SECT, xii.] DIVISIONS OF TIME. 95 



their decimal system of weights and measures. This subdivi- 

 sion is not now used in common life, nor has it been adopted 

 in any other country ; and, although some scientific writers in 

 France still employ that division of time, the custom is begin- 

 ning to wear out. At one period during the French revolu- 

 tion, the clock in the gardens of the Tuileries was regulated 

 to show decimal time. The mean length of the day, though 

 accurately determined, is not sufficient for the purposes either 

 of astronomy or civil life. The tropical or civil year of 365 d 

 5 h 48 m 49 S 7, which is the time elapsed between the conse- 

 cutive returns of the sun to the mean equinoxes or solstices, 

 including all the changes of the seasons, is a natural 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 by nature as a measure of long periods, 

 the incommensurability 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 compen- 

 sates the difference. But in process of time further correc- 

 tion will be necessary, because the fraction is less than the 

 fourth of a day. In fact, if a bissextile be suppressed at the 

 end of three out of four centuries, the year so determined 

 will only exceed the true year by an extremely small frac- 

 tion 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 frac- 

 tion neglected, the beginning of the year would precede that 



