An activation energy for the surface migration of tungsten atoms on the tungsten crystal lattice structure and under the influence of a high electric field has been measured using field emission techniques. The initially hemispherical field emitter tip surface deforms into a polyhedral shape in a process known as build-up, when the emitter is heated in the presence of large electrostatic forces. Build-up proceeds in a regular and reproducible manner; certain stages of build-up can be identified by characteristic changes in both the field emission patterns and the current vs time characteristics of the emitter. An activation energy of 2.44+/-0.05 ev/atom was determined, from the measured values of the time required to achieve a given degree of build-up at various operating temperatures. This value may be compared with the value of 3.14 ev/atom determined from the rate at which the tip of a heated tungsten emitter recedes in the absence of an electric field. Explanations for the difference are presented, involving two distinct factors: (1) a reduction in activation energy, through the effect of polarization of the surface atoms by the electrostatic field, by an amount which was determined in a special experiment; and (2) an inherent difference which remains after allowance has been made for the field effect. The latter is ascribed to the difference in the paths of migration in the two cases whereby, for the conditions existing in this experiment, the activation energy measured is that corresponding to migration primarily over the low index (100), (110), and (211) planes. A value of 2.79+/-0.08 ev/atom is obtained after correction for the field effect.