peoples pay little or no attention to them. Both in the case of the day and in that of the other time-units this clinging to a natural basis long proved a hindrance to a rational system of time-reckoning, which could only be achieved by breaking away from natural phenomena. For there are no fixed natural limits of day, but if morning and evening, or still more clearly sunrise and sunset, are chosen as the limits, these must change every day and the days will vary in length. Here the midnight period proved of assistance, since it facilitated the establishing of a fixed point of divergence. This was done in Rome, and the practice had its root in daily life, where in order to indicate the time of occurrence of events which took place in the night-time the calculation was pushed forwards on both sides towards midnight, until this became the limit of divergence. It is however an artificial epoch that must be found by calculation[195]. In the second place the hour of antiquity is a twelfth part of the whole time of daylight, and this duodecimal division was also transferred to the night, which had commonly been divided into four watches according to the practice borrowed from military life. This hour therefore varied in length according to the time of the year. The inconvenience of a varying division of this nature must have made itself felt in daily life, although in the south it was not so insupportable as it must have been in the north. It rendered the construction of the clock difficult, and above all was impracticable for scientific astronomy. Hence alongside of it appeared even in antiquity the hour of constant length or the double hour, viz. a twelfth or a twenty-fourth part respectively of the complete day. The double hour, notwithstanding Bilfinger’s assertion to the contrary, arose in Babylon (_kasbu_), and is connected with the duodecimal division of the zodiac[196]. This hour of constant length was not generally adopted until very late: the varying hour remained almost up to the end of the Middle Ages. Our modern hour has only been in general use since about the 14th century, when it was first spread by the construction of the striking-clock[197]. Its convenience for the business of practical life and the construction of the clock together secured the victory of the hour as 1/24th of the day, originally a numerical and astronomical division. A condition for its use was the fusion of day and night into one unit, since as long as these were kept separate the constant hour could not thrive. Both the complete day and its regular divisions however only won their way after a very long time, because men were unwilling to depart from the natural basis in time-reckoning. The substitution of the artificial for the natural time-reckoning has also, as far as the day is concerned, created a rational system of reckoning which has borrowed from the natural system only one feature, viz. the average length of the complete day. CHAPTER II.