  In this paper we return to the subject of Jacobi metrics for timelike and
null geodsics in stationary spactimes, correcting some previous misconceptions.
We show that not only null geodesics, but also timelike geodesics are governed
by a Jacobi-Maupertuis type variational principle and a Randers-Finsler metric
for which we give explicit formulae. The cases of the Taub-NUT and Kerr
spacetimes are discussed in detail. Finally we show how our Jacobi-Maupertuis
Randers-Finsler metric may be expressed in terms of the effective medium
describing the behaviour of Maxwell's equations in the curved spacetime. In
particular, we see in very concrete terms how the magnetolectric susceptibility
enters the Jacobi-Maupertuis-Randers-Finsler function.
