  The four-body equations of Alt, Grassberger and Sandhas are solved, for the
first time, for proton-${}^3\mathrm{He}$ scattering including the Coulomb
interaction between the three protons using the method of screening and
renormalization as it was done recently for proton-deuteron scattering. Various
realistic two-nucleon potentials are used. Large Coulomb effects are seen on
all observables. Comparison with data at different energies shows large
deviations in the proton analyzing power but quite reasonable agreement in
other observables. The effect of nucleon-nucleon magnetic moment interaction
and correlations between $\pd$ and $\pHe$ analyzing powers are studied.
