The Author considers, among others, a certain interpretation of Poynting's theorem, useful for (also magnetic) piezo-elasticity. This interpretation is connected with a simple determination W of the density of electromagnetic energy and with the power spent by the field to change polarisations. In connection with the above hinted interpretation two symmetric instances $_{2}E^\ast_{\alpha \beta}$ and $_{3}E^\ast_{\alpha \beta}$ of the electromagnetic energy tensor $E_{\alpha \beta}$ are considered. By them the basic relativistic conservation equations (with inclusion of electromagnetism and thermodynamics) become very useful for dealing with piezo-elastic fluids and solids respectively. The interest of $_{2}E^\ast_{\alpha \beta}$ and $_{3}E^\ast_{\alpha \beta}$ will be strengthened by certain uniqueness properties of $E_{\alpha \beta}$ to appear in a future paper.