It is a fact of common observation, at different times of the year,
that the forenoon and afternoon, as to daylight, are of unequal
length. Along in later autumn the shortness of the afternoons is very
noticeable, and the shortness of forenoons along in later winter.
Whatever makes common facts more intelligible adds to the general
intelligence and to the general good. It is to this end that the
following brief statements are made.
Nothing is more evident than that the sun requires just as much time
to go from the eastern horizon to the midday meridian as to go from
that meridian to the western horizon. But, strange to say, there are
but four days during the whole year in which the sun reaches the midday
meridian at just twelve o’clock. The true noon point varies from about
fifteen minutes before to about sixteen minutes after twelve o’clock.
These extreme points in one set of variations fall in the first week
of November and in the second week of February, not to designate exact
days for years in general.
The calendars show that in the latitude of Saratoga (essentially
Boston latitude) on November 3, 1898, the sun rose at 6.30 and set at
five o’clock, thereby making the forenoon a half hour longer than the
afternoon. On that day the sun reached the midday meridian at 11.45. On
February 13, 1899, the sun rose at just seven o’clock and set at 5.30,
thereby making the afternoon a half hour longer than the forenoon, and
on this day the sun reached the midday meridian at 12.15. These are
facts plainly open to general view, and therefore need no verifying.
The causes of the foregoing are not so apparent to common observation.
It must be borne in mind that the mean or average solar day is the
basis for all time measurements, therefore its exact length is of
the greatest importance. Yet the general solar day, from which the
average one is derived, is a very indefinite term as to its length.
Its length in general may be defined, under view of the sun’s apparent
motion, as the time extending from the instant that the sun’s center
crosses any given meridian of the earth on one day to the instant that
center crosses the same meridian on the following day--i. e., the time
intervening between these two instants is the length of a solar day.
The motion of the sun, however, is only apparent; the actual motion
is in the earth’s revolution upon its axis. We should have one day
a year long if the earth did not revolve on its axis at all, since
the revolution of the earth around the sun once a year would in the
course of the year bring all sides facing the sun. Consequently the
earth makes one more revolution upon its axis each year than the number
of solar days in that year, and a little consideration of this fact
will show that in each solar day the earth makes one full revolution
on its axis and about 1/365 of another, which fractional addition is
occasioned by one day’s progress of the earth along its orbit.
Another fact needs to be considered. Since the earth’s orbit is in the
form of an ellipse, with the sun at one of the foci, the earth must
pass nearer the sun in some parts of its orbit than in others. By the
laws of gravity, when nearer, the attraction between the earth and sun
is greater, and if this were not balanced by increased velocity along
its orbit the earth would fall into the sun; and, on the other hand,
when farther off this attraction is less, and if this were not balanced
by a diminution of velocity along its orbit the earth would fly off
into space. This varying velocity, together with other complications
too technical for a magazine article, gives varying lengths of orbit to
the several solar days of the year. If the earth’s orbit were laid out
upon paper and, by astronomical calculations, an exact proportionate
section were marked off for each solar day of the year, the variable
lengths of orbit for the different days of the year would plainly
appear to the eye.
But, as before explained, the time of a solar day is the time of one
revolution of the earth upon its axis, together with the fractional
part of another revolution occasioned by one day’s progress of the
earth along its orbit. Then it must follow that as the daily sections
of the orbit vary in length, the time of the solar day must vary in
length. No clock could be made to keep the variable time of true solar
days, and if this were possible, the hour, minute, etc., would be
variable of length, and hence no standard for time measurements. But
by working a simple arithmetical problem of addition and division an
average length of day for the year may easily be found. This average
day is the mean solar day adopted. Its time is arbitrary and exact,
forming a perfect standard for all time measurements. From this the
term _mean time_ gains its significance.
By referring to the foregoing earth’s orbit laid out on paper, with
the true solar days marked off in sections of mathematical exactness,
it will be seen that by dividing each section into two equal parts and
marking the division point with red ink, the true noon point of each
solar day in the year will be conspicuous upon the drawing, and in its
proportionate relations in every way. If now we set a pair of dividers
or compasses so that the opening shall reach over the exact space on
the orbit of one half of the mean solar day, and beginning at the red
noon point of one of the four days in the year when the true noon falls
at just twelve o’clock--say December 24th--and step the dividers around
on the orbit, making a blue point mark at each second step, then as the
blue points vary from the red so will the mean time which our clocks
keep vary from the true noon of each day of the year.
Variation in length of forenoon and afternoon, therefore, may be viewed
by common intelligence not only as a fact but as a necessity.