Tangential discontinuities and the optical analogy for stationary fields II. The optical analogy

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Abstract
It is shown that any stationary three-dimensional velocity field or magnetic field is a potential field in the two dimensional subspace of the Bernoulli surfaces S(Q) or isobaric surfaces S(p), respectively. From this it is shown that the streamlines and the lines of force follow the optical ray paths in S(Q) and S(p) for indices of refraction v and B, respectively. This formal analogy shows how the lines are refracted by variations of the pressure applied by the fluid and field on either side. In particular, it is shown how continuous variations of the pressure produce discontinuities (bifurcations) in the field, forming tangential discontinuities.