  Models of baryon structure predict a small quadrupole deformation of the
nucleon due to residual tensor forces between quarks or distortions from the
pion cloud. Sensitivity to quark versus pion degrees of freedom occurs through
the $Q^2$ dependence of the magnetic ($M_{1+}$), electric ($E_{1+}$), and
scalar ($S_{1+}$) multipoles in the $\gamma^* p \to \Delta^+ \to p \pi^0$
transition. We report new experimental values for the ratios $E_{1+}/M_{1+}$
and $S_{1+}/M_{1+}$ over the range $Q^2$= 0.4-1.8 GeV$^2$, extracted from
precision $p(e,e 'p)\pi^{\circ}$ data using a truncated multipole expansion.
Results are best described by recent unitary models in which the pion cloud
plays a dominant role.
