  We examine numerically and analytically the problem of the relativistic
velocity distribution in a 1-dim relativistic gas in thermal equilibrium. Our
derivation is based on the special theory of relativity, the central limit
theorem and the Lobachevsky structure of the velocity space of the theory,
where the rapidity variable plays a crucial role. For v^2/c^2 << 1 and 1/\beta
= k_B T/ m_0 c^2 << 1 the distribution tends to the Maxwell-Boltzmann
distribution.
