^{page 895 note *} Pochhammer, L.. J. f. Math., lxxxi. (1876), p. 33Google Scholar; Chree, C., Camb. Phil. Soc. Trans., xiv. (1889), p. 250Google Scholar; Tedone, O., Roma. Acc. Line. Rend. (5), xiii. (1904), p. 232Google Scholar; cf. Encyk. d. Math. Wiss., Band iv. S. 150.

^{page 898 note *} Pochhammer, L., Untersuchungen über das Gleichgewicht des elastischen Stabes, Kiel, 1879Google Scholar.

^{page 900 note *} Such a reference will be given briefly in the form, 1 (4).

^{page 900 note †} Cf. Art. 11.

^{page 901 note *} Art. 15, footnote.

^{page 902 note *} Cf. Art. 11.

^{page 903 note *} Another notation, also well known, is sometimes convenient, viz. we define ϵ_m as equal to 1 for m>0, but equal to ½ for m = 0. Thus = ½u₀+u₁+u₂ + …. ad ∞.

^{page 904 note *} Cf. Art. 50.

^{page 909 note *} In this and next Article, (1) and (2) state the terms required in the expansions of the various functions in ascending powers of β.

^{page 912 note *} The expansion of D₀ begins with the term ½(v – 8)β⁸.

^{page 913 note *} Love, Elasticity, Art. 130.

^{page 915 note *} The definition of the function G is

^{page 921 note *} When we come to calculate displacements due to a given force, the terms which vary according as p > or < p' disappear.

^{page 924 note *} Love, Elasticity, Arts. 121, 169.

^{page 943 note *} Pierpont, , The Theory of Functions of Real Variables, vol. i. p. 349Google Scholar.

^{page 956 note *} Cf. a method due to Almansi, E., Encyklop. d. Math. Wiss., iv. 25Google Scholar, 13d.

^{page 956 note †} Here b₀ means the least modulus of a zero of D_m

^{page 959 note *} Cf. Art. 47.

^{page 960 note *} Cf. Art. 47.

^{page 964 note *} Cf. Art. 43.

^{page 975 note *} By a similar process to that given for J_m(mx), where x is real, by Graf, und Gubler, , Einleitung in die Theorie der Bessel'schen Functionen erster Heft, Bern, 1898, S. 96Google Scholar.