[209] We have very little information respecting the early Grecian mode of computing time, and we know that though all the different states computed by lunar periods, yet most, if not all, of them had different names of months as well as different days of beginning and ending their months. All their immediate computations, however, were made by months: the lunar period was their immediate standard of reference for determining their festivals, and for other purposes, the solar period being resorted to only as a corrective, to bring the same months constantly into the same seasons of the year. Their original month had thirty days, and was divided into three decades, as it continued to be during the times of historical Athens (Hesiod. Opp. Di. 766). In order to bring this lunar period more nearly into harmony with the sun, they intercalated every year an additional month: so that their years included alternately twelve months and thirteen months, each month of thirty days. This period was called a Dieteris,—sometimes a Trieteris. Solon is said to have first introduced the fashion of months differing in length, varying alternately from thirty to twenty-nine days. It appears, however, that Herodotus had present to his mind the Dieteric cycle, or years alternating between thirteen months and twelve months (each month of thirty days), and no other (Herodot. i. 32; compare ii. 104). As astronomical knowledge improved, longer and more elaborate periods were calculated, exhibiting a nearer correspondence between an integral number of lunations and an integral number of solar years. First, we find a period of four years; next, the Octaëteris, or period of eight years, or seventy-nine lunar months; lastly, the Metonic period of nineteen years, or 235 lunar months. How far any of these larger periods were ever legally authorized, or brought into civil usage, even at Athens, is matter of much doubt. See Ideler, Uber die Astronomischen Beobachtungen der Alten, pp. 175-195; Macrobius, Saturnal. i. 13. [210] Herodot. i. 74; Aristot. Polit. i. 4, 5.