With the exception perhaps of extra premium, there is, it seems to me, no actuarial point in which the practice of assurance offices is so empirical as that of the allowance to be given for the surrender of a policy. The usual custom, so far as I am aware, is to find the value of the policy (generally by the table of mortality and interest used in calculating the reserve) and from that value to deduct a certain proportion, handing over the remainder to the policyholder. The amount of this deduction is purely arbitrary, and were it not for the equalizing effects of competition, would show very startling diversities; since, even with this counteracting effect, the differences in practice can hardly help striking anyone who has examined the amounts given as surrender value by the various offices interested in large reassurance cases which from any reason do not follow the rule of the parent company. In fact, making any return whatever under discontinued policies is the result of that struggle for existence called competition; and like all things growing from this root, the practice has been moulded much more by the pressure of circumstances than by theoretical considerations. Consequent on this method of growth we find extraordinary and indefensible anomalies imperatively calling for rectification. Further it seems to me, looking at the matter as a purely practical question and not one of actuarial fitness at all, there is no point more needful of examination. As things are at present, nobody can say positively whether as its proportion of the value the assurance office retains too little or too much. If the former, the sooner a practice resulting in loss is reformed, the better.

We have now, in conclusion, to deduce from the foregoing investigations the proper formulas for deducing a mortality table from observations arranged as in § 17. The preceding notation will not be strictly adhered to.