THE YEARLY PATH OF THE SUN-GOD.
Let us, then, imagine the ancient Egyptians, furnished with the natural
astronomical circle which is provided whenever there is an extended
plain, engaged in their worship at sunrise, praying to the "Lord of
the two Horizons." The rising (and setting) of stars we will consider
later; it is best to begin with those observations about which there is
the least question.
In the very early observations that were made in Egypt and Babylonia,
when the sun was considered to be a god who every morning got into
his boat and floated across space, there was no particular reason for
considering the amplitude at which the supposed boat left or approached
the horizon. But a few centuries showed that this rising or setting of
the sun in widely varying amplitudes at different parts of the year
depended upon a very definite law. We now, more fortunate than the
early Egyptians, of course know exactly what this law is, and with a
view of following their early attempts to grapple with the difficulties
presented to them we must pass to the yearly path of the sun, in order
to study the relation of the various points of the horizon occupied by
the sun at different times in the year.
Not many years ago Foucault gave us a means of demonstrating the fact
that the earth rotates on its axis. We have also a perfect method
of demonstrating that the earth not only rotates on its axis once a
day, but that it moves round the sun once a year, an idea which was
undreamt of by the ancients. As a pendulum shows us the rotation, so
the determination of the aberration of light demonstrates for us the
revolution of the earth round the sun.
We have, then, the earth endowed with these two movements--a rotation
on its axis in a day, and a revolution round the sun in a year. To see
the full bearing of this on our present inquiry, we must for a time
return to the globe or model of the earth.
To determine the position of any place on the earth's surface we say
that it is so many degrees distant from the equator, and also so
many degrees distant from the longitude of Greenwich: we have two
rectangular co-ordinates, latitude and longitude. When we conceive the
earth's equator extended to the heavens, we have a means of determining
the positions of stars in the heavens exactly similar to the means we
have of determining the position of any place on the earth. We have
already defined distance from the equator as north or south declination
in the case of a star, as we have north latitude or south latitude in
case of a place on the earth. With regard to the other co-ordinate,
we can also say that the heavenly body whose place we are anxious to
determine is at a certain distance from our first point of measurement,
whatever that may be, along the celestial equator. Speaking of heavenly
bodies, we call this distance right ascension; dealing with matters
earthy, we measure from the meridian of Greenwich and call the distance
longitude.
The movement of the earth round the sun is in a plane which is called
the plane of the ecliptic, and the axis of rotation of the earth is
inclined to that plane at an angle of something like 23½°. We can
if we choose use the plane of the ecliptic to define the positions of
the stars as we use the plane of the earth's equator. In that case we
talk of distance from the ecliptic as celestial latitude, and along the
ecliptic from one of the points where it cuts the celestial equator
as celestial longitude. The equator, then, cuts the ecliptic at two
points: one of these is chosen for the start-point of measurement along
both the equator and the ecliptic, and is called the first point of
Aries.
We have, then, two systems of co-ordinates, by each of which we can
define the position of the sun or a star in the heavens: equatorial
co-ordinates dealing with the earth's equator, ecliptic co-ordinates
dealing with the earth's orbit. Knowing that the earth moves round
the sun once a year, the year to us moderns is defined with the most
absolute accuracy. In fact, we have three years: we have a sidereal
year--that is, the time taken by the earth to go through exactly
360° of longitude; we have what is called the tropical year, which
indicates the time taken by the earth to go through not quite 360°, to
go from the first point of Aries till she meets it again; and since
the equinoctial point advances to meet the earth, we talk about the
precession of the equinoxes; this year is the sidereal year minus
twenty minutes. Then there is also another year called the anomalistic
year, which depends upon the movement of the point in the earth's orbit
where the earth is nearest to the sun; this is running away, so to
speak, from the first point of Aries, instead of advancing to meet it,
so that in this case we get the sidereal year plus nearly five minutes.
The angle of the inclination of the earth's plane of rotation to the
plane of its revolution round the sun, which, as I have said, is at the
present time something like 23½°, is called _the obliquity of the
ecliptic_. This obliquity is subject to a slight change, to which I
shall refer in a subsequent chapter.
In order to give a concrete idea of the most important points in the
yearly path of the earth round the sun, let us imagine four globes
arranged on a circle representing the earth at different points of its
orbit, with another globe in the centre representing the sun, marking
the two practically opposite points of the earth's orbit, in which the
axis is not inclined to or from the sun but is at right angles to the
line joining the earth in these two positions, and the two opposite
and intermediate points at which the north pole of the axis is most
inclined towards and away from the sun.
A diagram will show what will happen under these conditions. If we take
first the points at which the axis, instead of being inclined towards
the sun, is inclined at right angles to it, it is perfectly obvious
that we shall get a condition of things in which the movement of the
earth on its axis will cause the dark side of the earth and also the
light side represented by the side nearest to the sun, both being of
equal areas, to extend from pole to pole; so that any place on the
earth rotating under those conditions will be brought for half a period
of rotation into the sunlight, and be carried for half a period of the
rotation out of the sunlight; the day, therefore, will be of the same
length as the night, and the days and nights will therefore be equal
all over the world.
We call this the time of the equinoxes; the nights are of the same
length as the day in both these positions of the earth with regard to
the sun.
[Illustration: EARTH AND SUN AT THE EQUINOXES.]
In the next figure we have the other condition. Here the earth's axis
is inclined at the greatest angle of 23°½, towards, and away from,
the sun. If I take a point very near the north pole, that point will
not, in summer, be carried by the earth's rotation out of the light,
and a part equally near the south pole will not be able to get into
it. These are the conditions at and near two other points called the
solstices.
[Illustration: EARTH AND SUN AT THE SOLSTICES.]
On each of these globes I have drawn a line representing the overhead
direction from London. If we observe the angle between the direction of
the zenith and that to the sun in winter we find it considerable; but
if we take the opposite six-monthly condition we get a small angle.
In other words, under the first condition the sun at noon will be far
from the zenith of London, we shall have winter; and in the other
condition the sun will be as near as it can be to the zenith at noon,
we shall have summer. These two cases represent the two points in the
earth's orbit at which the sun has the greatest declination south and
north. With the greatest north declination the sun will come up high,
appear to remain at the same height above the horizon at noon for a
day or two, as it does at our summer solstice, and then go down again;
at the other point, when it has the greatest southern declination, it
will go down to the lowest point, as it does in our winter, stop, and
come up again--that is, the sun will stand still, so far as its height
above the horizon at noon is concerned, and the Latin word solstice
exactly expresses that idea. We have, then, two opposite points in the
revolution of the earth round the sun at which we have equal altitudes
of the sun at noon, two others when the altitude is greatest and least.
[Illustration: DIAGRAM SHOWING POSITION OF THE SUN IN RELATION TO THE
ZENITH OF LONDON AT THE NORTHERN WINTER SOLSTICE.]
[Illustration: DIAGRAM SHOWING POSITION OF THE SUN IN RELATION TO THE
ZENITH OF LONDON AT THE NORTHERN SUMMER SOLSTICE.]
We get the equal altitudes at the equinoxes, and the greatest and the
least at the solstices.
These altitudes depend upon the change of the sun's declination. The
change of declination will affect the azimuth and amplitude of the
sun's rising and setting; this is why, in our northern hemisphere, the
sun rises and sets most to the north in summer and most to the south
in winter. At the equinoxes the sun has always 0° Decl., so it rises
and sets due east and west all over the world. But at the solstices it
has its greatest declination of 23½° N. or S.; it will rise and set,
therefore, far from the east and west points; how far, will depend on
the latitude of the place we consider. The following are approximate
values:
Latitude of Amplitude of Sun
Place. at Solstice.
° ° ′
25 26 5
30 27 24
35 29 8
40 31 21
45 34 40
50 38 20
55 44 0
At Thebes, Lat. 25° 40′ N., representing Egypt, we find that the
amplitude of the sun at rising or setting at the summer solstice will
be approximately 26° N. of E. at rising, and 26° N. of W. at setting.
These solstices and their accompaniments are among the striking things
in the natural world. At the winter solstice we have the depth of
winter, at the summer solstice we have the height of summer; while
at the equinoxes we have but transitional changes; in other words,
while the solstices point, out for us the conditions of greatest heat
and greatest cold, the equinoxes point out for us those two times of
the year at which the temperature conditions are very nearly equal,
although of course in the one case we are saying good-bye to summer and
in the other to winter. In Egypt the summer solstice was paramount, for
it occurred at the time of the rise of the Nile, the beginning of the
Egyptian year.
Did the ancients know anything about these solstices and these
equinoxes? Were the almost mythical Hor-shesu or sun-worshippers
familiar with the annual course of the sun? That is one of the
questions which we have to discuss.