Simple counting was done on the fingers. “Reckon on your fingers,” says a character in Aristophanes,[275] “not with pebbles.” A common word for counting was πεμπάζειν [pempazein], “to reckon on the five fingers”; the division of the month into three periods of ten days can be traced to the same custom. But by various devices it was possible to count up to very large numbers on the fingers. Pebbles were also employed to assist in arithmetic. In the case of complicated accounts a reckoning board (ἄβακος [abakos] or ἄβαξ [abax]) was used, on which the pebbles varied in value according to their position. Such boards go back to early days at Athens, for Solon compared the life of a courtier to a pebble upon them, since he was now worth much and now little.[276] A character in a fourth-century comedy[277] sends for an abacus and pebbles, in order that he may do his accounts. The pebbles were arranged in grooves, being worth one or ten or a hundred and so forth, according to the groove in which they were placed. If they were put on the left-hand side of the board, their value was multiplied by five.[278] The various games of πεσσοί [pessoi], which somewhat resembled chess, were played on a somewhat similar board to this, and these chess-boards were known as ἄβακες [abakes]. Now the art of playing with πεσσοί [pessoi] is more than once coupled by Plato with arithmetic or mathematics generally in such a way as to show that the game must have involved mathematical skill.[279] As was usual in Athens, instruction went hand in hand with amusement, and, in playing games, the boys learned arithmetic willingly. A similar value seems to have attached to the game of knucklebones, which the boys in the _Lusis_ are found playing during their whole holiday. Each boy carried a large basket of knucklebones, and the loser in each game paid so many of them over to the winner. The art of playing this game is also coupled with mathematics by Plato;[280] so it must at any rate have encouraged the study of arithmetic, in his opinion. In the school scene of the British Museum amphora, a little bag, usually supposed to contain knucklebones, is figured: so they may even have been used in schools for teaching arithmetic. In another school scene this bag is present with a lyre and ruler; so it was evidently part of the school furniture. [Illustration: PLATE III. MUSIC-SCHOOL SCENES From a Hudria in the British Museum (E 171).]