  The Maxwell-Boltzmann (MB) distribution for velocities in ideal gases is
usually defined between zero and infinity. A double truncated MB distribution
is here introduced and the probability density function, the distribution
function, the average value, the rth moment about the origin, the
root-mean-square speed and the variance are evaluated. Two applications are
presented: (i) a numerical relationship between root-mean-square speed and
temperature, and (ii) a modification of the formula for the Jeans escape flux
of molecules from an atmosphere.
