(1) 360 degrees of Zodiac } --------------------- = 26,000 years } 50 seconds of arc } } (2) 1 day of time } ------------- = 26,000 years } 3-1/3 seconds } All } Approximate (3) 1 year of time } -------------- = 26,000 years } 20-1/3 minutes } } (4) 3-1/3 seconds } ------------- = 1/110 of a second} days in a year }
In (1) we see that a "precession" of 50 seconds of arc will bring the Spring equinox around in 26,000 years.
In (2) we see, as 50 seconds of arc represents the distance the earth will rotate in 3-1/3 seconds, a difference of one day will result in 26,000 years. That is since the clock regulated by the stars, or absolute rotations of the earth, would get behind 3-1/3 seconds per year, it would be behind a day in 26,000 years, as compared with a sidereal clock regulated by the Spring equinoctial point.
In (3) we see that as 50 seconds of arc is traversed by the earth, in its annual revolution, in 20-1/3 minutes, a complete circle of the Zodiac will be made in 26,000 years.
In (4) we see that as the difference between the year of the seasons and the Zodiacal year is 3-1/3 seconds of the earth's rotation, it follows that if this is divided by the number of days in a year we have the amount which a sidereal day is less than 4th, or an absolute rotation of the earth. That is, any meridian passes the Spring equinoctial point 1/110 of a second sooner than the time of one absolute rotation. These four equations are all founded on the precession of the equinoxes, and are simply different methods of stating it. Absolutely and finally, our time is regulated by the earth's rotation; but strange as it may appear, we do not take one rotation as a unit. As shown above, we take a rotation to a _movable point_ which creeps the 1/110 of a second daily. But after all, it is the _uniform_ rotation which governs. This is the one "dependable" motion which has not been found variable, and is the most easily observed. When we remember that the earth is not far from being as heavy as a ball of iron, and that its surface velocity at the equator is about 17 miles per minute, it is easy to form a conception of its uniform motion. Against this, however, we may place the friction of the tides, forcing up of mountain ranges, as well as mining and building skyscrapers--all tending to slow it. Mathematicians moving in the ethereal regions of astronomy lead us to conclude that it _must_ become gradually slower, and that _it is_ slowing; but the amount may be considered a vanishing quantity even compared with the smallest errors of our finest clocks; so for uncounted generations past--and to come--we may consider the earth's rotation uniform. Having now found a uniform motion easily observed and of convenient period, why not adopt it as our time unit? The answer has been partially given above in the fact that we are compelled to use a year, measured from the Spring equinoctial point, so as to keep our seasons in order; and therefore as we must have some point where the sidereal clocks and the meantime clocks coincide, we take the same point, and that point is the Spring equinox. Now we have three days:--