Fig. 2.

Gauss’s theorem. In blue, the flux calculated as the surface integral of the vector field $\overrightarrow{\mathbf{W}}$ obtained from commuters going to work. In red, the volume integral of ∇$\overrightarrow{\mathbf{W}}$. a Results in London for a circle of radius R centered at Waterloo Bridge. b A square perimeter around London with the same center and side 2R. In the figure, we show half the side as the x-axis variable to maintain the geographical scales similar to those of the circle radius. The same for Paris with a circle (c) and a square (d) centered at the Passage du Grand Cerf in the 2nd Arrondissement