The author continues the study of the birth function found in the first article by first considering special cases, namely birth constants in particular periods, birth functions changing by a constant amount per unit of time. In each case a formula for the birth function is obtained which is an exponential involving integrals and the root of an integral equation. After applications, solutions of the integral equation are given. The population function is treated in the last part of the paper, where the material already developed is used.