhancement is induced from the large fourth-order term of the host lattice potential originating from the electronic shielding effect of Coulomb force, heavy atomic mass of constituent ion, and volume expansion under the long-range periodicity of crystal structure. This mechanism is ascertained from characteristic phenomena of various kinds of conduction elements. For impurity-type H+-ion or defect conductor, the proportional form is shifted from that of superionic conductor because of weakened effect of host lattice vibration mode on H+-ion or O-ion defect. Photo-induced spectra of mobile ion in AgCl are understood, and a small quantum effect of H+ -ion is suggested. (C) 2009 Elsevier B.V. All rights reserved.