Statistics, generally considered, is a term of very comprehensive import, and is to be understood as having reference to an important collection of facts properly arranged and systematized in the form of numerical tables, for the purpose of conveying such information or data as may best assist in the investigation and discussion of particular subjects of inquiry. The general principles applicable to these investigations are, for the most part, intimately allied with the mathematical theory of probabilities, and constitute the true science of statistics. It will, moreover, be found, on examination, that the same identical principles lie at the foundation of all the physical and inductive sciences so far as they originally and necessarily depend upon experiment and observation.

In AIDS Bulletins Nos. 1 to 4 the Institute of Actuaries AIDS Working Party presented projections of HIV infection and AIDS based on a model developed by Wilkie. This paper explores the sensitivity of those projections to the various different assumptions which have to be made and presents results on a number of alternative sets of assumptions.

Considering the undeniable importance of a conformity to correct principles in carrying out the processes which must he resorted to for the purposes above mentioned, it is not a little remarkable that no work exclusively on the subject has hitherto appeared. If we except Mr. De Morgan’s and Mr. Sang’s Essays and the Observations scattered through the writings of Mr. Babbage, Mr. David Jones, Mr. Samuel Brown, and one or two others, we believe it may be truly said that scarcely any allusion to it is to be found.

In two previous papers (vol. li, p. 77 and p. 211) an account has been given, of the published work of Newton on the subject of Interpolation by means of formulas of Finite Differences, and references have been made to the important letter which Newton sent on 24 October 1676, to Oldenburg, the Secretary of the Royal Society, with the intention that it should be communicated to Leibnitz. The second paper closed with a quotation from this letter, in which Newton mentions “a method [for the “construction of tables by interpolation] which I had almost “decided to describe here for the use of computers.” It has been my good fortune to discover that Newton had prepared an account of his method for inclusion in the letter and that the draft is preserved in the University Library at Cambridge among the Portsmouth Collection of Books and Papers written by or belonging to Sir Isaac Newton. By the freely granted permission of the Syndicate of the Library, I am able to give a reproduction and transcription of the manuscript, and I have added a translation.

The measure by which the Chancellor of the Exchequer proposes to extend the benefits of life assurance and annuities to the nation at large has now been before the public some time. Few Bills have of late attracted so much attention, and have been so earnestly discussed by all classes, as this. But beyond what was elicited at an interview that took place between the Chancellor of the Exchequer and the Actuaries of several Offices, and some passing remarks on the subject made at the last meeting of the Institute of Actuaries, when we had the advantage of hearing Mr. Samuel Brown's excellent paper on Friendly Societies, the public have as yet had no opportunity of hearing the opinions of those, who after all are best able to judge. It now appears, that the Chancellor of the Exchequer is opposed to a general inquiry and the calling for “persons, papers and records” by the Select Committee, to whom the Bill has been referred, and it therefore becomes all the more desirable that the merits of the proposition of the Chancellor should be calmly and impartially discussed by the members of this Institute.

In the correspondence that has recently taken place respecting the origin of Gompertz's formula expressive of the law of mortality, it has been stated, much to my surprise, that the investigation first given by that gentleman in the Philosophical Transactions of the Royal Society for the year 1825 was defective and inaccurate. I do not here propose to reopen the controversy on the subject of the originality of discovery, or to enter upon a renewed discussion of certain other allegations that have been so efficiently disposed of by Professor De Morgan and Mr. Sprague; but, after the statement to which I have more particularly alluded, it is only right that I should avail myself of the present opportunity to communicate the circumstance that Mr. Gompertz kindly presented me with a copy of his valuable Memoir in January, 1839, in which the various misprints had, in the most legible manner, been previously corrected by himself, and that the processes so corrected are perfectly accurate in every respect. In order that any one may be enabled to judge of this for himself, I shall here give a faithful transcription of that portion of the Memoir which contains the mathematical investigation of the formula, as it will occupy but little space.

The European Economic Community came into existence on 1 January 1958, following the ratification of the Treaty of Rome by the parliaments of the six member countries, Belgium, France, Germany, Italy, Luxembourg and the Netherlands. The long-term aim of ‘The Six’ in setting up the Community was to achieve a unified economic unit with a common economic policy, and whilst commonly referred to in the United Kingdom as the Common Market it should not be thought of merely as an advanced form of customs union.

The subject of Group Life Insurance schemes has been quite recently discussed by the Society (J.S.S. Vol. III. No. 3) and no useful purpose can be served by a repetition of remarks regarding such schemes.

However, there are two points which deserve further consideration. The first of these relates to what might be termed underwriting rules—or, in other words, regulations to which every contract must conform. Each individual contract should be written, so far as possible, on such a basis as will preclude the writing of unsatisfactory business and in this connection such points as the number of lives to be covered, maximum and minimum amounts of insurance, etc., fall to be considered.

The history of the actuarial profession in South Africa starts, as far as is known, during the last decade of the nineteenth century when three actuaries arrived in the Cape Colony from the United Kingdom. Two of these took up positions with the two South African life offices which were then in existence and the third became Government Actuary to the Cape Colony. By the time the Union of South Africa was established in 1910, four more actuaries had arrived from the United Kingdom, and a further four had arrived by 1920. Some of these gentlemen established permanent homes in this country, while others returned overseas after varying periods of time. It was no doubt due to these early beginnings that the actuarial homes of South African actuaries are today London and Edinburgh.

The first South African-born actuary qualified as a Fellow of the Faculty in 1921, and since that time increasing numbers of South Africans have become qualified, mostly as Fellows of the Faculty.

The rate of mortality experienced by residents in India will supply an answer to an enquiry of the highest interest in an actuarial sense. The enquiry may even be considered of national importance so long as our countrymen seek their fortunes in a region where the effects of the climate on their prospects of health and longevity continue to be regarded as uncertain and hazardous.

Towards the end of Mr. Brown's term of office as President I submitted to him the Table which appears in the appendix to this paper asking whether he thought it of sufficient interest for publication in our Transactions. Mr. Brown replied by inviting me to go further and write a paper for the Faculty on the subject of Investments using the Table as an illustration of past history. Later our present President supported this idea and the notes which I now have the honour to submit are the outcome. Apart from the fact that I dealt with the history of Life Offices' Investments at some length when addressing the Students' Society a few years ago, it seemed to me that something more than a historical survey was desirable. There are few papers in our Transactions dealing with Investment Policy and this was the subject on which I decided. I think that the correct prelude to a discussion of Investment Policy is its own history, and so I give in Part I of this paper a very short general survey of the years from 1871 to 1935. The Table in the appendix will give information additional to what is contained in my remarks to those who wish to go further.

Prior to the commencement of the present century, no direct method had been adopted to ascertain the number of the population in England. Various estimates, founded upon Domesday Books, Subsidy Rolls, and payments of Hearth and Poll taxes furnish, with more or less exactness, the numbers at previous periods. Three such calculations relating to the population towards the close of the 17th century are mentioned by Macaulay as being entitled to peculiar attention. “Of these computations one was made in the year 1696 by Gregory King, Lancaster Herald, a political arithmetician of great acuteness and judgment. The basis of his calculations was the number of houses returned in 1690 by the officers who made the last collection of hearth money. The conclusion at which he arrived was that the population of England was nearly five millions and a half. About the same time, King William the Third was desirous to ascertain the comparative strength of the religious sects into which the community was divided. According to the reports laid before him from all the dioceses of the realm, the number of his English subjects must have been about 5,200,000. Lastly, in our own days, Mr. Finlaison, an actuary of eminent still, subjected the parochial registers to all the tests which the modern improvements in statistical science enabled him to apply. His opinion was, that, at the close of the seventeenth century, the population of England was a little under 5,200,000 souls. … We may, therefore, with confidence pronounce that, when James the Second reigned, England contained between five million and five million five hundred thousand inhabitants.”