Although about half the fronts appearing in current analyses lack a significant horizontal density contrast, and are thus not the phenomena described by Bjerknes, real fronts do occur from time to time and are important features of mid-latitude weather. How they arise can be studied by application of a frontogenesis function presented by Petterssen, or one due to Miller. These really describe the Lagrangian change of horizontal temperature gradient on an air parcel rather than the collapse of a gradient to a quasi-discontinuity, or frontogenesis. Although the Petterssen is more widely used, the Miller equation is simpler and less subject to paradoxical interpretation. For example convergence in the Petterssen equation always indicates positive frontogenesis. One can postulate a pattern of temperature and convergent wind, however, that yields zero frontogenesis. I this case the deformation effect in the Petterssen equation yields a balancing frontolysis so that the net effect is zero. The Miller equation straightforwardly produces zero. In either case the rate of frontogenesis is exponential: the rate of change depends un the magnitude of the gradient itself. This suggests that frontogenesis is a two-stage process. First, there must be a significant gradient. Otherwise a substantially frontogenetical wind field will have little effect. This significant gradient appears to arise principally from the horizontal gradient of diabatic heating or cooling. Second, this gradient must be compressed to a limiting magnitude in which the frontogenesis is balanced b small-scale mixing. The compression arises from the kinematic effects specified in the frontogenesis equations and is due to the horizontal advection of temperature by the non-geostrophic wind, ignored in quasi-geostrophic theory. Measurements of frontogenesis are compared with changes of temperature gradient in selected frontal situation in the northeastern United States.