of the sources $\textbf{J}$ and $\rho$. We call these terms the retarded vector potential $\textbf{A}$ and the retarded scalar potential $\Phi$: $$\textbf{A}=\frac{\mu_0}{4\pi}\!\int\!\frac{[\textbf{ J}]}{R}d^3x', \quad \Phi=\frac{1}{4\pi\epsilon_0} \!\int\! \frac{[\rho]}{R}d^3x'.$$ These are the potentials we were looking for. Thus, equation (4) takes the compact form $$\nabla\cdot \textbf{A} + \frac{1}{c^2}\frac{\partial\Phi}{\partial t}=0.$$ In the standard presentation of Maxwell’s equations, the relation (6) is interpreted as a gauge condition, the so-called Lorenz condition. In our presentation, equation (6) should be rather interpreted as a field equation for potentials. At this stage we wonder what other field equations satisfy the potentials **A** and $\Phi$. We then apply the d’Alembert operator $\Box^2\!\equiv\!\nabla^2\!-\!(1/c^2)\partial^2/\partial t^2$ to the potentials in (5), use the result [@6]: $$\square^2\bigg\{\frac{[{\cal F}]}{R}\bigg\}\!=\!-4\pi[{\cal F}]\delta(\textbf{x}\!-\!\textbf{x}'),$$ where ${\cal F}$ is a function of space and time and $\delta$ is the Dirac delta function, and finally integrate the resulting expressions over all space. After this calculation, we get two wave equations $$\Box^2 \textbf{A}=-\mu_0\textbf{J},\quad   \Box^2 \Phi=-\frac{\rho}{\epsilon_0}.$$ These are the second-order equations we were looking for. They imply expressions for the charge and current densities: $\textbf{J}\!=\!-\,\Box^2 \textbf{A}/\mu_0$ and $\rho\!=\!-\,\epsilon_0\Box^2\Phi$ that satisfy the continuity equation $$\nabla\cdot\!\textbf{ J}+\frac{\partial\rho}{\partial t}=-\frac{1}{\mu_0} \Box^2\Bigg(\nabla\cdot \textbf{A} + \frac{1}{c^2}\frac{\partial\Phi}{\partial t}        \Bigg)=0,$$ because of (6). The retarded potentials $\textbf{A}$ and $\Phi$ 