Mathematical_Recreations-Kraitchik-2e

CHAPTER FIVE
THE CALENDAR
TIME can be measured only by observing the motions of
bodies that move in unchanging cycles. The only motions
of this nature ar~ those of the heavenly bodies, which continue
in their courses with inimitable constancy and limitless
duration. Hence we owe to astronomy the establishment of
a secure basis for the measurement of time by determining
the lengths of the day, the month, and the year. The week
of seven days is an artificial unit, though it has been used
from time immemorial.
For measuring astronomical periods of time longer than
the day, two systems have been in common use. One uses
the lunation as the fundamental cycle, a lunation being the
time from one new moon to the next. The other is based on
the sun's year, and it is this which we shall study.
The first difficulty is that the length of the year is not commensurable
with the length of the day, for the year contains
about 365.242199 days. The history of the calendar is the
history of the attempts to adjust these incommensurable
units in such a way as to obtain a simple and practicable
system.
Our calendar story goes back to Romulus, the legendary
founder of Rome, who introduced a year of 300 days divided
into 10 months. His successor, Numa, added two months.
This hardly scientific calendar was used for the following six
and a half centuries until Julius Caesar introduced a more
exact year of 365.25 days. The difficulty of the extra quarter
of a day was handled by making the length of the ordinary
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