^{page 135 note *} Eddington, , The Nature of the Physical World (Cambridge, 1930), p. 209.Google Scholar

^{page 136 note *} Morgan, A. de, Penny Encyclopaedia (London, 1842)Google Scholar, Article “Symbols”.

^{page 136 note †} Ibid.

^{page 139 note *} Nature, Jan. 18, 1930. Review of the undermentioned.

^{page 139 note †} Cajori, F., A History of Mathematical Notations, Vol. 11, p. 341 (London, 1928).Google Scholar

^{page 139 note ‡} Ibid. Vol. 11, p. 343.

^{page 140 note *} Blätter für vers. Math. Vol. 11, p. 321 (1933).Google Scholar The same paper appears in Aktuárské Vědy, Vol. IV, p. 114 (1933-34).Google Scholar

^{page 141 note *} Whitehead, A. N., An Introduction to Mathematics, p. 115 (London, 1925).Google Scholar

^{page 141 note †} Ibid. p. 61.

^{page 141 note ‡} Article “Symbols” in Penny Encyclopaedia.

^{page 142 note *} Wickens discusses this definition in J.I.A. Vol. LVI, p. 116.

^{page 142 note †} This is, of course, clear from the symbolic expression also given, but we are here referring to the verbal definition.

^{page 143 note *} See Higham's, C. D. Presidential Address, 26 Nov. 1900, J.I.A. Vol. xxxv, P. 430.Google Scholar

^{page 148 note *} Sós's formulae (17) in his paper in Blätter für vers. Math., which are intended to correspond with van Haaften's formulae (10), (23), (34) and (46) in “Nouveaux Symboles (I)”, contain an unfortunate reversal of symbols and sign. They have here been corrected to agree with van Haaften's formulae.

^{page 150 note *} Todhunter, Compound Interest and Annuities Certain, 3rd ed. p. 16 (1931).

^{page 151 note *} The suitability of i for “invalidity” may here be noted; we find the French “Invalidité”, German “Invalidität”, Danish “Invaliditets”, Dutch “Invaliditeits”, Italian “Invalidità”–a generality which does not hold for the word “Interest”.

^{page 152 note *} “Nouveaux Symboles (11)”, Het verz. Arch. Vol. x11, p. 55.

^{page 160 note *} Blätter für vers. Math. Vol. II, p. 421.

^{page 162 note *} “Nouveaux Symboles (IX)”, Het verz. Arch. Vol. XIV, p. 102.

^{page 162 note †} “Nouveaux Symboles (III)”, Het verz. Arch. Vol. XII, p. 101.

^{page 163 note *} The capital Q was, of course, originally used only for total compound orderof-death probabilities such as and was extended to all total probabilities at the Second International Congress.

^{page 171 note *} This suggestion may be compared with that of René Poussin ( Traité élémentaire des Assurances sur la vie, p. 178 (Paris, 1906))Google Scholar, namely , etc.

^{page 172 note *} Trans. Tenth Cong. Vol. III, p. 286. As to the use of the dash, see para. 37 above.

^{page 174 note *} Cf. para. 89 et seq.

^{page 175 note *} See Steffensen, , Some Recent Researches in the Theory of Statistics and Actuarial Science (Camb. 1930)Google Scholar, and Lidstone, , J.I.A. Vol. LXI, p. 340.Google Scholar

^{page 176 note *} The multi-decrement pension fund theory has not been developed along quite the same lines.

^{page 176 note †} Zur mathematischen Theorie der Invaliditatsversicherung (Berne, 1907).Google Scholar

^{page 177 note *} The American notation is published at the end of each volume of T.A.S.A.

^{page 177 note †} Trans. Ninth Cong. Vol. in, p. 68.

^{page 181 note *} Trans. Ninth Cong. Vol. III p. 69.