  Hedgehog model predictions for the leading nonanalytic behavior (in
$m^{2}_{\pi }$) of certain observables are shown to agree with the predictions
of chiral perturbation theory up to an overall factor which depends on the
operator. This factor can be understood in terms of contributions of the
$\Delta$ isobar in chiral loops. These physically motivated contributions are
analyzed in an expansion in which both $m_{\pi}$ and $M_{\Delta}-M_N$ are taken
as small parameters, and are shown to yield large corrections to both hedgehog
models and chiral perturbation theory.
