1st. The solar day, or noon to noon by the sun.
2nd. An imaginary sun moving uniformly in the ecliptic.
3rd. A second imaginary sun moving uniformly parallel to the equator at all seasons of the year.
5th. One rotation of the earth measured from the node, or point, of the spring equinox.
The difference between 1st and 2nd is that part of the sun's error due to the elliptical orbit of the earth.
The other part of the sun's error--and the larger--between 2nd and 3rd is that due to the obliquity of the ecliptic to the equator.
The whole error between 1st and 3rd is the "equation of time" as shown for even minutes in the first chapter under the heading, "Sun on Noon Mark 1909."
Stated simply, for our present purpose, 1st is sundial time, and 3rd our 24-hour clock time.
This 2nd day is therefore a refinement of the astronomers to separate the two principal causes of the sun's error, and I think we ought to handle it cautiously, or my friend, Professor Todd, might rap us over the knuckles for being presumptuous.
This 5th day is the sidereal day of the astronomers and is the basis of our time, so it is entitled to a little attention. I shall confine "sidereal day" to this 5th to avoid confusion with 4th. If you will extend the plane of the equator into the star sphere, you have the celestial equator. When the center of the sun passes through this plane on his journey north, in the Spring, we say, "the sun has crossed the line." This is a distant point in the Zodiac which can be determined for any given year by reference to the fixed stars. To avoid technicalities as much as possible we will call it the point of the Spring equinox. This is really the point which determines the common year, or year of the seasons. Using popular language, the seasons are marked by four points,--Spring equinox--longest day--; Autumnal equinox--shortest day. This would be very simple if the equinoctial points would stay in the same places in the star sphere; but we find that they creep westward each year to the extent of 50 seconds of arc in the great celestial circle of the Zodiac. This is called the precession of the equinoxes. The year is measured from Spring equinox to Spring equinox again; but each year it comes 50 seconds of arc less than a full revolution of the earth around the sun. Therefore _if we measured our year by a full revolution_ we would displace the months with reference to the seasons till the hot weather would come in January and the cold weather in July in about 13,000 years; or a complete revolution of the seasons back to where we are, in 26,000 years. Leaving out fractions to make the illustration plain, we have:--