The Lindemann assumption of direct contact of neighboring atoms at fusion is replaced by the criterion that melting occurs when the root-mean-square amplitude of thermal vibration reaches a critical fraction ρ, presumed the same for all isotropic monatomic solids, of the distance of separation of nearest-neighbor atoms. The Debye-Waller theory of the temperature dependence of the intensity of Bragg reflection of x-rays is used, without further assumptions, to derive a generalized Lindemann law. In contrast to the Lindemann form, all physical quantities involved in this formulation are evaluated at the fusion point, and departure of the average energy of an atomic oscillation from the equipartition value is taken into account by the quantization factor of the Debye-Waller theory. If the Grüneisen constant γm of the solid at fusion is evaluated by its definition from the Debye frequency of the solid, use of the generalized Lindemann law and Clapeyron's equation permits one to express γm in terms of the bulk modulus of the solid at melting and the latent heat and volume change of fusion. By means of Grüneisen's law applied to the solid at fusion, γm can be expressed likewise in terms of the corresponding bulk modulus, thermal expansion, volume, …