^{page 44 note *} Buchanan's first group refers to unexpired terms 1–4, and by applying the proportion of premiums to sums assured for this group to the sums assured for unexpired term zero I obtained the premiums for unexpired term zero. He omitted these, presumably because their valuation factor is zero, none being due after the date of valuation, though the sums assured are payable the instant after. 1 have included them as they form no exception to the application of my method. They happen to form a group by themselves and their value comes to –1 instead of zero. It is a type of error that can never exceed 2 in magnitude, being due to setting down the α multiplier for premiums to the first place of decimals and the two products whose sum gives the value to the nearest integer. (For sums assured the α multiplier is set down to the nearest integer. For both sums assured and premiums the β multiplier is set down to the nearest integer.)

^{page 45 note *} I reconstructed the Z's from maturity ages derived from the published valuation ages. Those for unexpired terms 0 and 1 were not given, but I took for these the maturity age 58 for unexpired terms 2 and 3.