We rederive the Federighi-Pomraning boundary conditions for spherical harmonic calculations in transport theory in order to make explicit the original implicit assumptions in Federigh's derivation. In so doing, we put into perhaps its clearest form the old controversy about the uniqueness of these boundary conditions. One new point is that even Federigh's final equation does not have a unique solution, though the recursive procedure that he uses to get numbers does have only one stable solution.