Among other important results of these movements dependent upon precession we have the various changes in the pole-star from period to period, due to the various positions occupied by the pole of the earth's equator. We thus see how in this period of 25,000 years or thereabouts the pole-stars will change, for a pole-star is merely the star near the pole of the equator for the time being. At present, as we all know, the pole-star is in the constellation Ursa Minor. During the last 25,000 years the pole-stars have been those lying nearest to a curved line struck from the pole of the heavens with a radius equal to the obliquity of the ecliptic, which, as we have seen, is liable to change within small limits; so that about 10,000 or 12,000 years ago the pole-star was no longer the little star in Ursa Minor that we all know, but the bright star Vega, in the constellation Lyra. Of course 25,000 years ago the pole-star was practically the same as it is at present. Associated with this change in the pole-star, the point of intersection of the two fundamental planes (the plane of the earth's rotation and the plane of the earth's revolution) will be liable to change, and the period will be the same--about 25,000 years. Where these two planes cut each other we have the equinoxes, because the intersection of the planes defines for us the vernal and the autumnal equinoxes; when the sun is highest and lowest half-way between these points we have the solstices. In a period of 25,000 years the star which is nearest to an equinox will return to it, and that which is nearest a solstice will return to it. During the period there will be a constant change of stars marking the equinoxes and the solstices. The chief points in the sun's yearly path then will change among the stars in consequence of this precession. It is perfectly clear that if we have a means of calculating back the old positions of stars, and if we have any very old observations, we can help matters very much, because the old observations--if they were accurately made--would tell us that such and such a star rose with the sun at the solstice or at the equinox at some special point of ancient time. If it be possible to calculate the time at which the star occupied that position with regard to the sun, we have an astronomical means of determining the time, within a few years, at which that particular observation was made.