  Control of the Josephson current by varying a gate current has recently been
demonstrated in both 4-terminal and 3-terminal junctions. We show that, when
the the gates are weakly coupled to the Josephson junction, the Josephson
current versus gate current (or versus gate voltage) relation is the same for
both the 4- and 3- terminal geometries. At low temperature, the supercurrent
switches abruptly as a function of the gate voltage, but only slowly as a
function of the gate current.
