The parameters A and m in the power-law expression for the kinetic-energy dependence of the secondary-electron cascade of solid elements has been measured as a function of the atomic number of the sample. A pattern has been observed in the values of both A and m which is related to the variations in the Periodic Table. m is found to fall between 0.5 and 1.5 as predicted by theory. Also, it has been established that the coefficient A is correlated with the exponent m. The measured values of m are expected to be related to the exponent of another power law of the kinetic energy which is found to describe the energy dependence of the electron attenuation length for energies above about 400 eV. This expectation is checked against several existing models or empirical expressions for the attenuation length. Moderate agreement is found between m and (2-q) where q is the exponent of the energy dependence of the attenuation length described by Tokutaka et al. and the agreement is poorer with values of q derived from various theoretical treatments of the energy dependence of the inelastic mean free path. m is found to be correlated to the free-electron energy ${\mathit{E}}_{\mathit{p}}$ and A to the density of valence electrons in the solid.