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Exact analytical forms of solutions for Dispersion Relations for Amplitudesand 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 imaginarypart, use is made of analytic form for the total cross sections and forparameters of the $t$ dependence of the imaginary parts, with exponential andlinear factors.  A structure for the $t$ dependence of the real amplitude is written, withslopes  $B_R$ and a linear factor $\rho-\mu_R t$ that allows compatibility of thedata with the predictions from dispersion relations for the derivatives of thereal amplitude at the origin. A very precise description is made of all$d\sigma/dt$ data, with regular energy dependence of all quantities. It isshown that a revision of previous calculations of total cross sections, slopesand $\rho$ parameters in the literatures is necessary, and stressed that onlydeterminations based on $d\sigma/dt$ data covering sufficient $t$ range usingappropriate forms of amplitudes can be considered as valid.

Structure of Forward pp and p\=p Elastic Amplitudes at Low Energies