From the nature of a bone's endload and its local surface strains, the theory computes a modeling operator, Gamma (gamma), that predicts whether mechanical factors will cause lamellar bone modeling drifts, and where and of what kind. A given mechanical bone strain history then provides a separate modeling rate function, M, to specify the rate of such modeling drifts as fractions of the largest possible ones. Multiplying the two functions, e.g., gamma.M, then predicts mechanically controlled bone modeling responses for cortical and trabecular bone, both quantitatively and qualitatively. The theory correctly predicts each of the 6 known "principal adaptations" of lamellar bone, which provide a critical test of any such theory for this organ. The theory accounts for biologic, biomechanical, and clinical-pathologic knowledge not available in Wolff's time nor accounted for by most biomechanicians since. Existing proven methods can provide all numerical data needed to satisfy the theory's mathematical equations and already suggest provisional values for most of them. Its originator views the theory as the kernel of more and better theories to come rather than a finished work, a kernel that suggests a new and in some respects novel logical framework for analysing the problems, and a kernel that invites critique, refinement, and/or exploitation by others.