With the exception perhaps of extra premium, there is, it seems to me, noactuarial point in which the practice of assurance offices is so empiricalas that of the allowance to be given for the surrender of a policy. Theusual 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 thereserve) and from that value to deduct a certain proportion, handing overthe remainder to the policyholder. The amount of this deduction is purelyarbitrary, and were it not for the equalizing effects of competition, wouldshow very startling diversities; since, even with this counteracting effect,the differences in practice can hardly help striking anyone who has examinedthe amounts given as surrender value by the various offices interested inlarge reassurance cases which from any reason do not follow the rule of theparent company. In fact, making any return whatever under discontinuedpolicies is the result of that struggle for existence called competition;and like all things growing from this root, the practice has been mouldedmuch more by the pressure of circumstances than by theoreticalconsiderations. Consequent on this method of growth we find extraordinaryand indefensible anomalies imperatively calling for rectification. Furtherit seems to me, looking at the matter as a purely practical question and notone of actuarial fitness at all, there is no point more needful ofexamination. As things are at present, nobody can say positively whether asits proportion of the value the assurance office retains too little or toomuch. 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 theproper formulas for deducing a mortality table from observations arranged asin § 17. The preceding notation will not be strictly adhered to.