The Registrar-General's Decennial Supplement 1921—England and Wales—Part I, recently published, is of more than usual interest. It embodies the Report of the Government Actuary, Sir Alfred Watson, who was invited to undertake the task of preparing National Life Tables in connection with the Census of 1921.

In addition to the preparation of English Life Tables No. 9 for Males and Females separately, the only other tables prepared with similar completeness were those relating to Greater London, being the area comprised within the radius of about fifteen miles measured from Charing Cross. On the other hand, the mortality experience of no fewer than twenty-six sections of the country, differentiated by geographical position and density of population, was examined in considerable detail—a feature which, together with others referred to later, distinguishes this investigation from its predecessors.

It will, I think, be admitted by all who have given this matter any serious thought that it is impossible to deal adequately with the subject indicated by the above title, as in the first place the paper would run to an inordinate length, and in the second place the time is not yet when the effect of the war on the operations of insurance companies can be correctly measured. It may be that many years must elapse before things can be seen in their true perspective, and incidentally, I suppose, there will always be a certain difference of opinion as to how far any particular results can be attributed to the war itself, or to what extent they were influenced by other factors.

In fulfilment of the promise made in January 1926, I now present the results of further investigation into the mortality experienced by pensioners from the staffs of banks and insurance companies. It was intended that this paper should have been submitted last session, but absence from England during the winter of 1926-1927 precluded any possibility of that event.

The methods adopted for collecting and tabulating the annuity experience for the five years 1921-1925 carry out the arrangement that was accepted by the Committee at the time when the permanent investigation was set up. Members of the Committee who were not Members of the Committee when the decision was reached will appreciate that the method adopted is a census method and not a policy year or calendar year method of the type ordinarily used in the past for investigating mortality experience, e.g., such as was used in the OM experience (see however Appendix).

Our attention was called to Fourier's Series in a discussion on engineering subjects with Professor William E. Dalby, F.R.S., the Dean of the City and Guilds Central Technical College, London University. Judging by the use made of Fourier's Series in engineering problems, it seemed possible that it might apply equally well to actuarial and statistical science.

Sir George F. Hardy in his course of lectures on the Construction and Graduation of Tables of Mortality (p. 35) stated “A second test tha t has occasionally been applied when the graduation has been effected by means of a formula is that of making the sums of the squares of the deviations a minimum … This method, known as the method of Least Squares, is used very generally in connection with measurements in astronomy and other physical sciences …”