With a Cf252 source placed at the edge of a large cadmium-loaded liquid scintillator, it has been possible to obtain a measure of the number of prompt neutrons emitted from a single fission fragment of measured mass. The mass determination results from a concurrent time-of-flight measurement of the two fragment velocities. The 30-in. scintillator has a high detection efficiency, little dependent on the energy of the neutrons, and permits detection in a full hemisphere about the direction of one of the fragment flight paths. The average number of neutron counts per fission is found to increase with the mass number of the fragment approaching the neutron detector in much the same way in both the light- and heavy-fragment groups, with a sharp decrease occurring in passing from the light to the heavy group. A correction for the geometry of the neutron detection, assuming isotropic emission of the neutrons in the fragment frames, enhances slightly the sawtooth dependence of ν̄(A) and gives for the ratio of the average number of neutrons from the light fragment to that from the heavy fragment ν̄Lν̄H=1.02+/-0.02. One is led to believe that either the emission of the neutrons is far from isotropic or that the slightly lighter fragments possess considerably more excitation energy than the slightly heavier fragments when the mass division is nearly symmetric. Perhaps a new picture of the mass division is indicated.