^{page 260 note *} In speaking of the gain or loss to an office arising out of withdrawals, I refer only to their effect on the mortality experience, and not in any way to the allowances made for cancellation of the policies.

^{page 261 note *} The rough and graduated values of qx for the H^M(0-4) Table will be found in the Appendix, Table L, at the end of this paper. The rate of mortality by Farr' table is also added for comparison.

^{page 263 note *} The actual deaths were retained below age 10.

^{page 266 note *} I have assumed one age at entry and 10 years as the term of the possible currency of the policies, in order to bring the experience within narrow limits; and have preferred endowment assurances to term policies, in order to dintinguish the survivors of the term from lapses. If, however, Society A, instead of granting policies at one age at entry only, had issued assurances for all ages, the rate of mortality at age x + n would come out as follows:—Let _n R _x represent the number out of the entrants at age x, who (having survived death and discontinuance) pay their premiums at the commencement of year n of assurance, _nd_x representing the corresponding deaths in that year; then we should have from the records of Society A,

whilst from Society B's experience we should obtain

^{page 270 note *} This would have to be done for each age at entry up to, say, the 30th year of assurance—at any rate, up to the 15th—at a varying rate of discontinuance for each age at entry.

^{page 274 note *} The benefit to be derived from new assurers and withdrawals is here somewhat overstated. Some of the new assurers will lapse or surrender their policies, and as “discontinued” are included in the percentage (18·24) of withdrawals; they are therefore counted over twice.

^{page 292 note *} Vide also page 293.