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

ON THE DIVISIONS AND MEASURES OF TIMIE.

5

place on any day the earth may be moving in its orbit, the same place
on its surface always returns to the same fixed star at the same
moment of time. This fact arises from the vast distance of the earth
from the fixed stars, which is so immense that even the diameter of
the orbit of the earth, a distance of above 180,000,000 miles, is so
small in comparison as to be inappreciable.
To an observer on the earth the sun appears to move round a great
circle of the heavens in 365k days nearly, or through 59' 8" of a
degree of this circle in one day, which motion corresponds to threeminutes fifty-six and a half seconds of time. The average interval
between the sun appearing to leave, and to return to the same meridian
of the place, will be longer than the sidereal day by three minutes,
fifty-six and a half seconds, and has been defined to be the solar day.
And it is obvious that. the wean solar day,1 or the mean of all the
solar days in one year, will be constant, but sometimes longer and
sometimes shorter than an actual solar day, according to the velocity
of the earth in its orbit during that day. A clock, therefore, which
keeps mean solar time does not always indicate 12 o'clock at the moment
when the sun passes the meridian. The mean of solar days, being
con1stant, has been assumed as the unit of measure for the civil day.
The difference between true time and apparent solar time is greater
or less according to the sun's apparent motion, or rather according to
the actual angular velocity of the earth in any part of its orbit. The
solar day being the interval between the sun's apparent departure from
any given point in the heavens and its next return to that point, with
so much more as is added to its diurnal motion eastwards, it is obvious
the solar day is longer than the sidereal day.
The civil day is the same as the natural day, but in different ages
and among different people it was considered to begin at different times
of the day. Some nations reckoned the day to begin at sunrise,
others at sunset; some from noon, others from midnight. Hipparchus,
the Greek astronomer, who lived in the second century before the
Christian era, reckoned the day to begin from midnight, and his
example has been since followed by astronomers.
The origin of the custom of dividing the period of daylight into
twelve equal parts is unknown. There is no mention or allusion
made by Moses to any such division among the Egyptians at the time
of the Exodus. After this event the time from sunset to sunrise was
divided by the Hebrews into three equal parts, called watches. The
morning watch is noted in Exod. xiv. 14, and the middle watch
in Judges vii. 19. In later times, when the Romans held possession of Judea, the Hebrews adopted the Roman method of dividing
the night into four watches, all of which are stated in the thirteenth
chapter of St. MIark's gospel. The division of the day, the period
from sunrise to sunset, into twelve equal parts, is noted in John
xi. 9. The first hour began at sunrise, midday or noon was
1 The mean solar day has been described as the mean of the solar days of a year.
An imaginary sun is supposed or conceived to move uniformly in the equator with
the real sun's mean motion, and the interval between the departure of any meridian
from the mean sun and its returning to it, is the duration of the mean solar day.
Clocks and chronometers are adjusted to mean solar time; so that a complete revolution through 24 hours of the hour hand of the Astronomical clock should be performed in exactly the same interval as the revolution of the earth on its axis with
respect to the mean sun.