TIME-RECKONING. 107 
The natural solar day is at one season of the year 14 minutes 32 
seconds shorter, and at another 16 minutes 17 seconds longer than the 
mean. Thus the extreme variation is half an hour and 49 seconds. 
The earth revolves in its orbit in about 365} days. To avoid 
fractions of days, it has been found convenient to establish three 
years in succession of 365 days, and each fourth year 366 days. The 
latter are designated leap years. 
While an ordinary solar year has but 365 days, it has 366 sidereal 
days. 
A solar day, therefore, exceeds the length of a sidereal by about 
sesth part of a day, or nearly four minutes (3 minntes 55.9094 
seconds). 
The mean solar day, according as it is employed for civil or astro- 
nomical purposes, is designated the civil day, or the astronomical day. 
The former begins and ends at midnight ; the latter commences and 
ends at noon. The astronomical day is understood to commence 
twelve hours before the civil day, but its date does not appear until 
its completion, twelve hours after the corresponding civil date. The 
two dates, therefore, coincide only during the later half of the civil 
and the earlier half of the astronomical day. 
ANCIENT AND MODERN RECKONING OF TIME. 
It has been stated that all shorter periods of time than a day are 
conventional and arbitrary, there being no measure less than a day 
denoted by nature. The only exception is the interval marked by 
the rising and setting of the sun; a period of time varying with the 
latitude and changing from day to dvy with the seasons. 
The sub-division of the day into parts has prevailed from the 
remotest ages ; though different nations have not agreed, either with 
respect to the epoch of its commencement, the number of the sub- 
divisions, or the distribution of the several parts. 
The division of the day with which we are most familiar is that 
which separates the whole space of time occupied by a diurnal revo- 
lution of the earth into two equal parts; one part extending from 
midnight to noon, the other part from noon to midnight. These 
half days are sub-divided into twelve portions or hours, and these 
again into minutes and seconds. 
Astronomers do not divide the day into two sets of twelve hours. 
The astronomical day, extending from noon to noon, is reckoned by 
hours running from one to twenty-four. 
