In the diagram given on page 49, the various amplitudes are shown at which bodies of different declinations appear to rise and set in places with latitudes ranging from 19° to 51° N. It is a diagram to which frequent reference will be made in the sequel.
CHAPTER V.
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.