SECT. XII. LENGTH OF THE YEAR. 85 



cycle peculiarly suited for a measure of duration. It is estimated 

 from the winter solstice, the middle of the long annual night 

 under the north pole. But although the length of the civil year 

 is pointed out hy nature as a measure of long periods, the incom- 

 mensurability that exists between the length of the day and the 

 revolution of the sun renders it difficult to adjust the estimation 

 of both in whole numbers. If the revolution of the sun were 

 accomplished in 365 days, all the years would be of precisely 

 the same number of days, and would begin and end with the 

 sun at the same point of the ecliptic. But as the sun's revolution 

 includes the fraction of a day, a civil year and a revolution of 

 the sun have not the same duration. Since the fraction is nearly 

 the fourth of a day, in four years it is nearly equal to a revolution 

 of the sun, so that the addition of a supernumerary day every 

 fourth year nearly compensates the difference. But in process 

 of time further correction will be necessary, because the fraction 

 is less than the fourth of a day. In fact, if a bissextile be sup- 

 pressed at the end of three out of four centuries, the year so 

 determined will only exceed the true year by an extremely small 

 fraction of a day ; and if in addition to this a bissextile be sup- 

 pressed every 4000 years, the length of the year will be nearly 

 equal to that given by observation. Were the fraction neglected, 

 the beginning of the year would precede that of the tropical year, 

 so that it would retrograde through the different seasons in a 

 period of about 1507 years. The Egyptian year began with the 

 heliacal rising of Sirius (N. 150), and contained only 365 days, by 

 which they lost one year in every 1461 years, their Sothaic period, 

 or that cycle in which the heliacal rising of Sirius passes through 

 the whole year and takes place again on the same day. The 

 division of the year into months is very old and almost universal. 

 But the period of seven days, by far the most permanent divi- 

 sion of time, and the most ancient monument of astronomical 

 knowledge, was used by the Brahmins in India with the same 

 denominations employed by us, and was alike found in the 

 calendars of the Jews, Egyptians, Arabs, and Assyrians. It has 

 survived the fall of empires, and has existed among all successive 

 generations, a proof of their common origin. 



The day of the new moon immediately following the winter 

 solstice in the 707th year of Rome was made the 1st of January 

 of the first year of Julius Caesar. The 25th of December of his 



