The shock-wave velocity U and the particle velocity u for many condensed materials are linearly related by the equation U =a + b u along one or more sections of the Hugoniot. Departures from linearity can usually be attributed to porosity, elastic-wave precursors, or phase changes. If there are no such effects to cause nonlinearity, a is approximately equal to the adiabatic, bulk, or hydrodynamic sound velocity ak. Two equations involving the cohesive energy Ec are compared for 56 metals and 13 simple compounds (12 alkali metal halides and MgO): Ec = −(1/2)(a/b)2 and |Ec|=aμ2, where aμ is the shear wave velocity. It is shown that the experimental data are such that the energy of sublimation Es ≈ (1/2)(a/b)2 for the metals and compounds considered, Es≈ aμ2 for the metals, but Es≈ 0.4 aμ2 for the compounds. It is concluded that the shock-wave parameter equation, |Ec| = Es = (1/2)(a/b)2 is preferred because it applies without coefficient adjustments to both metals and simple compounds, and it may be applied to liquids as well as solids if the energy of vaporization Ev is substituted for Es. This equation is also applied to four polymers with |Ec| equated to the initial activation energy of failure Ea, which is equal to the energy of thermal decomposition. Despite the unsatisfactory nature of some shock-wave date (i.e., a ≠ ak), it appears the Ea ≈ (1/2)(a/b)2 although the fit is not as good as for the other materials considered. Therefore, the equations U = a + b u and Ec = −(1/2)(a/b)2 help provide information about the relations between macroscopic and microscopic properties of condensed materials.