^{page 107 note *} The sense in which the subscript [x] is used with d and L is slightly different from the accepted meaning, “x” denotes age last birthday at date of death or enumeration, while the addition of the brackets indicates that the lives have been assured for some period less than one year.

^{page 109 note *} This proportion is assumed to be independent of the entry age.

^{page 110 note *} A brief explanation of how these expressions are derived is given in Appendix IV.

^{page 114 note *} Similarly we shall denote by ₁d ^z_[x] the deaths in duration 0−1 in the calendar year z + 1 out of the entrants n^z _[x] of the year z, so that ₀d ^z_[x] + ₁d ^z_[x] will represent the total deaths in the first year of assurance out of the entrants n^z _[x].

^{page 114 note †} Here , so that, k remaining constant, k′ will vary with the age at entry. Such variation will, however, be slight, and for simplicity in working we shall treat k′ as independent of the age.

^{page 115 note *} f is clearly a factor similar to k′ and varying with the age, but for convenience in working it has been assumed constant and independent of the age.

^{page 116 note *} i.e. uniform distribution of entrants.

^{page 117 note *} Varying with the age.

^{page 120 note *} J.I.A., xlvi., 272.

^{page 123 note *} The algebraic form of ζ, η, etc., is given on p. 135.

^{page 125 note *} J.I.A., 46, 260.

^{page 125 note †} J.I.A., 38, 389.

^{page 125 note ‡} J.I.A., 46, 272.

^{page 128 note *} These figures relate to Office years not coincident with the calendar year ; but it is thought that this does not affect the extent to which “heaping-up” occurs at, the end of the Office year.

^{page 132 note *} See note on p. 135.

^{page 134 note *} See note on p. 135.