invention in intellectual games may have been made a thousand years or so ago, when some Hindu, whose name is lost, set to work upon the old draught-board and men, and developed out of them a war-game, where on each side a king and his general, with elephants, chariots, and cavalry, and the foot-soldiers in front, met in battle array. This was the earliest chess, which with some little change passed into the modern European chess that still holds pre-eminence among sports, taxing the mind to its utmost stretch of foresight and combination. Our modern draughts is a sort of simplified chess, where the pieces are all pawns till they get across the board and become queens. The story in the history-books that cards were invented in France to amuse Charles VI. is a fiction, for they were known in the East centuries earlier. But at any rate the Europeans make with them combinations of skill and chance which excel anything contrived by their Asiatic inventors. Games which exercise either body or mind have been of high value in civilization as trainers of man's faculties. Games of pure chance played for money stand on quite a different footing; they have been from the first a delusion and a curse. In our own time, there is perhaps no more pitiable sign of the slowness with which scientific ideas spread, than to hear the well-dressed crowds round the gaming-table at Monaco talking about runs of luck, and fancying that it makes a difference whether one backs the black or the red. This goes on although schoolboys are now taught the real doctrine of chances, and how to reckon the fixed percentage of each week's stakes that will be raked in by the croupier, and not come back.

CHAPTER XIII.

SCIENCE.

Science, 309-Counting and Arithmetic, 310-Measuring and Weighing, 316-Geometry, 318-Algebra, 322-Physics, 323-Chemistry, 328-Biology, 329-Astronomy, 332-Gecgraphy and Geology, 335 -Methods of Reasoning, 336-Magic, 338.

SCIENCE is exact, regular, arranged knowledge. Of common knowledge savages and barbarians have a vast deal, indeed the struggle of life could not be carried on without it. The rude man knows much of the properties of matter, how fire burns and water soaks, the heavy sinks and the light floats, what stone will serve for the hatchet and what wood for its handle, which plants are food and which are poison, what are the habits of the animals that he hunts or that may fall upon him. He has notions how to cure, and much better notions how to kill. In a rude way he is a physicist in making fire, a chemist in cooking, a surgeon in binding up wounds, a geographer in knowing his rivers and mountains, a mathematician in counting on his fingers. All this is knowledge, and it was on these foundations that science proper began to be built up, when the art of writing had come in and society had entered on the civilized stage. We have to trace here in outline the rise and progress of

science. And as it has been especially through counting and measuring that scientific methods have come into use, the first thing to do is to examine how men learnt to count and measure.

Even those who cannot talk can count, as was well shown by the deaf-and-dumb lad Massieu, who wrote down among the recollections of his childhood before the Abbé Sicard educated him, "I knew the numbers before my instruction; my fingers had taught me them." We ourselves as children began arithmetic on our fingers and now and then take to them still, so that there is no difficulty in understanding how a savage whose language has no word for a number above three will manage to reckon perhaps a list of fifteen killed and wounded, how he will check off one finger for each man, and at last hold up his hand three times to show the result. The next question is, how numeral words came to be invented. This is answered by many languages, which show in the plainest way how counting on fingers and toes led to making numerals. When a Zulu wants to express the number six, he says tatisitupa, which means "taking the thumb;" this signifies that the speaker has counted all the fingers of his left hand, and begun with the thumb of the right. When he comes to seven, for instance when he has to express that his master bought seven oxen, he will say u kombile, that is, "he pointed"; this signifies that in counting he had come to the pointing-finger or forefinger. In this way the words "hand," "foot," "man,” have in various parts of the world become numerals. An example how they are worked may be taken from the language of the Tamanacs of the Orinoco; here the term for five means "whole hand," six is "one of the other hand," and so on up to ten or "both hands"; then "one to the foot" is eleven, and so on to "whole foot" or fifteen, "one to the other

foot" or sixteen, and thence to "one man," which signifies twenty, one to the hands of the next man" being twentyone, and the counting going on in the same way to "two men" which stands for forty, &c. &c. Now this state of things teaches a truth which has sometimes been denied, that the lower races of men have, like ourselves, the faculty of progress or self-improvement. It is evident that there was a time when the ancestors of these people had in their languages no word for fifteen or sixteen, nor even for five or six, for if they had they could not have been so stupid as to change them for their present clumsy phrases about hands and feet and men. We see back to the time when, having no means of reckoning such numbers except on their fingers and toes, they found they had only to describe in words what they were doing, and such a phrase as "both hands" would serve them as a numeral for ten. Then they would keep up these as numerals after their original sense was lost, like the Vei negros who called the number twenty mo bande, but had forgotten that this must have meant a person finished." The languages of nations long civilized seldom show such plain meaning in their numerals, perhaps because they are so ancient and have undergone such change. But all through the languages of the world, savage or civilized, with exceptions too slight to notice here, there is ineffaceable proof that the numerals arose out of the primitive counting on fingers and toes. This always led men to reckon by fives, tens, and twenties, and so they reckon still. The quinary kind of counting (by fives) is that of tribes like the negros of Senegal, who count one, two, three, four, five, five-one, five-two, &c.; we never count numbers thus in words, but we write them so in the Roman numerals. The decimal counting (by tens) is the most usual in the world, and our ordinary counting is done by it, thus eighty-three is eight

tens and three." The vigesimal counting (by twenties) which is the regular mode in many languages, has its traces. left in the midst of the decimal counting of civilized Europe, as in English "fourscore and three," French "quatre-vingt trois," that is "four twenties and three." Thus it can hardly be doubted that the modern world has inherited direct from primitive man his earliest arithmetic worked on nature's counting-board-the hands and feet. This also explains (p. 18) why the civilized world uses a numeral system based on the inconvenient number ten, which will not divide either by three or four. Were we starting our arithmetic afresh, we should more likely base it on the duodecimal rotation, and use dozens and grosses instead of tens and hundreds.

To have named the numbers was a great step, but words hardly serve beyond the very simplest arithmetic, as any one may satisfy himself by trying to multiply "seven thousand eight hundred and three" by "two hundred and seventeen ' in words, without helping himself by turning them in thought into figures. How did men come to the use of numeral figures? To this question the beginning of an answer may be had from barbaric picture-writing, as where a North American warrior will make four little marks //// to show that he has taken four scalps. This is very well for the small numbers, but becomes clumsy for higher ones. So already when writing was in its infancy, the ancients had fallen upon the device of making special marks for their fives, tens, hundreds, &c., leaving the simple strokes to be used only for the few units over. This is well seen in Fig. 76 which shows how numeration was worked in ancient Egypt and Assyria. Nor has this old method died out in the world, for the Roman numerals I., V., X., L., still in common use among ourselves, are arranged on much the same principle.