book of mystic diagrams. When this combination of a number of two-faced lots is used by gamblers, this perhaps represents the earlier stage of gaming, which may have led up to the invention of dice, in which the purpose of variety is so much more neatly and easily attained. The first appearance of dice lies beyond the range of history, for, though they have not been traced in the early periods in Egypt, there is in the Rig-Veda the hymn which portrays the ancient Aryan gambler stirred to frenzy by the fall of the dice. It is not clear even which came first of the various objects that have served as dice.
In the classic world girls used the astragali or hucklebones as playthings, tossing them up and catching them on the back of the hand; and to this day we may see groups of girls in England at this ancient game, reminding us of the picture by Alexander of Athens, in the Naples Museum, of the five goddesses at play. It was also noticed that these bones fall in four ways, with the flat, concave, convex, or sinuous side up, so that they form natural dice, and as such they have been from ancient times gambled with accordingly. In India Nature provides certain five-sided nuts that answer the purpose of dice. Of course, when the sides are alike, they must be marked or numbered, as with the four-sided stick-dice of India, and that which tends to supersede all others, the six-sided kubos, which gave the Greek geometers the name for the cube. Since the old Aryan period many a broken gamester has cursed the hazard of the die. We moderns are apt to look down with mere contempt at his folly. But we judge the ancient gamester too harshly if we forget that his passion is mixed with those thoughts of luck or fortune or superhuman intervention which form the very mental atmosphere of the soothsayer and the oracle-prophet. With devout prayer and sacrifice he would propitiate the deity who should give him winning throws; nor, indeed, in our own day have such hopes and such appeals ceased among the uneducated. To the educated it is the mathematical theory of probabilities that has shown the folly of the gamester's staking his fortune on his powers of divination. But it must be borne in mind that this theory itself was, so to speak, shaken out of the dice-box. When the gambling Chevalier de Méré put the question to Pascal in how many throws he ought to get double-sixes, and Pascal solving the problem started the mathematical calculation of chances, this laid the foundation of the scientific system of statistics which more and more regulates the arrangements of society. Thus accurate method was applied to the insurance-table, which enables a man to hedge against his ugliest risks, to eliminate his chances of fire and death by betting that he shall have a new roof over his head and a provision for his widow. Of all the wonderful turns of the human mind in the course of culture, scarce any is more striking than this history of lots and dice. Who, in the middle ages, could have guessed what would be its next outcome—that magic sunk