We report measurements of the mass current as a function of pressure d
ifference, I(DELTAP), for superfluid He-3 flowing through an aperture
whose dimensions are on the order of the temperature dependent coheren
ce length. The goal of the experiment is to see to what extent this we
ak link behaves like a simple Josephson junction. A model has been dev
eloped which predicts I(DELTAP) for the case where the weak link is an
alyzed as a series connection of resistance, inductance and ideal Jose
phson junction. This model is found to be inadequate to explain the ce
ntral feature of the data, i.e. the current increases monotonically wi
th DELTAP.