It may be noted that the change in coordination number of boron from 3 to 4 indicated from an X-ray study of the borate glasses24 would predict the more rapid decrease in compressibility with increasing alkali content observed at low concentrations of alkalis. However, no crossing of compressibilitycomposition curves would be apparent from such an explanation. (5) Comparison of Expansivity and Compressibility DataExpansivity data and compressibility data are usually considered to yield similar information on interatomic forces. This interrelationship is open to question except for ideal gases.26 The fallacies encountered by assuming such a relationship for glasses are clearly shown by a comparison of the behavior of expansivities and compressibilities of the glasses. The alkali borates exhibit an expansivity with a well-defined minimum in the composition range 0 to 30The compressibilities on the other hand uniformly decrease with increasing RzO content and a t the maximum concentration have dropped by at least one half. For the alkali silicates a uniform twofold increase in expansivity occurs with increased alkali ont tent.^(^) The compressibility, however, exhibits a very minor uniform decrease over the same range of compositions. The compressibility data on the silicates may involve a maximum for at least one alkali and some curvatures at low composition, but the expansivity data appear to extrapolate smoothly to the L4 (a) J. Biscoe and B. E. Warren, "X-Ray Diffraction Study of Soda-Boric Oxide Glass," J . A m . Cerum. SOC., 21 [8] 287-93 (1938). (b) R. L. Green, "X-Ray Diffraction and Physical Properties of Potassium Borate Glasses," ibid., 25 [3] 83-89 (February 1, 1942). 16 P. W. Bridgman, Physics of High Pressure, Chapter V. G. Bell and Sons, Ltd., London, 1949. 445 pp.value for vitreous SiOz. One apparent explanation for the discrepancies between dependence of compressibility and expansivity data on alkali content lies in the fact that in isobaric expansion the thermal energy introduced may be distributed among many degrees of freedom.*& A glass will possess many different types of degrees of freedom and it is a very questionable assumption that all degrees of freedom, even granting equipartition of energy, affect the volume in a uniform m p n e r . On isothermal compression, however, the molecules are forcibly displaced to new positions, potential energies are directly involved, and the thermal energy is not varied from external causes. On isothermal compression, the internal energy initially decreases, since more heat is liberated than required by the PAV work performed, but ultimately it increases on continued compression. This apparent anomaly can be accounted for on the basis of potential energie~.~5 Bridgman25 discusses this question in some detail in considering the pressure coefficient and concludes, in essence, that when pressure does not arise from purely kinetic sources (as in all condensed phases), expansivity and compressibility are not, in general, manifestations of equivalent phenomena, It ...

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