^{page 380 note *} Crelier, , Sur le développement de certaines irrationelles en fraction continue.Comptes Rendus … (Paris), cxxviii. pp. 229–231 (year 1899).Google Scholar

^{page 383 note *} Unfortunately omitted from most modern text-books. See Serret, 's Cours d'algèbre supérieure, 4° éd. (1877), i. p. 49.Google Scholar

^{page 383 note †} It would be better to insert here the words “if the periods be different”; for they may be really identical, the mode of writing in the case of certain periods being deceptive on this point. Thus, when A = 7, α = 2, β = 15, we where the periods, although seemingly different, are not really so. A still better instance is got from A-= 7, α = 1, β = 30.

^{page 385 note *} Serret, 's Cours d'algèbre supérieure, i. (1877), p. 46Google Scholar, or Chrystal, 's Algebra, ii. (1889), p. 430.Google Scholar

^{page 386 note *} It is extremely probable that among the papers of the late Mr C. E. Bickmore, Fellow of New College, Oxford, who was an earnest and capable student of this branch of algebra, there are to be found quite a number of results as yet unpublished and worthy of being made known. In a letter dated 29th April 1895, in which some noteworthy theorems are given from a paper prepared for the Oxford Mathematical Society, he says: “Our Society is too poor to print anything.” It would appear that French mathematicians are not similarly hampered (v. Lond. Math. Soc. Proc., xxxiv. p. 129).