  We study finite-size corrections to the free energy of the
Sherrington-Kirkpatrick spin glass in the low temperature phase. We investigate
the role of longitudinal fluctuations in these corrections, neglecting the
transverse contribution. In particular, we are interested in the exponent
$\alpha$ defined by the relation $f-f_\infty\sim N^{-\alpha}$. We perform both
an analytical and numerical estimate of the analytical result for $\alpha$.
From both the approaches we get the result: $\alpha=0.8$.
