  Using Maxwell's mental imagery of a tube of fluid motion of an imaginary
fluid, we derive his equations $\operatorname{curl} \mathbf{E} =
-\frac{\partial \mathbf{B}}{\partial t}$, $\operatorname{curl} \mathbf{H} =
\frac{\partial \mathbf{D}}{\partial t} + \mathbf{j}$, $\operatorname{div}
\mathbf{D} = \varrho$, $\operatorname{div} \mathbf{B} = 0$, which together with
the constituting relations $\mathbf{D} = \varepsilon_0 \mathbf{E}$, $\mathbf{B}
= \mu_0 \mathbf{H}$, form what we call today Maxwell's equations. Main tools
are the divergence, curl and gradient integration theorems and a version of
Poincare's lemma formulated in vector calculus notation. Remarks on the history
of the development of electrodynamic theory, quotations and references to
original and secondary literature complement the paper.
