  Exact analytical forms of solutions for Dispersion Relations for Amplitudes
and Dispersion Relations for Slopes are applied in the analysis of pp and $\rm
{p \bar p}$ scattering data in the forward range at energies below
$\sqrt(s)\approx 30 \GeV$. As inputs for the energy dependence of the imaginary
part, use is made of analytic form for the total cross sections and for
parameters of the $t$ dependence of the imaginary parts, with exponential and
linear factors.
  A structure for the $t$ dependence of the real amplitude is written, with
slopes
  $B_R$ and a linear factor $\rho-\mu_R t$ that allows compatibility of the
data with the predictions from dispersion relations for the derivatives of the
real amplitude at the origin. A very precise description is made of all
$d\sigma/dt$ data, with regular energy dependence of all quantities. It is
shown that a revision of previous calculations of total cross sections, slopes
and $\rho$ parameters in the literatures is necessary, and stressed that only
determinations based on $d\sigma/dt$ data covering sufficient $t$ range using
appropriate forms of amplitudes can be considered as valid.
