Rapidity distributions of protons from central $^{197}$Au + $^{197}$Au collisions measured by the E895 Collaboration in the energy range from 2 to 8 AGeV at the Brookhaven AGS are presented. Longitudinal flow parameters derived using a thermal model including collective longitudinal expansion are extracted from these distributions. The results show an approximately linear increase in the longitudinal flow velocity, $<\beta\gamma>_{L}$, as a function of the logarithm of beam energy.
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