July i, 1892. J 



SCIENCE. 



tibiale occurs in the tarsus of the recent genera Cercolabes 

 and Erethizon as it does in that of Coryphodon ; therefore 

 the presence of this bone must be considered as one of the 

 primitive characters of the skeleton of this extinct group of 

 Ungulates. 



The relations of the tibiale facet to the other facets of the 

 astragalus may vary a good deal, and in many cases the 

 tibiale facet appears to be absent, whereas it is really not 

 separated from the navicular facet of the astragalus. 



In conclusion, I wish to add that I was led to write this 

 abstract in order to show the numerous variations of the 

 species of Coryphodon, and that in this group it is exceed- 

 ingly difficult to say where one species ends and another 

 begins. In most cases the characters run into each other so 

 insensibly that it is almost impossible to separate the species. 

 However, I believe there are about eight good species of 

 Coryphodon whose characters show a progression from the 

 primitive to the more specialized types; this progression and 

 specialization affecting the teeth more particularly, as already 

 described. 



American Museum of Natural History, New York. 



INDIAN NUMERALS. 



BT EDWARD P. WILSON. 



In an essay on " The Origin of Languages," published 

 several years ago by Mr. Hale, the idea is suggested that, 

 as, for example, among our native Indians a family may, 

 while hunting or in time of warfare, have chanced to become 

 separated entirely from the rest of the tribe, father, mother, 

 and elder members of the family may all have perished, and 

 two or three little children have been left alone. Such chil- 

 dren, Mr. Hale thinks, would gradually invent a new lan- 

 guage of their own, retaining, perhaps, a few words or parts 

 of words of their mother tongue. In this manner, he thinks, 

 may be accounted for the remarkable diversity of tongues 

 among the Indians of the Pacific coast, where among the 

 mountains and forests a family might thus easily become 

 isolated, and the comparative oneness of speech on the great 

 central plains of this continent and in such an open country 

 as Australia. 



If there is any good foundation for such a theory as the 

 above, we should expect that the old words retained by these 

 young founders of new varieties of speech would be words 

 of the simplest character and those most often in use in the 

 domestic circle. And, indeed, I think we do find that fire, 

 water, I, you, one, two, three, four, five are the words that 

 generally approach the nearest to one another in a compari- 

 son of the different vocabularies. 



The North American Indians, as a general rule, count by 

 the decimal system, as do most civilized peoples; but it is 

 noticeable that, after giving a distinct name to each figure 

 from one to five, they, in many of the dialects, seem to com- 

 mence anew with the figure six, the first part of that num- 

 eral sometimes being a contraction, or other form, of the 

 numeral one, and the latter part of the word seeming to 

 point on towards ten. Thus, in the Ojebway we have (1) 

 pejig, (2) uij, (3) niswi, (4) niwin, (5) nanan, (6) ningod- 

 waswi, (7) nijwaswi, (8) nishwaswi, (9) shangaswi, (10) 

 midaswi. It will be noticed here that from six to ten inclu- 

 sive the termination is asivi. Ning.o, with which six begins, 

 is another form of pejig (l) never used alone, but only in 

 composition, thus: ningo-gijik, one day; ningo-tibaiigan, 

 one measure. In the Cree language (another Algonkin dia- 

 lect) the first ten numerals are as follows: (1) peySk, (2) 



niso, (3) nisto, (4i neo, (5) niya'nSn, (6) nikotwasik, (7) 

 tepaktlp, (8) ayena'new,(9) keka mita'tat, (10) mita'tat. Here 

 it will be noticed that these Cree numerals resemble those of 

 the Ojebways from one to six, but with seven they branch 

 out into distinct words; then with ten they come together 

 again, mita'tat not being dissimilar to midas'wi, and still 

 more like midatching, the Ojebway equivalent for " ten 

 times." Neither is the Cree numeral for nine so unlike that 

 of the Ojebways as might at first sight appear. Keka 

 mita'tat means "nearly ten," and this suggests that the 

 Ojebway word shangaswi may mean the same, chegaiy or 

 chig' being the Ojebway for near. 



The reason for the decimal system being so prevalent all 

 over the world, both among civilized and barbarous people, 

 is doubtless the fact that human beings are possessors of ten 

 fingers, five on each hand. The common manner of count- 

 ing among the Indians is to turn down the little finger of 

 the left hand for one, the next finger in order for two, the 

 next for three, the next for four, and the thumb for five; 

 then the thumb of the right hand for six, and so on until 

 the little finger of the right hand is turned down for ten. 

 In indicating numbers to others, the left hand held up with 

 all the fingers turned down except the little finger would 

 mean one; that and the next finger to it held up would 

 mean two and so on. In counting by tens they will close 

 the fingers of each hand to indicate each ten, or they will 

 hold both hands up with the palms outward and fingers ex- 

 tended for each ten. 



Some Indian tribes in counting resort to their toes as well 

 as their fingers, and thus follow the vigesimal system. The 

 Indians of Guiana, it is said, call five a hand, ten two hands, 

 and twenty a man. 



The Dakotas have a peculiar system of their own. When 

 they have gone over the fingers and thumbs of both hands, 

 one finger is temporarily turned down for one ten. At the 

 end of the next ten another finger is turned, and so on to a 

 hundred. Opawinge, one hundred, is derived from pawinga, 

 to go around in circles, to make gyrations. 



Indians are not generally good arithmeticians. In their 

 native state they have no idea of making even the simplest 

 mental calculation. To add or subtract they will use sticks, 

 pebbles, or other such objects. 



To illustrate the manner in which various tribes (some of 

 them of different stocks) count from ten upwards, examples 

 are herewith given from the Ojebway, Blackfoot, Micmac, 

 and Dakota languages: With the Ojebways 10 is midaswi; 

 11, 12 are midaswi ashi pejig, midaswi ashi nij; 20, 30 are 

 nij tana, nisimidana; 21, nij-tana ashi pejig; 100, ningo- 

 dwak; 101, ningodwak ashi pejig. With the Blackfeet 10 

 is kepo; 11, 13, kepo nitsiko'poto; 20, 30, nitiippo, niippo; 

 100, kepippo. With the Micmacs 10 is mtuin; 11, 12, 

 mtuln tcel naukt, mtiiln tcel tabu: 20, 30 are tabu inskaak, 

 nasinskiiak; 21, tabu inskaiik tcel na-ukt; 100, kQskim- 

 tiilnakiin; 101, kuskimtulnakiiu tcel na-ukt. With the 

 Dakotas (or Sioux) 10 is wiktcemna; 11, 12, wiktcemna 

 saupa wanjidan (10 more one), wiktcemna sanpa nonpa; 20, 

 30 are wiktcemna nonpa (ten two), wiktcemna yamni; 21, 

 wiktcemna noupa sanpa wanjidan (ten two more one) ; 100 is 

 opawinge, meaning a circle. 



In some of the Indian languages there is more than one 

 set of the cardinal numbers. Animate objects may be 

 counted with one set, inanimate with another. They may 

 have a particular set for counting fish or for counting skins; 

 perhaps a set for counting standing objects, and another set 

 for counting sitting objects, etc. 



