When your Secretary asked me some months ago if I would talk to you about research I made some enquiries and was told that many of you would like to undertake some kind of research work but found it hard to think of suitable subjects. Even if you had subjects, how were you to set to work and what were the possible pitfalls? I am doubtful if I can be of much help to you, and in one sense each man who wants to do any original work must do it in his own way and must find his own subject. The ideal subjects are those of which no one else has ever thought. There is an infinite number of them, and they have been “waiting on the tedious shores of Lethe millions of ages” for “existence and a name” till you bring them to life. To any one of you who may find and solve such a problem “I am not worthy” to speak for he has that touch of inspiration that we poor mortals call genius, being perhaps fearful of using the word “divinity,” but even such an one may like to try his prentice hand before he embarks on his great adventure.

For the purposes of this paper the term “curve-fitting” is not synonymous with “graduation.” It is restricted to graduation by means of an explicit algebraic or trigonometrical formula: graphic and summation methods are excluded. Even so the subject is unlimited, and this paper cannot provide more than an explanation of a few general principles, and a brief exposition of some of the problems of special interest to the actuary.

Our starting point is this: we have decided to fit a curve (vx) to a series of crude figures (ux) and the problems that confront us are:—

(a) What formula are we to ascribe to vx?

(b) How are we to choose the constants in vx in the best possible way?

(c) How are we to test the goodness of fit and to compare the results of different graduations?

The immense growth of Industrial Assurance in Great Britain during the last 80 years is a matter of common knowledge. A plain record of the technical developments which have from the first formed an unobtrusive background would make an interesting story. We should read of the great cost of financing expansion, of the prolonged and ultimately successful struggle to raise the reserves to a satisfactory actuarial standard, and finally, of surpluses sufficiently large to cause actuaries and others furiously to think in arriving at satisfactory methods of distributing them.

There is neither space nor time to tell the story here. We must begin by accepting the fact that relatively large surpluses are now commonly revealed on the valuation of Industrial Assurance funds and that various problems have to be solved in deciding upon the best methods to be adopted in dealing with them.

A great deal of interest was aroused by a paper entitled “The Numerical Rating System,” which was submitted to this Society by Mr. C. F. Wood a few years ago. In that paper Mr. Wood showed how the numerical ratings are used in arriving at the final terms, standard or otherwise, on which policies are issued. A basic rating for build ranging from 95 upwards, is first determined and to this basic rating are added ratings for any adverse features that are reported, these additional ratings varying from as few as 10 points for minor impairments such as remote history of pleurisy or kidney disease, slightly elevated blood pressure and absence of longevity in family history, to heavy ratings of 100 or more for very serious impairments such as mitral regurgitation and other heart impairments, glycosuria and recent history of pulmonary tuberculosis. Having allotted the appropriate numerical ratings to each adverse feature, the total is obtained and from it are deducted certain small allowances for plan and good family history if the case is entitled to them.

By the untimely death of Mr. C. W. Kenchington on the 30th October, 1934, the Students' Society has lost one of its earliest honorary members, and students generally have lost a good friend who was wise in counsel and sympathetic in their difficulties. Long before the Institute embarked on the present comprehensive scheme of tuition, Mr. Kenchington acted as tutor for all four parts of the examinations, and later in Birmingham he interested himself, not only in actuarial students, but also in those taking the examinations of the Chartered Insurance Institute.

Distance from London prevented him from being as regular in attendance at the fortnightly meetings of the Society as he would have wished, but on a number of occasions he made the journey to Town to take the chair or deliver a lecture. When the “Consolidation of Reading” project had reached a critical stage Mr. Kenchington, at the unanimous request of the Committee, consented to act as Editor-in-Chief of the series of booklets, and it is not generally known to what a considerable extent the publication of the first booklet was due to his encouragement and gentle urging.