A new technique for measuring galaxy mass, based on the gravitational deflection of light, is described. The method does not require stereoscopic detectability or virial or orbital assumptions and can apply to galaxies of all types. Images from 46,954 galaxies were examined in order to find a particular coherent image distortion associated with gravitational lenses of 11,789 foreground galaxies. The equivalent statistical circular velocities of the galaxies are determined as a function of the mass cutoff radius for the foreground galaxy data set. The 2 sigma upper limit to the average circular velocity is found to be less than 170 km per sec for a mass envelope extending to beyond 50 kpc/h radius. The corresponding total mass limit to this radius is 1.7 x 10 to the 11th solar mass. It is concluded that there is not sufficient mass associated with the individual galaxies to achieve the critical density for closure.