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270 order which for ages had been in use above it. The ancient Egyptian and the still-used Roman and Chinese numeration are indeed founded on savage picture-writing, while the abacus and the swan-pan, the one still a valuable school-instrument, and the other in full practical use, have their germ in the savage counting by groups of objects, as when South Sea Islanders count with coco-nut stalks, putting a little one aside every time they come to 10, and a large one when they come to 100, or when African negroes reckon with pebbles or nuts, and every time they come to 5 put them aside in a little heap.

We are here especially concerned with gesture-counting on the fingers, as an absolutely savage art still in use among children and peasants, and with the system of numeral words, as known to all mankind, appearing scantily among the lowest tribes, and reaching within savage limits to developments which the highest civilization has only improved in detail. These two methods of computation by gesture and word tell the story of primitive arithmetic in a way that can be hardly perverted or misunderstood. We see the savage who can only count to 2 or 3 or 4 in words, but can go farther in dumb show. He has words for hands and fingers, feet and toes, and the idea strikes him that the words which describe the gesture will serve also to express its meaning, and they become his numerals accordingly. This did not happen only once, it happened among different races in distant regions, for such terms as 'hand' for 5, 'hand-one' for 6, 'hands' for 10, 'two on the foot' for 12, 'hands and feet' or 'man' for 20, 'two men' for 40, &c., show such uniformity as is due to common principle, but also such variety as is due to independent working-out. These are 'pointer-facts' which have their place and explanation in a development-theory of culture, while a degeneration-theory totally fails to take them in. They are distinct records of development, and of independent