Now it is plain that if it keeps moving continuously to the east it will at last come round to the same point again, and the whole period of its revolution can easily be calculated from the distance it moves each year. The result of such a calculation shows that the whole revolution is completed in 25,870 years, after which time all will be again as it is now in this respect.

Fig. 11.

If we draw a figure of the zodiac, as below, and know that at this time the vernal equinox takes place when the sun is in the Fishes, then, the constellation of the Ram being to the west of this, the date at which the equinox was there must be before our present date, while at some time in the future it will be in Aquarius.

Now if in any old description we find that the equinox is referred to as being in the Ram or in the Bull, it tells us at once how long ago such a description was a true one, and, therefore, when it was written. This is the way in which the Zodiac carries with it an intimation of its date. Thus in the example lately referred to of the Persians and their four stars, it must have been about 5,000 years ago, according to the above calculation, that these were in the positions assigned, which is therefore the date of this part of Persian astronomy, if we have rightly conjectured the stars referred to.

We have already said that the signs of the zodiac are not now the same as the zodiacal constellations, and this is now easily understood. It is not worth while to say that the sun enters such and such a part of the Fishes at the equinox, and changes every year. So the part of the heavens it does then enter—be it Fishes, or Aquarius, or the Ram—is called by the same name—and is called a sign; the name chosen is the Ram or Aries, which coincided with the constellation of that name when the matter was arranged. There is another equally important and instructive result of this precession of the equinox. For the earth's axis is always perpendicular to the plane of the equator, and if the latter moves, the former must too, and change its position with respect to the axis of the ecliptic, which remains immovable. And the ends of these axes, or the points they occupy among the stars, called their poles, will change in the same way; the pole of the equator, round which the heavens appear to move, describing a curve about the pole of the ecliptic; and since the ecliptic and equator are always nearly at the same angle, this curve will be very nearly a circle, as represented on preceding page.

Fig. 12.

Now the pole of the equator is a very marked point in the heavens, because the star nearest to it appears to have no motion. If then we draw such a figure as above, so as to see where this pole would be at any given date, and then read in any old record that such and such a star had no motion, we know at once at what date such a statement must have been made. This means of estimating dates is less certain than the other, because any star that is nearer to the pole than any other will appear to have no motion relatively to the rest, unless accurate measurements were made. Nevertheless, when we have any reason to believe that observations were carefully made, and there is any evidence that some particular star was considered the Pole Star, we have some confidence in concluding the date, examples of which will appear in the sequel; and we may give one illustration now, though not a very satisfactory one. Hipparchus cites a passage from the sphere of Eudoxus, in which he says, Est vero stella quædam in eodem consistens loco, quæ quidem polus est mundi. (There is a certain immovable star, which is the pole of the world.)

Now referring to our figure, we find that about 1300 B.C. the two stars, β Ursæ Minoris and κ Draconis were fairly near the pole, and this fact leads us to date the invention of this sphere at about this epoch, rather than a little before or a little after, although, of course, there is nothing in this argument (though there may be in others), to prevent us dating it when α Draconis was near the pole, 2850 B.C. This star was indeed said by the Chinese astronomers in the reign of Hoangti to mark the pole, which gives a date to their observations. The chief use of this latter method is to confirm our conclusions from the former, rather than to originate any. Let us now apply our knowledge to the facts.