There is a high chance against your picking up any recent number of the Bulletin de l'Association des Actuaires suisses which does not contain an article dealing with the theory of the changing population ‘Le renouvellement, quelques problèmes connexes et les équations intégrates du cycle fermé (Féraud, vol. XLI, 1941, p. 81) and ‘Über die Integralgleichung der Bevölkerungstheorie’ (Hadwiger, vol. XXXVIII, 1939, p. I) are two titles of papers belonging to this category. The English names for the relevant notions can be found in many publications by Lotka (e.g. ‘The theory of industrial replacement’, Skand, Aktuar Tidskr. 1940; ‘On an integral equation in population analysis’, Ann. math. Statist. 1939; ‘The structure of a growing population’, Human Biology, vol. III) and one can nearly always see that a paper deals with this subject by noticing an equation of the following form:

from which the function G (t) is to be determined. (For a purely mathematical investigation of this ‘integral equation of the second type’ see Feller, ‘On the integral equation of renewal theory’, Ann. math. Statist. Vol. XII, 1941, and compare also C. D. Rich, J.I.A. Vol. LXV).