^{page 166 note *} Next to the obscurity of its origin, the most remarkable thing about the Roman notation is its continuance and persistence without undergoing curtailment in respect of brevity, or evolution in respect of greater adaptability. The Arabian, Assyrian, and later Greek systems adopted the device of place-value (e.g. 4000; even the Herodian system had its ingenious device of the circumscribing while, on the other hand, the Roman system which existed contemporaneously and coextensively with the Empire is, if we may except the later and restricted employment of such forms as as inflexible and cumbrous as when first it appeared on the page of history. For mathematical purposes its disadvantages are obvious and great. Its only rule is that the larger number precedes the smaller—with this exception, that fours and nines, of whatever rank, may be written in terms of fives and tens (as IV, XL, CD; IX, XC, CM).

^{page 171 note *} A curious use of the body is described by Thomas, N. W. in his Natives of Australia (London, 1906), p. 27Google Scholar: “… They touch various parts of the body in succession, the wrist, the arm, the head, etc., each standing for a particular day, until the intended date is reached. The two or more parties to the arrangement can then keep count of the flight of time by this ingenious system of mnemonics, and meet on the appointed day with as much certainty as if they noted their engagement in a diary.”

^{page 174 note *} The form IIII is still commonly used on watches and clocks.

^{page 174 note †} It is interesting to recollect that in the “Latin” form of benediction the thumb, index, and middle finger are extended to symbolise the Trinity.

^{page 178 note *} “A curious feature of the native languages is that few have any numerals ahove three or four. … Anything above the highest numeral is ‘many.’”—N. W. Thomas, op. cit., p. 27.

“Spix and Martius [Reise in Brazilien, p. 387] say of the low tribes of Brazil, ‘They count commonly by their finger joints, so up to three only, Any larger number they express by the word “many.”’”—Tylor, , Primitive Culture, 4th ed., London, 1903, i. 242.Google Scholar

^{page 178 note †} See First Annual Report of the Bureau of Ethnology … Smithsonian Institution, 1879–80 (Washington, 1881), pp. 355–6.

^{page 178 note ‡} Mommsen, (Die unteritalischen Dialekte, Leipzig, 1850, p. 33)Google Scholar gives the form and evolution of the Koman sign for fifty as follows:—

^{page 179 note *} It may be inferred that, at this elementary stage, when the values 500 and 1000 had not been evolved nor had any signs been allotted to them, the highest known denomination, viz. 100, would monopolise the total symbol for “man” (see p. 181). This inference is corroborated by the fact that the sign for 100 occurs in the cognate Etruscan system as ⊕ and one may assume that not until the higher values 500 and 1000 were evolved was the Roman sign for 100 differentiated from the sign for “man,” which was thus set free to represent 1000. An analogy may be found in the fact that, while many tribes use the term “man” to denote 20 (i.e. the fingers and toes), the Tasmaniane actually reach the limit of “man” with one hand (i.e. 5). See Tylor, , Primitive Culture, 4th ed., London, 1903, i. 242–264.Google Scholar

^{page 181 note *} I. Evans, op. cit., p. 338; cf. pp. 297, 302, 341. II. Clodd, op. cit., pp. 59, 70; cf. pp. 36, 66, 67, 72.

^{page 181 note †} The following passage supports our hypothesis in a remarkable way:—“If we pass from the rude Greenlanders to the comparatively civilised Aztecs, we shall find on the northern as on the southern continent traces of early finger-numeration surviving among higher races. The Mexican names for the first four numerals are as obscure in etymology as our own. But when we come to 5 we find this expressed by macuilli; and as ma (ma-itl) means ‘hand,’ and cuiloa ‘to paint or depict,’ it is likely that the word for 5 may have meant something like ‘hand-depicting.’ In 10, matlactli, the word ma, ‘hand,’ appears again, while tlactli means half, and is represented in the Mexican picture-writings by the figure of half a man from the waist upward; thus it appears that the Aztec 10 means the ‘hand-half’ of a man, just as among the Towka Indians of South America 10 is expressed as ‘half a man,’ a whole man being 20. When the Aztecs reach 20 they call it cempoalli, ‘one counting,’ with evidently the same meaning as elsewhere—one whole man, fingers and toes.”—Tylor, , Primitive Culture, 4th ed., London, 1903, i. p. 249.Google Scholar

^{page 181 note ‡} “… Das römische ür 1000], das in unzähligen Variationen die ausgebreitetste Anwendung gefunden hat.”—Mommsen, Die unteritalischen Dialekte, p. 34.