words for the expression of number,—patrio, 1, pitteni, 2, mahuani, 3. Above 3 they proceed by combinations, as 1 and 3 for 4, 1 and 1 and 3 for 5. Counting above 10 is, however, entirely inconceivable to them, and any number beyond that limit they indicate by tohaine, many. The Conibos,²⁶ of the same region, had, before their contact with the Spanish, only atchoupre, 1, and rrabui, 2; though they made some slight progress above 2 by means of reduplication. The Orejones, one of the low, degraded tribes of the Upper Amazon,²⁷ have no names for number except nayhay, 1, nenacome, 2, feninichacome, 3, ononoeomere, 4. In the extensive vocabularies given by Von Martins,²⁸ many similar examples are found. For the Bororos he gives only couai, 1, maeouai, 2, ouai, 3. The last word, with the proper finger pantomime, serves also for any higher number which falls within the grasp of their comprehension. The Guachi manage to reach 5, but their numeration is of the rudest kind, as the following scale shows: tamak, 1, eu-echo, 2, eu-echo-kailau, 3, eu-echo-way, 4, localau, 5. The Carajas counted by a scale equally rude, and their conception of number seemed equally vague, until contact with the neighbouring tribes furnished them with the means of going beyond their original limit. Their scale shows clearly the uncertain, feeble number sense which is so marked in the interior of South America. It contains wadewo, 1, wadebothoa, 2, wadeboaheodo, 3, wadebojeodo, 4, wadewajouclay, 5, wadewasori, 6, or many.

Turning to the languages of the extinct, or fast vanishing, tribes of Australia, we find a still more noteworthy absence of numeral expressions. In the Gudang dialect²⁹ but two numerals are found—pirman, 1, and ilabiu, 2; in the Weedookarry, ekkamurda, 1, and kootera, 2; and in the Queanbeyan, midjemban, 1, and bollan, 2. In a score or more of instances the numerals stop at 3. The natives of Keppel Bay count webben, 1, booli, 2, koorel, 3; of the Boyne River, karroon, 1, boodla, 2, numma, 3; of the Flinders River, kooroin, 1, kurto, 2, kurto kooroin, 3; at the mouth of the Norman River, lum, 1, buggar, 2, orinch, 3; the Eaw tribe, koothea, 1, woother, 2, marronoo, 3; the Moree, mal, 1, boolar, 2, kooliba, 3; the Port Essington,³⁰ erad, 1, nargarick, 2, nargarickelerad, 3; the Darnly Islanders,³¹ netat, 1, naes, 2, naesa netat, 3; and so on through a long list of tribes whose numeral scales are equally scanty. A still larger number of tribes show an ability to count one step further, to 4; but beyond this limit the majority of Australian and Tasmanian tribes do not go. It seems most remarkable that any human being should possess the ability to count to 4, and not to 5. The number of fingers on one hand furnishes so obvious a limit to any of these rudimentary systems, that positive evidence is needed before one can accept the statement. A careful examination of the numerals in upwards of a hundred Australian dialects leaves no doubt, however, that such is the fact. The Australians in almost all cases count by pairs; and so pronounced is this tendency that they pay but little attention to the fingers. Some tribes do not appear ever to count beyond 2—a single pair. Many more go one step further; but if they do, they are as likely as not to designate their next numeral as two-one, or possibly, one-two. If this step is taken, we may or may not find one more added to it, thus completing the second pair. Still, the Australian's capacity for understanding anything which pertains to number is so painfully limited that even here there is sometimes an indefinite expression formed, as many, heap, or plenty, instead of any distinct numeral; and it is probably true that no Australian language contains a pure, simple numeral for 4. Curr, the best authority on this subject, believes that, where a distinct word for 4 is given, investigators have been deceived in every case.³² If counting is carried beyond 4, it is always by means of reduplication. A few tribes gave expressions for 5, fewer still for 6, and a very small number appeared able to reach 7. Possibly the ability to count extended still further; but if so, it consisted undoubtedly in reckoning one pair after another, without any consciousness whatever of the sum total save as a larger number.

The numerals of a few additional tribes will show clearly that all distinct perception of number is lost as soon as these races attempt to count above 3, or at most, 4. The Yuckaburra³³ natives can go no further than wigsin, 1, bullaroo, 2, goolbora, 3. Above here all is referred to as moorgha, many. The Marachowies³⁴ have but three distinct numerals,—cooma, 1, cootera, 2, murra, 3. For 4 they say minna, many. At Streaky Bay we find a similar list, with the same words, kooma and kootera, for 1 and 2, but entirely different terms, karboo and yalkata for 3 and many. The same method obtains in the Minnal Yungar tribe, where the only numerals are kain, 1, kujal, 2, moa, 3, and bulla, plenty. In the Pinjarra dialect we find doombart, 1, gugal, 2, murdine, 3, boola, plenty; and in the dialect described as belonging to “Eyre's Sand Patch,” three definite terms are given—kean, 1, koojal, 2, yalgatta, 3, while a fourth, murna, served to describe anything greater. In all these examples the fourth numeral is indefinite; and the same statement is true of many other Australian languages. But more commonly still we find 4, and perhaps 3 also, expressed by reduplication. In the Port Mackay dialect³⁵ the latter numeral is compound, the count being warpur, 1, boolera, 2, boolera warpur, 3. For 4 the term is not given. In the dialect which prevailed between the Albert and Tweed rivers