113 Plutarch, _Agis_, II. Plutarch says that the custom was observed “at intervals of nine years” (δι᾽ ἐτῶν ἐννέα), but the expression is equivalent to our “at intervals of eight years.” In reckoning intervals of time numerically the Greeks included both the terms which are separated by the interval, whereas we include only one of them. For example, our phrase “every second day” would be rendered in Greek διὰ τρίτης ἡμέρας, literally “every third day.” Again, a cycle of two years is in Greek _trieteris_, literally “a period of three years”; a cycle of eight years is _ennaeteris_, literally “a period of nine years”; and so forth. See Censorinus, _De die natali_, 18. The Latin use of the ordinal numbers is similar, _e.g._ our “every second year” would be _tertio quoque anno_ in Latin. However, the Greeks and Romans were not always consistent in this matter, for they occasionally reckoned in our fashion. The resulting ambiguity is not only puzzling to moderns; it sometimes confused the ancients themselves. For example, it led to a derangement of the newly instituted Julian calendar, which escaped detection for more than thirty years. See Macrobius, _Saturn._ i. 14. 13 _sq._; Solinus, i. 45-47. On the ancient modes of counting in such cases see A. Schmidt, _Handbuch der griechischen Chronologie_ (Jena, 1888), pp. 95 _sqq._ According to Schmidt, the practice of adding both terms to the sum of the intervening units was not extended by the Greeks to numbers above nine. _ 114 Die Dorier_,2 ii. 96. M43 Superstitions of the Australian aborigines as to shooting stars. 115 E. Man, _Aboriginal Inhabitants of the Andaman Islands_, pp. 84 _sq._ 116 W. E. Roth, _North Queensland Bulletin, No. 5, Superstition, Magic, and Medicine_ (Brisbane, 1903), p. 8. 117 A. W. Howitt, _The Native Tribes of South-East Australia_, p. 429. 118 A. W. Howitt, _op. cit._ p. 430. One of the earliest writers on New South Wales reports that the natives attributed great importance to the falling of a star (D. Collins,_Account of the English Colony in New South Wales_ (London, 1804), p. 383). 119 Spencer and Gillen, _Northern Tribes of Central Australia_, p. 627. 120 Spencer and Gillen, _op. cit._ pp. 488, 627 _sq._ 121 G. Thilenius, _Ethnographische Ergebnisse aus Melanesien_, ii. (Halle, 1903) p. 129. M44 Superstitions of the negroes and other African races as to shooting stars. 122 H. A. Junod, _Les Ba-ronga_ (Neuchatel, 1898), p. 470. 123 A. C. Hollis, _The Masai_ (Oxford, 1905), p. 316. 124 J. Campbell, _Travels in South Africa_ (London, 1815), pp. 428 _sq._ _ 125 Id._, _Travels in South Africa, Second Journey_ (London, 1822), ii. 204.