simple or less convenient in any particular, than when he is at work with the strictly decimal portions of his scale. He passes from the one style of counting to the other, and from the second back to the first again, entirely unconscious of any break or change; entirely unconscious, in fact, that he is using any particular system, except that which the daily habit of years has made a part himself. Deep regret must be felt by every student of philology, that the primitive meanings of simple numerals have been so generally lost. But, just as the pebble on the beach has been worn and rounded by the beating of the waves and by other pebbles, until no trace of its original form is left, and until we can say of it now only that it is quartz, or that it is diorite, so too the numerals of many languages have suffered from the attrition of the ages, until all semblance of their origin has been lost, and we can say of them only that they are numerals. Beyond a certain point we can carry the study neither of number nor of number words. At that point both the mathematician and the philologist must pause, and leave everything beyond to the speculations of those who delight in nothing else so much as in pure theory. THE END. INDEX OF AUTHORS. Adam, L., 44, 159, 166, 175. Armstrong, R.A., 180. Aymonier, A., 156. Bachofen, J.J., 131. Balbi, A., 151. Bancroft, H.H., 29, 47, 89, 93, 113, 199. Barlow, H., 108. Beauregard, O., 45, 83, 152. Bellamy, E.W., 9. Boas, F., 30, 45, 46, 65, 87, 88, 136, 163, 164, 171, 197, 198. Bonwick, J., 24, 27, 107, 108. Brinton, D.G., 2, 22, 46, 52, 57, 61, 111, 112, 140, 199, 200. Burton, R.F., 37, 71. Chamberlain, A.F., 45, 65, 93. Chase, P.E., 99. Clarke, H., 113. Codrington, R.H., 16, 95, 96, 136, 138, 145, 153, 154. Crawfurd, J., 89, 93, 130. Curr, E.M., 24-27, 104, 107-110, 112. Cushing, F.H., 13, 48. De Flacourt, 8, 9. De Quincey, T., 35. Deschamps, M., 28. Dobrizhoffer, M., 71. Dorsey, J.O., 59. Du Chaillu, P.B., 66, 67, 150, 151. Du Graty, A.M., 138. Ellis, A.A., 64, 91. Ellis, R., 37, 142. Ellis, W., 83, 119. Erskine, J.E., 153, 154. Flegel, R., 133. Gallatin, A., 136, 159, 166, 171, 199, 204, 206, 208. Galton, F., 4. Gatschet, A.S., 58, 59, 68. Gilij, F.S., 54. Gill, W.W., 18, 118. Goedel, M., 83, 147. Grimm, J.L.C., 48. Groeber, G., 182. Guillome, J., 181. Haddon, A.C., 18, 105. Hale, H., 61, 65, 93, 114-116, 122, 130, 156, 163, 164, 171. Hankel, H., 137. Haumonte, J.D., 44. Hervas, L., 170. Humboldt, A. von, 32, 207. Hyades, M., 22. Kelly, J.W., 157, 196. Kelly, J., 180. Kleinschmidt, S., 52, 80. Lang, J.D., 108. Lappenberg, J.M., 127. Latham, R.G., 24, 67, 107. Leibnitz, G.W. von, 102, 103. Lloyd, H.E., 7. Long, C.C., 148, 186. Long, S.H., 121. Lubbock, Sir J., 3, 5. Lull, E.P., 79.