The method of calculating the values of prospective pensions which I am about to describe differs in some respects from those given in the standard papers on the subject, and will be found, I think, to possess advantages of its own. I shall deal with its application to the case of pensions based on salaries, when the amount of the pension is a uniform percentage of salary for each year of service taken account of.

I have followed Mr. Manly in the use of the following symbols (see his paper of 1901—J.I.A. xxxvi, 209), namely, lx to denote the number living and remaining on the active list at age x as given in the Service Table, and Dx and Nx to correspond; rx to denote the number retiring from failure of health between ages x and x + 1, sx to denote the salary receivable between ages x and x + 1, and Dsx to denote Dx X sx. When however lx, Dx, Nx, or Dsx have a circumflex accent, these symbols have the ordinary meanings, and the functions are based respectively on the Pensioners Mortality Table. I have found it necessary to employ also a certain number of new symbols which are described in the Key to the Special Notation (see pp. 31, 32). I have also followed Mr. Manly in the assumptions made in the paper mentioned above, that the retirements or superannuations applicable to any year of age take place at the end of the year, and that the pension commences at the same time and is payable yearly thereafter.

The paper which I have the honour of submitting to the Faculty may be briefly described as a plea for Research in Life Assurance, with the object of throwing light on many of the problems which arise in connection with the practical work of our business.

As the most satisfactory way of obtaining successful results it advocates the establishment of a Bureau of Research—preferably of a permanent nature.

The successive stages in the history of life assurance business are closely associated with certain developments of actuarial science, and in particular with the appearance of the great Life Tables, the Northampton, the Carlisle, the Seventeen Offices, and the Twenty Offices experience. More recently the British Offices experience of 1863-1893 has been published, and it can by no means be asserted that all the lessons to be derived from this important mass of statistics have been learnt. Many valuable opinions have been expressed on particular points, in Great Britain, in North America, and elsewhere, but as a rule any proposals as to rates of premium would appear to have left some appreciable margin for adverse contingencies as regards allowance for mortality, for interest, and for expenses. Yet in the practical conduct of business under competitive conditions, the problem that ever presses for solution touches closely the present actual cost price, and although this may be but a will-o'-the-wisp, and undoubtedly varies greatly in different circumstances, it is probable that experienced actuaries will always find features worthy of discussion in connection with it.

In the discussion which followed the reading of my paper “Principles of Book-keeping for Insurance Students” (T.F.A. iv. 21), some remarks were made by Mr. M'Lauchlan about the Agents' Ledger, suggesting the possibility of doing without it. In the following paper I have attempted to show how this can be done, though I have gone on somewhat different lines from those he had in view at the time. Since this paper was written I have ascertained that some offices have dispensed with the Agents' Ledger, either altogether or to a large extent.

The subject is one which may seem of somewhat minor importance, but, on investigation, it will be found that, even under present-day conditions, it requires careful attention by life assurance offices and by all societies and funds which have liabilities depending upon the duration of human life. As an illustration of its importance it may be mentioned that it is well known that statements of ages made in the past by the public for the purposes of census and death returns contain a considerable number of errors, both intentional and unintentional: and it can readily be understood that life assurance offices would certainly involve themselves in serious loss if they dispensed with satisfactory proof of age. Were they to do so the resulting errors in age would be relatively far in excess of the corresponding errors contained in census returns, owing to the monetary advantages which could be gained by understating the age at the date of effecting a policy of assurance, and to these advantages acting as an incentive to fraud. Accordingly, it is recognised by all life assurance offices—though not always by their assured—that proof of age is a requirement which must be complied with before payment of a claim.

I have the honour of submitting to the Faculty the results of investigations into the rates of mortality among Males and into the rates of mortality, marriage, and fruitfulness of marriage among Bachelors of the British Peerage in the latter half of the nineteenth century.

Sir,—The case of Chrystal's Trustee v. Chrystal, reported 1912 S.C. 1003; 49 S.L.R. 726; 1912, 1 S.L.T. 500, appears to me to be of special interest to the Faculty.