I Have the honour to submit to the Faculty six Life Tables based on the population of Scotland as ascertained at the Census of 1921 and on the deaths registered during the years 1920 to 1922. Of the six Tables three deal with the male population and three with the female population, the three of each sex consisting of a general Table, a Table applicable to the married, and one applicable to the unmarried. The widowed population and deaths of widowers and of widows are included with those of the married.

The earliest mortality tables were constructed from inadequate and relatively defective data. This was obvious to their authors, and the need for fuller, more accurate and more homogeneous data impressed itself upon subsequent constructors of mortality tables, and has materially affected the outlook on mortality tables even up to the present time.

Leaving out of account the construction of the Northampton and Carlisle Tables, we find on the one side a series of mortality tables based upon census returns dating from the English Life No. 3 to the English Life No. 8. These tables were constructed by various methods, usually implying that either the deaths and population or the rate of mortality could be expressed by a finite difference curve.

Investigation into experience from 1903 to 1923 of five Scottish Banks' Widows' Funds; Bachelors, Married Men + Widowers, Wives and Widows, dealt with separately for mortality (total exposed to risk 99,354, 1305 deaths); Bachelors and Widowers separately for marriage experience (757 marriages).

Description pf methods of obtaining Exposed to Risk, etc., with special reference to exclusion of War period for younger male lives.

Males:—Low mortality at younger ages ; same improvement not maintained at older ages ; Bachelor mortality much higher than for Married Men at all ages. Females :—Exceptionally light mortality at younger ages ; improvement continued to some extent to oldest ages. Comparisons made with Hewat's 1893 experience.

Marriage:—Rates for Bachelors less than Hewat's at early ages, higher at principal marrying ages, and then again lower. Rates for Widowers much higher than for Bachelors. Difference between ages of husband and wife at marriage of Bachelors three years less than by Hewat.

Comparisons of Monetary Values—Whole Life Annuities and Annuities to Widows by first and second Marriages of Bachelors, etc.—with values by Hewat and Huie.

Valuation of Fund by new tables compared with valuation by Hewat and Huie ; reserves very similar for old-established Fund ; liabilities for young Bachelor entrants lighter.

Collective method, based on deaths in period. Liability in Valuation substantially lower than by Reversionary Annuity method; examination of difference, traced mainly to effects of War on marriage status. Discussion of the two methods, with references to Schjoll's alternative Collective method, based on living at end of period.

Tables at 3, 3½, and 4 per cent.; all tables given by Hewat and Huie relating to payments on marriage and to widows' annuities. Collective Method ; tables at 3½ per cent.

Few actuaries are required to deal with problems of graduation, and some may be inclined to regard the subject-matter of this paper as highly unpractical; nevertheless it had its origin in questions which presented themselves for solution in the course of everyday work. Some may even be disposed to regard graduation as a kind of juggling with figures, the results of which have to be taken on trust; and they have a certain amount of justification in that the processes are not always fully explained. To satisfy these doubts full details of the methods employed are given in the Appendix, and one or two examples are completely worked out, so that students will be enabled to follow the process from beginning to end.