  We study the Josephson effect through a one-dimensional system of interacting
electrons, connected to two superconductors by tunnel junctions. The
interactions are treated in the framework of the one-channel Luttinger model.
At zero temperature, the Josephson critical current is found to decay
algebraically with increasing distance between the junctions. The exponent is
proportional to the strength of the Coulomb interaction. If the Luttinger
liquid has a finite size, the Josephson current depends on the total number of
electrons modulo 4. These parity effects are studied for the ring, coupled
capacitively to a gate-voltage and threaded by a magnetic flux. The Josephson
current changes continuously as a function of the gate voltage and {\em
stepwise} as a function of the magnetic flux. The electron-electron interaction
introduces {\em qualitatively} new features compared to the non-interacting
case.
