  In a recent paper, Aimo Hinkkanen and Ilpo Laine proved that the
transcendental solutions to Painleve's second differential equation w"=a+zw+w^3
have either order of growth 3 or else 3/2. We complete this result by proving
that there exist no sub-normal solutions (order of growth 3/2) other than the
so-called Airy solutions.
