The second fundamental theorem of reactor theory states that a good estimate of the non-leakage probability from a bare reactor is given by the Fourier transform of the infinite medium kernel evaluated at the asymptotic buckling of the reactor. Inönü has investigated the validity of this theorem for the one-velocity slab reactor with isotropic scattering by means of a variational technique. He finds its use gives very good results even for quite small reactors with dimensions of the order of a few mean free paths. In the present paper the effect of anisotropy in the scattering on the validity of the theorem is investigated by a variation-iteration technique. It is concluded that the theorem is, in general, less reliable the more anisotropic the scattering.