Mariette's plan shows a second temple oriented to N. 6° E., which we may perhaps be justified in taking as N. 9° E., since his azimuth of the great temple differs from Biot's and my own by 3°.
The corresponding declination would be 68° N. of E., the declination of Dubhe in 4200 B.C. and of γ Draconis in 4300 B.C. The temple may well, therefore, have been erected when both stars had the same amplitude, the apparent difference of 100 years being due to the uncertainty of the measures available.
The second point, then, is that when Dubhe, which, while it rose and set, was the brightest star near the pole which did so, became circumpolar; γ Draconis, when it ceased to be circumpolar, fulfilled these conditions; astronomically, then, it became the natural successor of α Ursæ Majoris.
I have before pointed out that it is not impossible that a temple once oriented to a certain star, and long out of use on account of the precessional movement, may be utilised for another, and be rehabilitated in consequence, when that same movement brings another conspicuous star into the proper rising amplitude.
This consideration at once leads to my third point, which is, that after Dubhe became circumpolar the temple of Hathor at Denderah would become useless—there would be no star to watch—unless a new star was chosen.
Now, let us suppose this to have been so, and that the natural successor of the star in question were chosen. Studying the facts as before approximately, as final data are not yet available, we have the declination 59¾° N. This was the declination of γ Draconis about 3500 B.C., assuming hills 2° high, which I think is too much; 3300 B.C., with hills 1½° high.
In the present case the orientation fits γ Draconis in the historic period, but it also fits Dubhe in the times of the Hor-shesu, the dimly-seen followers of Horus, or sun-worshippers, before the dawn of the historic period.
Next let us go back to the inscriptions. We found that King Pepi is portrayed over and over again in the crypts, and, which is more important, that the plan of the temple on parchment, dating from the times of the Shesu-Hor, had actually been walled up in the temple during the reign of the same king, no doubt at the ceremony of restoration or laying a new foundation stone, as is sometimes done to this day.
Now, Pepi's date, according to the chronologists, is 3200 B.C., a difference of 100 years only from the rough orientation date.
We see, therefore, the full importance of the work done in Pepi's reign. The āk of the Thigh was no longer of use; but a new star was now available. Hathor was rehabilitated. Perhaps even the priests alone knew that the star had been changed.