The purpose of this paper is to discuss briefly the implications for investors of the commoner forms of alterations in a company's capital structure, in the rights of its shareholders, or in the amount of its loan or issued capital, which may occur in practice. The object is to consider general principles only, and no attempt will be made to deal with all possible situations or with the many exceptions which may arise as a result of special rights or provisions in the articles or deeds governing the issues concerned.

Before discussing the implications of particular cases the main features of different types of stock-exchange investment and some broad considerations which govern their value to investors will be briefly reviewed.

In Pension Fund work there arises the problem of determining the cost of a pension dependent upon salary and length of service, and it is often required to ascertain how this cost would be affected if a different salary scale were substituted for that upon the basis of which calculations have already been made. Attention will be confined in this Note to the type of scale most common in practice, namely, the ‘ratio’ scale wherein the successive values form a series of proportional numbers showing the average ratios by which present salaries may be expected to increase from age to age in the future.

We will suppose that the contribution, expressed as ą percentage of salary, is required on one scale when it has been calculated on another scale, or that the various effects of using several possible scales are to be determined. It may happen that the nature of the scales, or to be more precise their relative nature, is such that in order to find a solution to this problem we must consider the effect of the change separately upon the value of the pension benefit and upon the value of a contribution of 1 % of salary; or it may even be necessary to recalculate the required figure on each of the different bases.

The study of methods of measurement of the rate of population growth is one of the most fundamental aspects of demographic science and one which, from its nature, should be of particular interest to the actuarial profession. It is therefore fitting that this paper should be devoted to a discussion of this side of the subject, particularly in view of the importance which the analysis of population trends has assumed in modern times as the result of the decline in birth-rates experienced by this country in common with most of the leading civilized nations.

Leaving out of account losses and gains by migration, the future development of a given population is determined by the numbers of children that people have, the proportions of these who survive and the sizes of the families which they have in their turn, the cycle continuing indefinitely. Whilst the consequences of changes in mortality must not be underestimated it is clearly the wide possible range of variation in birth-rates which plays by far the more important part in shaping future population trends. The measurement of population growth therefore rests largely on the analysis of fertility, a subject of considerable complexity.