abiding monument of primæval culture. This framework, the all but universal scheme of reckoning by fives, tens, and twenties, shows that the childish and savage practice of counting on fingers and toes lies at the foundation of our arithmetical science. Ten seems the most convenient arithmetical basis offered by systems founded on hand-counting, but twelve would have been better, and duodecimal arithmetic is in fact a protest against the less convenient decimal arithmetic in ordinary use. The case is the not uncommon one of high civilization bearing evident traces of the rudeness of its origin in ancient barbaric life.