Maxwell’s equations revisited – mental imagery and mathematical symbols

Using Maxwell’s mental imagery of a tube fluid motion an imaginary fluid, we derive his equations $\operatorname{curl} \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$, \mathbf{H} \frac{\partial \mathbf{D}}{\partial t} + \mathbf{j}$, $\operatorname{div} \mathbf{D} \varrho $, \mathbf{B} 0$, which together with the constituting relations $\mathbf{D} \varepsilon _0 \mathbf{E}$, $\mathbf{B} \mu \mathbf{H}$, form what call today equations. Main tools are divergence, curl and gradient integration theorems version Poincare’s lemma formulated in vector calculus notation. Remarks on history development electrodynamic theory, quotations references to original secondary literature complement paper.