page 71 note * If this modification be introduced, Care must, however, be taken that the cases of death are throughout located in their true years of duration.

page 74 note * The function Ē_[x]+1 really represents the number exposed [in the (t + l)th year] to risk of death or withdrawal; and would be appropriately employed in calculations (1) of benefits the continuance of which depends upon the member's being alive and in full membership (such as the annuity by which the members' subscriptions would be valued) (2) of benefits which would necessarily cease on the occurrence of either death or withdrawal (such as an allowance during sickness or non-employment).

page 77 note * The formulæ are numbered consecutively in the Appendices; and to avoid confusion, the same numbering has been employed in those formulæ cited in the text.

page 89 note * It would thus appear that the ratio of withdrawals as deduced from the values in column (4) would give some approximation to the force of withdrawal; and this suggestion, which appears to have been originally made by Mr. G. King, is referred to by Mr. Ryan (J.I.A., xxxi, 310). I cannot, however, trace the original reference, attributed to Mr. King, in the pages of the Journal. The divisor E_[x]+t , in column (8), is not appropriate for deducing the true force of withdrawal (as is pointed out by Mr. Ryan, loc. cit.); and I have been unable, from the values given in columns (2) to (8) of Schedule (D), to deduce any expression which would give a true (or very approximate) representation of the rate of withdrawal in successive years of duration.