In the course of a paper read before the Institute in January 1885 (J.I.A., xxv, 141), I suggested a certain method of making approximate valuations on different bases of the liabilities of a life assurance company under its whole-life policies. Shortly afterwards I had occasion to make a valuation of the liabilities of a particular company, and I took the opportunity of testing the suggested method of approximate valuation by actual comparison of the results arrived at by its application with those derived from a rigidly accurate class valuation, and I have thought that it would be interesting to the members of the Institute to have an explanation of the process employed in making use of the approximate method, and a statement of the results of the comparison.

In the course of an investigation I have lately made, into the rate of mortality that has prevailed among the female lives insured in the Scottish Equitable Life Assurance Society, I have tried various methods of arranging the facts furnisht by the books of the office; and I think it may be useful to persons engaged in similar investigations, if I describe these methods, and state the conclusions at which I have arrived as to the best course of procedure.

The method of valuation generally adopted in practice is that known as the Prospective Method; by it, the value of a policy is obtained by a consideration of the future, and is the discounted value of the payment to be made, less the discounted value of the payments (if any) to be received; discounted, that is, in each case, for both mortality and interest.

Although the subject of probability is of such vital importance to insurance, no great detailed study was given to it until the sixteenth century. This was nearly two thousand years after the world's first insurance venture, that of Antimenes on behalf of Greek slave-owners against loss of their slaves (the early Greeks had also a good system of marine insurance). As in many fields of study, the early students of probability met with a great deal of opposition, which must have extended well into the nineteenth century, judging from the evidence of de Morgan's book of 1838.

It is now June 1959—only eight years after the first magnetic tape computer was put to work in the U.S. Bureau of the Census. But it was not until mid-1954 that the appropriate auxiliary machines needed to complement this computer became available. In a very real sense, magnetic tape data processing facilities suitable for business operations are only five years old at this time.

Yet, in so short a time, possibly 300 or more tape-operated data processing systems have already been installed in the United States. A great deal has been written and said regarding the use of this equipment and its impact on current practices. There is much yet to be said. As we come to grips with the immediate and difficult job of putting it to work we can be encouraged by the very substantial progress already achieved by both manufacturers and users. In just a few years, the initial approach to computers has changed so much that the key question ‘Can electronic computers be relied upon?’ has become for many ‘Which one should I get?’

Some years ago, before the enactment of the Ten Hours Factory Bill, I had the honour to be engaged by the Earl of Shaftesbury (then Lord Ashley) on an investigation of the average distances traversed daily by children and others employed as “piecers” in the cotton mills about Manchester and the surrounding districts. After taking the various dimensions of the mules or spinningjennies, and making the requisite observations as to the number of strokes of each machine per minute, and the average number of breakages of the threads at each stroke, I found that the necessary calculation involved a preliminary discussion of a somewhat curious mathematical problem.

The paper is an attempt to bring out the exact relationship between what has been called the ‘modified osculatory process’ and the older formulae of osculatory interpolation. The conditions upon which the modified process is stated to be based are shown to be insufficient in themselves to produce a determinate formula even after the degree has been made as low as possible, and a general formula is derived which satisfies these conditions and of which the formulae hitherto employed are particular cases. The general formula contains, as might be expected, certain arbitrary constants which reflect the relaxation of certain of the conditions insisted on by the older formulae.

Illustrative graduations are performed by means of the general formulIllustrative graduations are performed by means of the general formula

and the results are compared with previous graduations of the same data by Jenkins's fifth difference formula (which may be obtained by putting b=0 in the general formula), viz.:—

This is the particular case of the general formula which has hitherto been used in practice.

The subject of sickness insurance does not appear to have been previously discussed before this Institute except in relation to Friendly Societies and the National Health Insurance Act. There is, however, a most comprehensive paper by Mr W. A. Robertson, the present President of the Faculty, in the Transactions, Vol. xiv, page 21. Disability in the sense of long-term sickness insurance has been considered on several occasions, but purely as an added benefit to life assurance contracts. The results shown by the American offices, who at one time transacted a large volume of this business, have been anything but encouraging.