^{page 61 note 1} [Greater uniformity has since been obtained, for Hardy's Formula is almost universally used at the present day. The Assurance Companies Act, 1909, Fifth Sched. A, 10, lays it down that the rate shall be “calculated upon the mean fund of each year during the period since the last investigation, without deduction of income tax.” Strictly followed, this would lead to the (gross) force of interest; but in practice “mean fund” is usually read as “mean fund excluding the interest income of the year,” and so the gross rate is arrived at.]

^{page 62 note 1} [An interesting and instructive correspondence as to the proper form of the denominator when the gross rate is required will be found in the Insurance Record from 16th March to 11th May 1917.]

^{page 65 note 1} [Cf. the subsequent demonstration of De Morgan's formula by Mr.Newling, Sidney W. F.I.A., J.I.A. xxxvii. 437.]Google Scholar

^{page 69 note 1} [Cf. a Note “On a Method of determining approximately the rate yielded by a redeemable Bond,” by Armstrong, J. R. F.F.A., J.I.A. 50, p. 247Google Scholar, where a similar method was independently developed, prior to the publication of Hardy's Notes.]

^{page 71 note 1} [See note at pp. 85–86 on method of obtaining this expression.]

^{page 71 note 2} [The values of k in the Table do not appear to be obtainable by direct calculation. They were presumably found by a method of interpolation.]

^{page 77 note 1} The investigation in this paragraph is an attempt to reconstruct the process by which the final term in the numerator of Formula (8) may possibly have been obtained. The approximate formulas incidentally given for i are intended to be entirely subsidiary to the object in view. In the opinion of the writer the α's should be regarded as trial values, and closer approximations, if required, should be obtained by calculating θ directly from the expression in paragraph 1.

^{page 80 note 1} The true value of i to seven places is 0324252.

^{page 81 note 1} See Morgan, De: J.I.A., xii. 206Google Scholar; Differential and Integral Calculus, pp. 328-337, 774-6; English, Cydopœdia, Article “Taylor's Theorem.” A note on the formula will appear in a forthcoming number of the J.I.A., vol. 51.