I have before me as I write a picture of the southern heavens, drawn by myself, in which this vacant space--eccentric in position but circular in shape--is shown. The centre lies close by the Lesser Magellanic cloud--between the stars Kappa Toucani and Eta Hydri of our modern maps, but much nearer to the last named. Near this spot, then, we may be sure, lay the southern pole of the star-sphere when the old constellations, or at least the southern ones, were invented. (If there had been astronomers in the southern hemisphere Eta Hydri would certainly have been their pole-star.) Now it is a matter of no difficulty whatever to determine the epoch when the southern pole of the heavens was thus placed.[57] Between 2100 and 2200 years before the Christian era the southern constellations had the position described, the invisible southern pole lying at the centre of the vacant space of the star-sphere--or rather of the space free from constellations. It is noteworthy that for other reasons this period, or rather a definite epoch within it, is indicated as that to which must be referred the beginning of exact astronomy. Amongst others must be mentioned this--that in the year 2170 B.C. _quam proximè_, the Pleiades rose to their highest above the horizon at noon (or technically made their noon culmination), at the spring equinox. We can readily understand that to minds possessed with full faith in the influence of the stars on the earth, this fact would have great significance. The changes which are brought about at that season of the year, in reality, of course, because of the gradual increase in the effect of the sun's rays as he rises higher and higher above the celestial equator, would be attributed, in part at least, to the remarkable star-cluster coming then close by the sun on the heavens, though unseen. Thus we can readily understand the reference in Job to the 'sweet influences of the Pleiades.' Again at that same time, 2170 B.C. when the sun and the Pleiades opened the year (with commencing spring) together, the star Alpha of the Dragon, which was the pole-star of the period, had that precise position with respect to the true pole of the heavens which is indicated by the slope of the long passage extending downwards aslant from the northern face of the Great Pyramid; that is to say, when due north below the pole (or at what is technically called its sub-polar meridional passage) the pole-star of the period shone directly down that long passage, and I doubt not could be seen not only when it came to that position during the night, but also when it came there during the day-time. But some other singular relations are to be noted in connection with the particular epoch I have indicated.