An analysis of the thermal properties of vitreous ice shows that both its heat capacity Cp and its entropy above 100 K are partly configurational in origin. The configurational contribution increases with temperature, and the excess Cp and entropy near the solid-liquid transformation temperature are 36.7 and 2.1 J K-1 mo1-1, respectively. The increase is interpreted as indicating the onset of molecular mobility in vitreous ice. The configurational Cp, of the melt of vitreous ice at 133.6 K, of ≈ 36.7 J K-1 mo1-1, is the same as the configurational Cp, of water at 273 K. Thus, the short-range order in the melt differs little from that in water at 273 K. The maximum calorimetric residual entropy of vitreous ice is 13.4 J K-1 mol-1, which is in fair agreement with the maximum value of 9.2 J K-1 mol-1 anticipated for a tetrahedral random-network model with fully disordered positions of H atoms. Thermodynamic consideration of a glass transition in supercooled liquid water indicates that there is no continuity of state between supercooled water and vitreous ice and, therefore, the structure and thermodynamic properties of a possible glassy state of water should be different from that of vapour-deposited vitreous ice. This paper is published in full in Philosophical Magazine, Eighth Ser., Vol. 35, No. 4, 1977, p. 1077-90.