Bose-Einstein correlations and momentum distributions are calculated f
or a longitudinally expanding boson source, where the expanding system
has a finite size in space-time rapidity. Such systems are physically
realized by any of the single jets in high energy e(+)e(-), lepton-ha
dron and hadron-hadron collisions as well as by high energy heavy ion
collisions, where the projectile is not really heavy. The 1D expansion
generates a thermal length-scale in the longitudinal direction, which
together with the finite length of the expanding tube effects both th
e momentum distribution and the Bose-Einstein correlation function. Th
e Bose-Einstein correlations are shown to be more sensitive to the sma
ller, while the momentum distribution to the longer of the two longitu
dinal length-scales.