LET EX be the exposed to risk at age x; F (x, 0) be the ordinate at x of a frequency curve used instead of Ex : the frequency curve is not necessarily a graduation of Ex. but may be and in some circumstances will be;

The size of the population of this country is a question of considerable interest and importance. Attention has been drawn to it in recent years owing to the continued fall in the birth-rate, and it has formed the topic of innumerable articles in the popular press and elsewhere. The subject of population growth is one on which the actuary should be most qualified to judge and yet it is seldom discussed by actuaries as a whole. The reason probably is that to some extent it is cut and dried; the past history of the size and structure of the population is recorded and analysed in official publications and calls for little argument, while future estimates where they cannot be made by fairly straightforward methods are largely a matter of guesswork. The problem of the rate of population growth has been investigated from a theoretical view very fully by certain foreign writers. The purpose of this paper is to give a description of one aspect of the subject and to illustrate it by calculations based on the statistics of this country.