Elementary arithmetic, with brief notices of its history... by Robert Potts.

ON THE DIVISIONS AND MEASURES OF TIME.

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account in the seventh and eighth chapters of the Book of Genesis,
that the rising of the waters began on the seventeenth day of the
second month, and continued until the seventeenth day of the seventh
month, a period of five months, or one hundred and fifty days. The
account also supplies evidence that the year was reckoned to consist
of twelve months of thirty days each, or of three hundred and sixty
days. For it states that the deluge began on the seventeenth day of
the second month of the six hundredth year of Noah's life, and that he
and his family left the ark on the twenty-seventh day of the second
month of the following year, that is, after three hundred and seventy
days, or a year of twelve months of thirty days each, and ten days.
This mode of reckoning the month and the year having descended
from Noah and his sons, was naturally followed by their descendants.
And in the early period of the world's history the year was reckoned
according to the phases or appearances of the moon, and not according
to any comparison of the apparent motions of the sun and the moon.
In the course of time it was ascertained that the lunar month of
30 days was greater than the true length of the time in which the
moon passed through the changes, and that the true length was less
than 30 but more than 29 days.
It was also observed that the year of 360 days was less than the
period in which the sun appeared to move round the circle of the
heavens, and that this period was more than 365 but less than 366
days. It will be seen that the month of 30 days and the year of 12
months of 30 days, could not be made to correspond exactly with the
motions either of the sun or of the moon, but that these reckonings
would always fall short of the true year. Neither could the months
be made always to correspond with the seasons to which they were
first adjusted, but in the space of about 34 years they would be found
reckoned in opposite parts of the year.
If each lunar month did consist of an exact number of days, and
each year of an exact number of lunar months, there would have
been no difficulty in adjusting them with each other. But as neither
the lunar month consists of an exact number of days, nor the solar
year an exact number of lunar months, difficulties arose in the attempts
made to adjust these different measures of time to one another.
In order to remedy the discrepancies and to make the reckonings of
the seasons agree with the motions of the sun and the moon, different methods were adopted by different nations. Some regulated their
years by the moon, and others by the sun, making from time to time
such an addition of days as to bring the periods of reckoning to.
correspond with the lunar and solar motions whenever the lunar year
ranged too widely from the solar year. Herodotus writes (ii. 3, 4),^
that he was informed by the priests at Heliopolis, the chief seat ofi'
Egyptian learning, that "the Egyptians were the first to discovery
the year, dividing the year into twelve parts, and this knowledge, they
said, they obtained from the stars." And he adds his opinion, "that;
they reckon their years more judiciously than the Greeks; for these
intercalate a whole month every other year, but the Egyptians, dividing
the year into 12 months of 30 days each, add every year a space of 5
days besides, by which means the order of the seasons is made to
return with uniformity." From the fact of Egypt having been one of the
earliest of civilised nations, it is not improbable that this adjustment of
the periods of the moon and of the sun is due to the ancient Egyptians.