Momentum and the growth-free segment of a population

In the scenario of a sudden drop in fertility to replacement level. Preston (1986) argued that the population segment under age T, the length of generation, remained growth-free. Here we first present a new relationship for the momentum of any observed population as the ratio of 1) the proportion of the observed population under the mean age at childbearing to 2) the proportion of its life table population under that mean age. We then use that relationship to demonstrate Preston's approximation. Growth factors for other population segments are also presented. When the initial population is stable, momentum can be approximated as a function of the net reproduction rate alone.