The physical correlation between the fictive temperature dependence of the cooling rate of the melts and the temperature dependence of the equilibrium viscosity has been found by doing differential scanning calorimetric and viscometric measurements on a silicate melt, and by performing finite element simulations of the fiber drawing from that melt. This correlation is governed by a correlation factor K-c (in Pa K) which is constant and universal for silicate glasses. The factor K-c is obtained in the cooling rate range from 10(-2) to 10(6) K/s and is in good agreement with that theoretically predicted. The physical feature of the correlation is discussed in the paper. When the fictive temperature equals the actual temperature, a linear relation exists between the cooling rate and the Maxwell relaxation rate, the slope of which depends on the fragility of the glass melts. The Avramov equation is extended to describe the cooling rate dependence of the fictive temperature. The cooling rate equation contains only one adjusting parameter, i.e., the fragility parameter alpha. (C) 2004 American Institute of Physics.