The idea of a census goes back into the mists of antiquity. It is reported that the Romans under Servius Tullius, the sixth King of Rome about the sixth century B.C., took a census every fifth year and the right of citizenship depended on the making of a complete return. The main objects of the census seem to have been the raising of men and money for further conquests. But the concept of sampling which is often thought to be of more modern origin must have been there even if dormant, for the process of taking a small quantity of material for tasting or testing in order to determine the quality of the bulk has gone on for centuries. However, the big impetus for ideas and practical applications of sampling methods seems not to have come until just after the immense strides taken around 1600 in the field of probability by such men as Cardano, Galileo and later Pascal and Fermat. There is direct evidence that Pascal's work inspired De Witt, the Dutchman who calculated the first life annuities, and no doubt others were similarly inspired.

Members of this Society and of the parent Institute have considered, from time to time, questions affecting the investment of life insurance funds. In the early days ‘Bailey's Canons’ were propounded, and comparatively recently J. B. H. Pegler's ‘Actuarial Principles of Investment’ and H. G. Clarke's ‘Broad Analysis of the Problem’ have been discussed. Also, the more practical aspects of the subject have received due consideration: notably Stock Exchange Investments by A. S. Holness, Loans and Mortgages by W. Murray Simpson and Real Property by G. B. Lane, F.S.I., and W. A. Leach, F.S.I., in 1944, and further by A. C. Wheeler and K. A. C. Wheeler in 1953.

My purpose is to present certain legal points affecting these investments. I hope my remarks may to some extent be supplementary to these previous contributions on the subject of investments, and I shall try to avoid covering the same ground.

Social insurance is becoming increasingly important in the economic and social life of many countries. In several the expenditure on insurance benefits has been estimated to be over 10% of the national income. About forty-five nations now have insurance schemes in which the state plays a part, and about seventy have compulsory private or state ‘workmen's compensation’ insurance. Others have assistance schemes. There is continual expansion in the number of countries operating schemes and in the scope of these schemes.

In this paper a summary is given of the types of benefit commonly found, and the methods used to assess contributions, and financial systems in use, are then discussed. Although Great Britain was one of the pioneers of social insurance, very few schemes have been modelled on ours and it is instructive to examine the differences.

1. The subject of analysis of surplus has been given much study by actuaries both for the intellectual satisfaction it affords and for the practical value of the results of such inquiry. One of the earliest papers in our literature is that of G. H. Ryan in 1892 (J.I.A. 30), the first half of which was entitled ‘On a Method for determining the Gain or Loss from Mortality in an Annuity Company’. Since that date, however, attention has been devoted almost entirely to the analysis of surplus of a life fund, in view of the problems involved in its distribution, and Ryan's restricted treatment remains the only reference for students with regard to the analysis of surplus of an annuity fund. The purpose of the following notes, therefore, is to illustrate symbolically a full analysis of such a fund comprising immediate, deferred and contingent annuities, obtaining a complete reconciliation, and at the same time to indicate briefly the practical difficulties and the consequent steps in the analysis at which curtailment would be necessary in practice. Discussion of the relative importance of sources of surplus is outside the scope of these notes.

Two conditions have been proposed (Anderson & Dow, 1948) for the census method of constructing a mortality table to be ‘strictly correct’: (1) that at the beginning and end of the investigation, ages of lives are evenly spread over the year of age x to x + 1, or (2) that numbers and distributions of ages are the same at beginning and end.

In effect, these alternative conditions are proposed to insure that the approximate formula for the total period of exposure to risk, derived from annual census,

shall be reasonably correct. It is, however, of interest to examine the method more closely, under the hypothesis that the total period of exposure to risk can be determined with negligible error, as would theoretically be possible by holding censuses with sufficient frequency.

Current interest in world population and resources has resulted in the publication of several books in which the increase in world population over the last two thousand years has been traced or at least referred to. It may therefore be of interest to summarize some of the population statistics available for Greek and Roman times and the methods which have been used to obtain estimates of totals from them.

It is known that in many of the provinces of the Roman Empire a census was taken every 14 years which compares favourably in accuracy and completeness with those of modern times. Individual census returns have survived which show that in Egypt in the first two centuries A.D. the whole population was enumerated by households and by age, sex and occupation, but the only record of totals which have been preserved is a statement in Josephus's Jewish Wars to the effect that the population of Egypt excluding Alexandria was, according to the census returns, 7,500,000.