  Pion-nucleon elastic scattering in the dominant $P_{33}$ channel is examined
in the model in which the interaction is of the form $\pi + N\leftrightarrow N,
\Delta(1232)$. New expressions are found for the elastic pion-nucleon
scattering amplitude which differ from existing formula both in the kinematics
and in the treatment of the renormalization of the nucleon mass and coupling
constant. Fitting the model to the phase shifts in the $P_{33}$ channel does
not uniquely fix the parameters of the model. The cutoff for the pion-nucleon
form factor is found to lie in the range $\beta = 750\pm350$ MeV/c. The masses
of the nucleon and the $\Delta$ which would arise if there were no coupling to
mesons are found to be $m_{_N}^{(0)}= 1200\pm 200$ MeV and $m_\Delta^{(0)} =
1500\pm 200$ MeV. The difference in these bare masses, a quantity which would
be accounted for by a residual gluon interaction, is found to be $\delta
m^{(0)}=350\pm 100$ MeV.
