In the paper , written during 1944-45 at the Ballistics Research Laboratories, Aberdeen, Maryland, the author developed certain methods for the smooth approximation of empirical tables. He would have profited greatly from the results of the paper by Quade and Collatz, but heard of its existence only as late as the Fall of 1964. Rather, the paper was strongly suggested by the actuarial work on Osculatory Interpolation so aptly summarized and extended in Greville's paper. In 1944-45 applicable methods were needed, and there was no time to develop their mathematical properties. The present monograph aims at doing that. It is based on a number of papers in our list of references, but mainly on the eight papers. The opportunity of describing the whole animal in one place, rather than limb by limb, leads to economy; moreover, the assembling of the limbs becomes more functional and biologically viable.