This arrangement, conformable to the lunar year, only gave 354 days to the civil year, and as this was too short by ten days, twenty-one hours, this difference, by accumulation, produced nearly eighty-seven days at the end of eight years, or three months of twenty-nine days each. To bring the lunar years into accordance with the solstices, it was necessary to add three intercalary months every eight years. The phases of the moon being thus brought into comparison with the rotation of the earth, a cycle was discovered by Meton, now known as the Metonic cycle, useful also in predicting eclipses, which comprised nineteen years, during which time 235 lunations will have very nearly occurred, and the full moons will return to the same dates. In fact, the year and the lunation are to one another very nearly in the proportion of 235 to 19. By observing for nineteen years the positions and phases of the moon, they will be found to return again in the same order at the same times, and they can therefore be predicted. This lunar cycle was adopted in the year 433 B.C. to regulate the luni-solar calendar, and it was engraved in letters of gold on the walls of the temple of Minerva, from whence comes the name _golden number_, which is given to the number that marks the place of the given year in this period of nineteen. Caliphus made a larger and more exact cycle by multiplying by four and taking away one day. Thus he made of 27,759 days 76 Julian years, during which there were 940 lunations. The Roman calendar was even more complicated than the Greek, and not so good. Romulus is said to have given to his subjects a strange arrangement that we can no longer understand. More of a warrior than a philosopher, this founder of Rome made the year to consist of ten months, some being of twenty days and others of fifty-five. These unequal lengths were probably regulated by the agricultural works to be done, and by the prevailing religious ideas. After the conclusion of these days they began counting again in the same order; so that the year had only 304 days. The first of these ten months was called _Mars_ after the name of the god from whom Romulus pretended to have descended. The name of the second, Aprilis, was derived from the word _aperire_, to open, because it was at the time that the earth opened; or it may be, from Aphrodite, one of the names of Venus, the supposed grandmother of AEneas. The third month was consecrated to _Maia_, the mother of Mercury. The names of the six others expressed simply their order--Quintilis, the fifth; Sextilis, the sixth; September, the seventh; and so on. Numa added two months to the ten of Romulus; one took the name of _Januarius_, from _Janus_: the name of the other was derived either from the sacrifices (_februalia_), by which the faults committed during the course of the past year were expiated, or from _Februo___, the god of the dead, to which the last month was consecrated. The year then had 355 days.