The asymptotic behaviour of F_(L) in the double scaling limit

In the kinematic region of small $x$ and large $Q^2$ in deep inelastic scattering, presently being explored by HERA, we present an analysis of the evolution of the longitudinal structure function $F_L^{p}(x, Q^2)$ in the double scaling limit of Ball and Forte. We fit the evolution to a $1/x^\lambda$ behaviour and extract the value of $\lambda$. We also study the behaviour of $R=F_2/2xF_1 -1$. We present comparisons of both $F_L$ and $R$ with the corresponding MRS fits in this region of $x$ and $Q^2$.