  The point of instability of a Bose-Einstein Condensate (BEC) due to
attractive interactions was studied. Stable 85-Rb BECs were created and then
caused to collapse by slowly changing the atom-atom interaction from repulsive
to attractive using a Feshbach resonance. At a critical value, an abrupt
transition was observed in which atoms were ejected from the condensate. By
measuring the onset of this transition as a funstion of number and attractive
interactions strength, we determined the stability condition to be
N|a|/(aho)=0.461(12)(54), slightly lower than the predicted value of 0.574.
