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The Number Concept: Its Origin and Development

Chapter 21: Footnotes:
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The study examines how the concept of number arises and develops across languages and cultures, surveying counting practices, limitations of numeral systems, and the origins and formation of number words. It collects and compares cardinal numeral systems in different bases, including binary, quinary, and vigesimal, and traces constructive methods such as additive and subtractive formation. Emphasis is placed on linguistic evidence, comparative lists of numerals, the omission of ordinal treatment, and incidental observations on animal and child numeracy. The work aims to show structural patterns and limits that shape numeral vocabularies while relying on extensive multilingual sources.


Footnotes:

1Brinton, D. G., Essays of an Americanist, p. 406; and American Race, p. 359.

2This information I received from Dr. Brinton by letter.

3Tylor, Primitive Culture, Vol. I. p. 240.

4Nature, Vol. XXXIII. p. 45.

5Spix and Martius, Travels in Brazil, Tr. from German by H. E. Lloyd, Vol. II. p. 255.

6De Flacourt, Histoire de le grande Isle de Madagascar, ch. xxviii. Quoted by Peacock, Encyc. Met., Vol. I. p. 393.

7Bellamy, Elizabeth W., Atlantic Monthly, March, 1893, p. 317.

8Grundriss der Sprachwissenschaft, Bd. III. Abt. i., p. 94.

9Pruner-Bey, Bulletin de la Société d'Anthr. de Paris, 1861, p. 462.

10“Manual Concepts,” Am. Anthropologist, 1892, p. 292.

11Tylor, Primitive Culture, Vol. I. p. 245.

12Op. cit., loc. cit.

13“Aboriginal Inhabitants of Andaman Islands,” Journ. Anth. Inst., 1882, p. 100.

14Morice, A., Revue d'Anthropologie, 1878, p. 634.

15Macdonald, J., “Manners, Customs, etc., of South African Tribes,” Journ. Anthr. Inst., 1889, p. 290. About a dozen tribes are enumerated by Mr. Macdonald: Pondos, Tembucs, Bacas, Tolas, etc.

16Codrington, R. H., Melanesians, their Anthropology and Folk-Lore, p. 353.

17E.g. the Zuñis. See Cushing's paper quoted above.

18Haddon, A. C., “Ethnography Western Tribes Torres Strait,” Journ. Anth. Inst., 1889, p. 305. For a similar method, see Life in the Southern Isles, by W. W. Gill.

19Tylor, Primitive Culture, Vol. I. p. 246.

20Brinton, D. G., Letter of Sept. 23, 1893.

21Ibid. The reference for the Mbocobi, infra, is the same. See also Brinton's American Race, p. 361.

22Tylor, Primitive Culture, Vol. I. p. 243.

23Op. cit., loc. cit.

24Hyades, Bulletin de la Société d'Anthr. de Paris, 1887, p. 340.

25Wiener, C., Pérou et Bolivie, p. 360.

26Marcoy, P., Travels in South America, Vol. II p. 47. According to the same authority, most of the tribes of the Upper Amazon cannot count above 2 or 3 except by reduplication.

27Op. cit., Vol. II. p. 281.

28Glossaria Linguarum Brasiliensium. Bororos, p. 15; Guachi, p. 133; Carajas, p. 265.

29Curr, E. M., The Australian Race, Vol. I. p. 282. The next eight lists are, in order, from I. p. 294, III. p. 424, III. p. 114, III. p. 124, II. p. 344, II. p. 308, I. p. 314, III. p. 314, respectively.

30Bonwick, J., The Daily Life and Origin of the Tasmanians, p. 144.

31Latham, Comparative Philology, p. 336.

32The Australian Race, Vol. I. p. 205.

33Mackenzie, A., “Native Australian Langs.,” Journ. Anthr. Inst., 1874, p. 263.

34Curr, The Australian Race, Vol. II. p. 134. The next four lists are from II. p. 4, I. p. 322, I. p. 346, and I. p. 398, respectively.

35Curr, op. cit., Vol. III. p. 50.

36Op. cit., Vol. III. p. 236.

37Müller, Sprachwissenschaft. II. i. p. 23.

38Op. cit., II. i. p. 31.

39Bonwick, op. cit., p. 143.

40Curr, op. cit., Vol. I. p. 31.

41Deschamps, L'Anthropologie, 1891, p. 318.

42Man, E. H. Aboriginal Inhabitants of the Andaman Islands, p. 32.

43Müller, Sprachwissenschaft, I. ii. p. 29.

44Oldfield, A., Tr. Eth. Soc. Vol. III. p. 291.

45Bancroft, H. H., Native Races, Vol. I. p. 564.

46“Notes on Counting, etc., among the Eskimos of Point Barrow.” Am. Anthrop., 1890, p. 38.

47Second Voyage, p. 556.

48Personal Narrative, Vol. I. p. 311.

49Burton, B. F., Mem. Anthr. Soc. of London, Vol. I. p. 314.

50Confessions. In collected works, Edinburgh, 1890, Vol. III. p. 337.

51Ellis, Robert, On Numerals as Signs of Primeval Unity. See also Peruvia Scythia, by the same author.

52Stanley, H. M., In Darkest Africa, Vol. II. p. 493.

53Stanley, H. M., Through the Dark Continent, Vol. II. p. 486.

54Haumontè, Parisot, Adam, Grammaire et Vocabulaire de la Langue Taensa, p. 20.

55Chamberlain, A. F., Lang. of the Mississaga Indians of Skugog. Vocab.

56Boas, Fr., Sixth Report on the Indians of the Northwest, p. 105.

57Beauregard, O., Bulletin de la Soc. d'Anthr. de Paris, 1886, p. 526.

58Ray, S. H., Journ. Anthr. Inst., 1891, p. 8.

59Op. cit., p. 12.

60Müller, Sprachwissenschaft, IV. i. p. 136.

61Brinton, The Maya Chronicles, p. 50.

62Trumbull, On Numerals in Am. Ind. Lang., p. 35.

63Boas, Fr. This information was received directly from Dr. Boas. It has never before been published.

64Bancroft, H. H., Native Races, Vol. II. p. 753. See also p. 199, infra.

65Mann, A., “Notes on the Numeral Syst. of the Yoruba Nation,” Journ. Anth. Inst., 1886, p. 59, et seq.

66Müller, Sprachwissenschaft, IV. i. p. 202.

67Trumbull, J. H., On Numerals in Am. Ind. Langs., p. 11.

68Cushing, F. H., “Manual Concepts,” Am. Anthr., 1892, p. 289.

69Grimm, Geschichte der deutschen Sprache, Vol. I. p. 239.

70Murdoch, J., American Anthropologist, 1890, p. 39.

71Kleinschmidt, S., Grammatik der Grönlandischen Sprache, p. 37.

72Brinton, The Arawak Lang. of Guiana, p. 4.

73Petitot, E., Dictionnaire de la langue Dènè-Dindjie, p. lv.

74Gilij, F. S., Saggio di Storia Am., Vol. II. p. 333.

75Müller, Sprachwissenschaft, II. i. p. 389.

76Op. cit., p. 395.

77Müller, Sprachwissenschaft, II. i. p. 438.

78Peacock, “Arithmetic,” in Encyc. Metropolitana, 1, p. 480.

79Brinton, D. G., “The Betoya Dialects,” Proc. Am. Philos. Soc., 1892, p. 273.

80Ridley, W., “Report on Australian Languages and Traditions.” Journ. Anth. Inst., 1873, p. 262.

81Gatschet, “Gram. Klamath Lang.” U. S. Geog. and Geol. Survey, Vol. II. part 1, pp. 524 and 536.

82Letter of Nov. 17, 1893.

83Müller, Sprachwissenschaft, II. i. p. 439.

84Hale, “Indians of No. West. Am.,” Tr. Am. Eth. Soc., Vol. II. p. 82.

85Brinton, D. G., Studies in So. Am. Native Languages, p. 25.

86Tr. Am. Philological Association, 1874, p. 41.

87Tylor, Primitive Culture, Vol. I. p. 251.

88Müller, Sprachwissenschaft, IV. i. p. 27.

89See infra, Chapter VII.

90Ellis, A. B., Ewe Speaking Peoples, etc., p. 253.

91Tylor, Primitive Culture, Vol. I. p. 256.

92Stanley, In Darkest Africa, Vol. II. p. 493.

93Chamberlain, A. F., Proc. Brit. Ass. Adv. of Sci., 1892, p. 599.

94Boas, Fr., “Sixth Report on Northwestern Tribes of Canada,” Proc. Brit. Ass. Adv. Sci., 1890, p. 657.

95Hale, H., “Indians of Northwestern Am.,” Tr. Am. Eth. Soc., Vol. II. p. 88.

96Op. cit., p. 95.

97Müller, Sprachwissenschaft, II. ii. p. 147.

98Schoolcraft, Archives of Aboriginal Knowledge, Vol. IV. p. 429.

99Du Chaillu, P. B., Tr. Eth. Soc., London, Vol. I. p. 315.

100Latham, R. G., Essays, chiefly Philological and Ethnographical, p. 247. The above are so unlike anything else in the world, that they are not to be accepted without careful verification.

101Pott, Zählmethode, p. 45.

102Gatschet, A. S., The Karankawa Indians, the Coast People of Texas. The meanings of 6, 7, 8, and 9 are conjectural with me.

103Stanley, H. M., In Darkest Africa, Vol. II. p. 492.

104Müller, Sprachwissenschaft, II. i. p. 317.

105Toy, C. H., Trans. Am. Phil. Assn., 1878, p. 29.

106Burton, R. F., Mem. Anthrop. Soc. of London. 1, p. 314. In the illustration which follows, Burton gives 6820, instead of 4820; which is obviously a misprint.

107Dobrizhoffer, History of the Abipones, Vol. II. p. 169.

108Sayce, A. H., Comparative Philology, p. 254.

109Tr. Eth. Society of London , Vol. III. p. 291.

110Ray, S. H., Journ. Anthr. Inst., 1889, p. 501.

111Stanley, In Darkest Africa, Vol. II. p. 492.

112Op. cit., loc. cit.

113Tylor, Primitive Culture, Vol. I. p. 249.

114Müller, Sprachwissenschaft, IV. i. p. 36.

115Martius, Glos. Ling. Brasil., p. 271.

116Tylor, Primitive Culture, Vol. I. p. 248.

117Roth, H. Ling, Aborigines of Tasmania, p. 146.

118Lull, E. P., Tr. Am. Phil, Soc., 1873, p. 108.

119Ray, S. H. “Sketch of Api Gram.,” Journ. Anthr. Inst., 1888, p. 300.

120Kleinschmidt, S., Grammatik der Grönlandischen Spr., p. 39.

121Müller, Sprachwissenschaft, I. ii. p. 184.

122Op. cit., I. ii. p. 18, and II. i. p. 222.

123Squier, G. E., Nicaragua, Vol. II. p. 326.

124Schoolcraft, H. R., Archives of Aboriginal Knowledge, Vol. II. p. 208.

125Tylor, Primitive Culture, Vol. I. p. 264.

126Goedel, “Ethnol. des Soussous,” Bull. de la Soc. d'Anthr. de Paris, 1892, p. 185.

127Ellis, W., History of Madagascar, Vol. I. p. 507.

128Beauregard, O., Bull. de la Soc. d'Anthr. de Paris, 1886, p. 236.

129Schoolcraft, H. R., Archives of Aboriginal Knowledge, Vol. II. p. 207.

130Tylor, Primitive Culture, Vol. I. p. 249.

131Op. cit. Vol. I. p. 250.

132Peacock, Encyc. Metropolitana, 1, p. 478.

133Op. cit., loc. cit.

134Schoolcraft, H. R., Archives of Aboriginal Knowledge, Vol. II. p. 213.

135Op. cit., p. 216.

136Op. cit., p. 206.

137Mariner, Gram. Tonga Lang., last part of book. [Not paged.]

138Morice, A. G., “The Déné Langs,” Trans. Can. Inst., March 1890, p. 186.

139Boas, Fr., “Fifth Report on the Northwestern Tribes of Canada,” Proc. Brit. Ass. Adv. of Science, 1889, p. 881.

140Do. Sixth Rep., 1890, pp. 684, 686, 687.

141Op. cit., p. 658.

142Bancroft, H. H., Native Races, Vol. II. p. 499.

143Tr. Ethnological Soc. of London, Vol. IV. p. 92.

144Any Hebrew lexicon.

145Schröder, P., Die Phönizische Sprache, p. 184 et seq.

146Müller, Sprachwissenschaft, II. ii. p. 147.

147On Numerals in Am. Indian Languages.

148Ellis, A. B., Ewe Speaking Peoples, etc., p. 253. The meanings here given are partly conjectural.

149Pott, Zählmethode, p. 29.

150Schoolcraft, op. cit., Vol. IV. p. 429.

151Trumbull, op. cit.

152Chamberlain, A. F., Lang, of the Mississaga Indians, Vocab.

153Crawfurd, Hist. Ind. Archipelago, 1, p. 258.

154Hale, H., Eth. and Philol., Vol. VII.; Wilkes, Expl. Expedition, Phil. 1846, p. 172.

155Crawfurd, op. cit., 1, p. 258.

156Op. cit., loc. cit.

157Bancroft, H. H., Native Races, Vol. II. p. 498.

158Vignoli, T., Myth and Science, p. 203.

159Codrington, R. H., The Melanesian Languages, p. 249.

160Op. cit., loc. cit.

161Codrington, R. H., The Melanesian Languages, p. 249.

162Wickersham, J., “Japanese Art on Puget Sound,” Am. Antiq., 1894, p. 79.

163Codrington, R. H., op. cit., p. 250.

164Tylor, Primitive Culture, Vol. I. p. 252.

165Compare a similar table by Chase, Proc. Amer. Philos. Soc., 1865, p. 23.

166Leibnitzii Opera, III. p. 346.

167Pruner-Bey, Bulletin de la Soc. d'Anthr. de Paris, 1860, p. 486.

168Curr, E. M., The Australian Race, Vol. I. p. 32.

169Haddon, A. C., “Western Tribes of the Torres Straits,” Journ. Anthr. Inst., 1889, p. 303.

170Taplin, Rev. G., “Notes on a Table of Australian Languages,” Journ. Anthr. Inst., 1872, p. 88. The first nine scales are taken from this source.

171Latham, R. G., Comparative Philology, p. 352.

172It will be observed that this list differs slightly from that given in Chapter II.

173Curr, E. M., The Australian Race, Vol. III. p. 684.

174Bonwick, Tasmania, p. 143.

175Lang, J. D., Queensland, p. 435.

176Bonwick, Tasmania, p. 143.

177Müller, Sprachwissenschaft, II. i. p. 58.

178Op. cit., II. i. p. 70.

179Op. cit., II. i. p. 23.

180Barlow, H., “Aboriginal Dialects of Queensland,” Journ. Anth. Inst., 1873, p. 171.

181Curr, E. M., The Australian Race, Vol. II. p. 26.

182Op. cit., Vol. II. p. 208.

183Op. cit., Vol. II. p. 278.

184Op. cit., Vol. II. p. 288.

185Op. cit., Vol. I. p. 258.

186Op. cit., Vol. I. p. 316.

187Op. cit., Vol. III. p. 32. The next ten lists are taken from the same volume, pp. 282, 288, 340, 376, 432, 506, 530, 558, 560, 588, respectively.

188Brinton, The American Race, p. 351.

189Martius, Glossaria Ling. Brazil., p. 307.

190Op. cit., p. 148.

191Müller, Sprachwissenschaft, II. i. p. 438.

192Peacock, “Arithmetic,” Encyc. Metropolitana, 1, p. 480.

193Brinton, Studies in So. Am. Native Langs., p. 67.

194Op. cit., loc. cit.

195Brinton, Studies in So. Am. Native Langs., p. 67. The meanings of the numerals are from Peacock, Encyc. Metropolitana, 1, p. 480.

196Mason, Journ. As. Soc. of Bengal, Vol. XXVI. p. 146.

197Curr, E. M., The Australian Race, Vol. III. p. 108.

198Bancroft, H. H., Native Races, Vol. I. p. 274.

199Clarke, Hyde, Journ. Anthr. Inst., 1872, p. clvii. In the article from which this is quoted, no evidence is given to substantiate the assertion made. It is to be received with great caution.

200Hale, H., Wilkes Exploring Expedition, Vol. VII. p. 172.

201Op. cit., p. 248.

202Hale, Ethnography and Philology, p. 247.

203Loc. cit.

204Ellis, Polynesian Researches, Vol. IV. p. 341.

205Gill, W. W., Myths and Songs of the South Pacific, p. 325.

206Peacock, “Arithmetic,” Encyc. Metropolitana, 1, p. 479.

207Peacock, Encyc. Metropolitana, 1, p. 480.

208Sprachverschiedenheit, p. 30.

209Crawfurd, History of the Indian Archipelago, Vol. I. p. 256.

210Pott, Zählmethode, p. 39.

211Op. cit., p. 41.

212Müller, Sprachwissenschaft, II. i. p. 317. See also Chap. III., supra.

213Long, S. H., Expedition, Vol. II. p. lxxviii.

214Martius, Glossaria Ling. Brasil., p. 246.

215Hale, Ethnography and Philology, p. 434.

216Müller, Sprachwissenschaft, II. ii. p. 82.

217The information upon which the above statements are based was obtained from Mr. W. L. Williams, of Gisborne, N.Z.

218Primitive Culture, Vol. I. p. 268.

219Ralph, Julian, Harper's Monthly, Vol. 86, p. 184.

220Lappenberg, J. M., History of Eng. under the Anglo-Saxon Kings, Vol. I. p. 82.

221The compilation of this table was suggested by a comparison found in the Bulletin Soc. Anth. de Paris, 1886, p. 90.

222Hale, Ethnography and Philology, p. 126.

223Müller, Sprachwissenschaft, II. ii. p. 183.

224Bachofen, J. J., Antiquarische Briefe, Vol. I. pp. 101–115, and Vol. II. pp. 1–90.

225An extended table of this kind may be found in the last part of Nystrom's Mechanics.

226Schubert, H., quoting Robert Flegel, in Neumayer's Anleitung zu Wissenschaftlichen Beobachtung auf Reisen, Vol. II. p. 290.

227These numerals, and those in all the sets immediately following, except those for which the authority is given, are to be found in Chapter III.

228Codrington, The Melanesian Languages, p. 222.

229Müller, Sprachwissenschaft, II. ii. p. 83.

230Op. cit., I. ii. p. 55. The next two are the same, p. 83 and p. 210. The meaning given for the Bari puök is wholly conjectural.

231Gallatin, “Semi-civilized Nations,” Tr. Am. Eth. Soc., Vol. I. p. 114.

232Müller, Sprachwissenschaft, II. ii. p. 80. Erromango, the same.

233Boas, Fr., Proc. Brit. Ass'n. Adv. Science, 1889, p. 857.

234Hankel, H., Geschichte der Mathematik, p. 20.

235Murdoch, J., “Eskimos of Point Barrow,” Am. Anthr., 1890, p. 40.

236Martius, Glos. Ling. Brasil., p. 360.

237Du Graty, A. M., La République du Paraguay, p. 217.

238Codrington, The Melanesian Languages, p. 221.

239Müller, Sprachwissenschaft, II. i. p. 363.

240Spurrell, W., Welsh Grammar, p. 59.

241Olmos, André de, Grammaire Nahuatl ou Mexicaine, p. 191.

242Moncelon, Bull. Soc. d'Anthr. de Paris, 1885, p. 354. This is a purely digital scale, but unfortunately M. Moncelon does not give the meanings of any of the numerals except the last.

243Ellis, Peruvia Scythia, p. 37. Part of these numerals are from Martius, Glos. Brasil., p. 210.

244Codrington, The Melanesian Languages, p. 236.

245Schweinfurth, G., Linguistische Ergebnisse einer Reise nach Centralafrika, p. 25.

246Park, M., Travels in the Interior Districts of Africa, p. 8.

247Pott, Zählmethode, p. 37.

248Op. cit., p. 39.

249Müller, Sprachwissenschaft, IV. i. p. 101. The Kru scale, kindred with the Basa, is from the same page.

250Park, in Pinkerton's Voyages and Travels, Vol. XVI. p. 902.

251Park, Travels, Vol. I. p. 16.

252Schweinfurth, G., Linguistische Ergebnisse einer Reise nach Centralafrika, p. 78.

253Park, Travels, Vol. I. p. 58.

254Goedel, “Ethnol. des Soussous,” Bull. Soc. Anth. Paris, 1892, p. 185.

255Müller, Sprachwissenschaft, I. ii. p. 114. The Temne scale is from the same page. These two languages are closely related.

256Op. cit., I. ii. p. 155.

257Op. cit., I. ii. p. 55.

258Long, C. C., Central Africa, p. 330.

259Müller, Sprachwissenschaft, IV. i. p. 105.

260Pott, Zählmethode, p. 41.

261Müller, op. cit., I. ii. p. 140.

262Müller, Sprachwissenschaft, IV. i. p. 81.

263Pott, Zählmethode, p. 41.

264Müller, op. cit., I. ii., p. 210.

265Pott, Zählmethode, p. 42.

266Schweinfurth, Linguistische Ergebnisse, p. 59.

267Müller, Sprachwissenschaft, I. ii. p. 261. The “ten” is not given.

268Stanley, Through the Dark Continent, Vol. II. p. 490. Ki-Nyassa, the same page.

269Müller, op. cit., I. ii. p. 261.

270Du Chaillu, Adventures in Equatorial Africa, p. 534.

271Müller, Sprachwissenschaft, III. i. p. 65.

272Du Chaillu, Adventures in Equatorial Africa, p. 533.

273Müller, op. cit., III. ii. p. 77.

274Balbi, A., L'Atlas Eth., Vol. I. p. 226. In Balbi's text 7 and 8 are ansposed. Taru for 5 is probably a misprint for tana.

275Du Chaillu, op. cit., p. 533. The next scale is op. cit., p. 534.

276Beauregard, O., Bull. Soc. Anth. de Paris, 1886, p. 526.

277Pott, Zählmethode, p. 46.

278Op. cit., p. 48.

279Turner, Nineteen Years in Polynesia, p. 536.

280Erskine, J. E., Islands of the Western Pacific, p. 341.

281Op. cit., p. 400.

282Codrington, Melanesian Languages, pp. 235, 236.

283Peacock, Encyc. Met., Vol. 1. p. 385. Peacock does not specify the dialect.

284Erskine, Islands of the Western Pacific, p. 360.

285Turner, G., Samoa a Hundred Years Ago, p. 373. The next three scales are from the same page of this work.

286Codrington, Melanesian Languages, p. 235. The next four scales are from the same page. Perhaps the meanings of the words for 6 to 9 are more properly “more 1,” “more 2,” etc. Codrington merely indicates their significations in a general way.

287Hale, Ethnography and Philology, p. 429. The meanings of 6 to 9 in this and the preceding are my conjectures.

288Müller, Sprachwissenschaft, IV. i. p. 124.

289Aymonier, E., Dictionnaire Francaise-Cambodgien.

290Müller, Op. cit., II. i. p. 139.

291Müller, Sprachwissenschaft, II. i. p. 123.

292Wells, E. R., Jr., and John W. Kelly, Bureau of Ed., Circ. of Inf., No. 2, 1890.

293Pott, Zählmethode, p. 57.

294Müller, Op. cit., II. i. p. 161.

295Petitot, Vocabulaire Française Esquimau, p. lv.

296Müller, Sprachwissenschaft, II. i. p. 253.

297Müller, Op. cit., II. I.i. p. 179, and Kleinschmidt, Grönlandisches Grammatik.

298Adam, L., Congres Int. des Am., 1877, p. 244 (see p. 162 infra).

299Gallatin, “Synopsis of Indian Tribes,” Trans. Am. Antq. Soc., 1836, p. 358. The next fourteen lists are, with the exception of the Micmac, from the same collection. The meanings are largely from Trumbull, op. cit.

300Schoolcraft, Archives of Aboriginal Knowledge, Vol. II. p. 211.

301Schoolcraft, Archives of Aboriginal Knowledge, Vol. V. p. 587.

302In the Dakota dialects 10 is expressed, as here, by a word signifying that the fingers, which have been bent down in counting, are now straightened out.

303Boas, Fifth Report B. A. A. S., 1889. Reprint, p. 61.

304Boas, Sixth Report B. A. A. S., 1890. Reprint, p. 117. Dr. Boas does not give the meanings assigned to 7 and 8, but merely states that they are derived from 2 and 3.

305Op. cit., p. 117. The derivations for 6 and 7 are obvious, but the meanings are conjectural.

306Boas, Sixth Report B. A. A. S., 1889. Reprint, pp. 158, 160. The meanings assigned to the Tsimshian 8 and to Bilqula 6 to 8 are conjectural.

307Hale, Ethnography and Philology, p. 619.

308Op. cit., loc. cit.

309Hale, Ethnography and Philology, p. 619.

310Müller, Sprachwissenschaft, II. i. p. 436.

311Op. cit., IV. i. p. 167.

312Op. cit., II. i. p. 282.

313Op. cit., II. i. p. 287. The meanings given for the words for 7, 8, 9 are conjectures of my own.

314Müller, Sprachwissenschaft, II. i. p. 297.

315Pott, Zählmethode, p. 90.

316Müller, op. cit., II. i. p. 379.

317Gallatin, “Semi-Civilized Nations of Mexico and Central America,” Tr. Am. Ethn. Soc., Vol. I. p. 114.

318Adam, Lucien, Congres Internationale des Americanistes, 1877, Vol. II. p. 244.

319Müller, Sprachwissenschaft, II. i. p. 395. I can only guess at the meanings of 6 to 9. They are obviously circumlocutions for 5-1, 5-2, etc.

320Op. cit., p. 438. Müller has transposed these two scales. See Brinton's Am. Race, p. 358.

321Marcoy, P., Tour du Monde, 1866, 2ème sem. p. 148.

322Op. cit., p. 132. The meanings are my own conjectures.

323An elaborate argument in support of this theory is to be found in Hervas' celebrated work, Arithmetica di quasi tutte le nazioni conosciute.

324See especially the lists of Hale, Gallatin, Trumbull, and Boas, to which references have been given above.

325Thiel, B. A., “Vocab. der Indianier in Costa Rica,” Archiv für Anth., xvi. p. 620.

326These three examples are from A. R. Wallace's Narrative of Travels on the Amazon and Rio Negro, vocab. Similar illustrations may be found in Martius' Glos. Brasil.

327Martius, Glos. Brasil., p. 176.

328Adam, L., Congres International des Americanistes, 1877, Vol. II. p. 244. Given also supra, p. 53.

329O'Donovan, Irish Grammar, p. 123.

330Armstrong, R. A., Gaelic Dict., p. xxi.

331Spurrell, Welsh Dictionary.

332Kelly, Triglot Dict., pub. by the Manx Society.

333Guillome, J., Grammaire Française-Bretonne, p. 27.

334Gröber, G., Grundriss der Romanischen Philologie, Bd. I. p. 309.

335Pott, Zählmethode, p. 88.

336Van Eys, Basque Grammar, p. 27.

337Pott, Zählmethode, p. 101.

338Op. cit., p. 78.

339Müller, Sprachwissenschaft, I. ii. p. 124.

340Op. cit., p. 155.

341Op. cit., p. 140.

342Op. cit., loc. cit.

343Schweinfurth, Reise nach Centralafrika, p. 25.

344Müller, Sprachwissenschaft, IV. i. p. 83.

345Op. cit., IV. i. p. 81.

346Op. cit., I. ii. p. 166.

347Long, C. C., Central Africa, p. 330.

348Peacock, Encyc. Met., Vol. I. p. 388.

349Müller, Sprachwissenschaft, III. ii. p. 64. The next seven scales are from op. cit., pp. 80, 137, 155, 182, 213.

350Pott, Zählmethode, p. 83.

351Op. cit., p. 83,—Akari, p. 84; Circassia, p. 85.

352Müller, Sprachwissenschaft, II. i. p. 140.

353Pott, Zählmethode, p. 87.

354Müller, Sprachwissenschaft, II. ii. p. 346.

355Op. cit., III. i. p. 130.

356Man, E. H., “Brief Account of the Nicobar Islands,” Journ. Anthr. Inst., 1885, p. 435.

357Wells, E. R., Jr., and Kelly, J. W., “Eng. Esk. and Esk. Eng. Vocab.,” Bureau of Education Circular of Information, No. 2, 1890, p. 65.

358Petitot, E., Vocabulaire Française Esquimau, p. lv.

359Boas, Fr., Proc. Brit. Ass. Adv. Sci., 1889, p. 857.

360Boas, Sixth Report on the Northwestern Tribes of Canada, p. 117.

361Boas, Fr., Fifth Report on the Northwestern Tribes of Canada, p. 85.

362Gallatin, Semi-Civilized Nations, p. 114. References for the next two are the same.

363Bancroft, H. H., Native Races of the Pacific States, Vol. II. p. 763. The meanings are from Brinton's Maya Chronicles, p. 38 et seq.

364Brinton, Maya Chronicles, p. 44.

365Siméon Rémi, Dictionnaire de la langue nahuatl, p. xxxii.

366An error occurs on p. xxxiv of the work from which these numerals are taken, which makes the number in question appear as 279,999,999 instead of 1,279,999,999.

367Gallatin, “Semi-Civilized Nations of Mexico and Central America,” Tr. Am. Ethn. Soc. Vol. I. p. 114.

368Pott, Zählmethode, p. 89. The Totonacos were the first race Cortez encountered after landing in Mexico.

369Op. cit., p. 90. The Coras are of the Mexican state of Sonora.

370Gallatin, Semi-Civilized Nations, p. 114.

371Humboldt, Recherches, Vol. II. p. 112.

372Squier, Nicaragua, Vol. II. p. 326.

373Gallatin, Semi-Civilized Nations, p. 57.