The transport of monoenergetic neutrons in spherical geometry with forward scattering and vacuum boundary conditions is considered. The scaled transport equation is solved using the F-N method by considering the pseudo-slab problem. Numerical results for the fundamental and higher order eigenvalues are presented for several significant figures. Some selected results are compared with those obtained using various methods in the literature. Finally, a few remarks about the behavior of the critically eigenvalue of the neutron transport equation with forward scattering is given.