  We consider the island formula for the entropy of subsets of the Hawking
radiation in the adiabatic limit where the evaporation is very slow. We find a
simple concrete `on-shell' formula for the generalized entropy which involves
the image of the island out in the stream of radiation, the `island in the
stream'. The resulting recipe for the entropy allows us to calculate the
quantum information properties of the radiation and verify various constraints
including the Araki-Lieb inequality and strong subadditivity.
