Potentials having two orthogonal families of curves as trajectories

We study, using the tool of Joukovsky's orthogonal coordinates, the determi nation of the potentials having two families of orthogonal trajectories. We show for compatible cases the existence and the uniqueness, up to a consta nt factor, of the solution. We note the importance of the 'isothermal' nets of curves. We study as an example the net of geometrically similar conic c urves and orthogonal trajectories.