Observations on the sun's annual course led to the fixing of it along a zodiac of twelve signs, corresponding roughly to twelve lunar months, and defined by constellations, or groups of stars, having a fanciful resemblance to animals or deified heroes. Those zodiacal signs are of immense antiquity and world-wide universality. We find them in the earliest mythology of Chaldæa and Egypt, in the labours of Hercules, in the traditions of a deluge associated with the sign of Aquarius, and even, though in a somewhat altered form, in such distant countries as China and Mexico. Probably they originated in Chaldæa, where the oldest records and universal tradition show the primitive Accadians to have been astronomers, who from time immemorial had made observations on the heavenly bodies, and who remained down to the Roman Empire the most celebrated astrologers, though it is not quite clear whether Egyptian astronomy and astrology were imported from Chaldæa or invented independently at an equally remote period.

Even if we admit, however, Procter's suggestion that the pyramids had an astrological origin in addition to their primary object as tombs, it is difficult to understand how such enormous structures could have been built. The Great Pyramid must have been built on a plan designed from the first, and not by any haphazard process of adding a layer each year according to the number of years the monarch happened to reign. How could he foresee the exact number of years of an unusually long life and reign, or what security could he have that, if he died early, his successor would complete his pyramid in addition to erecting one of almost equal magnitude for himself? How could three successive kings have devoted such an amount of the nation's capital and resources to the building of three such pyramids as those of Cheops, Chephren, and Mycerinus, without provoking insurrections?

Herodotus has a piece of gossip, probably picked up from some ignorant guides, which represents Cheops and Chephren as detested tyrants, who shut up the temples of the gods, and confounds the national hatred of the shepherd kings, who conquered Egypt some 2000 years later, with that of these pyramid-builders; but this is confuted by the monuments, which show them as pious builders or restorers of temples of the national gods in other localities, as for instance at Bubastis, where the cartouche of Chephren was lately found by M. Naville on an addition to the Temple of Isis. All the records also of the fourth or pyramid-building dynasty, and of the two next dynasties, show it to have been a period of peace and prosperity.

The pyramids therefore must still remain a subject enveloped in mystery, but enough is certain from the undoubted astronomical facts disclosed in their construction to show the advanced state of this science at this remote period. Nor is this all, for the dimensions of the Great Pyramid, when stripped of the fanciful coincidences and mystical theories of Piazzi Smyth, still show enough to prove a wonderful knowledge of mathematics and geometry. The following may be taken as undoubted facts from the most accurate measurements of their dimensions.

1st. The triangular area of each of the four sloping sides equals the square of the vertical height. This was mentioned by Herodotus, and there can be no doubt that it was a real relation intended by the builders.

2nd. The united length of the four sides of the square base bears to the vertical height the same proportion as that of the circumference of a circle to its radius. In other words it gives the ratio, which under the symbol π plays such an important part in all the higher mathematics. There are other remarkable coincidences which seem to show a still more wonderful advance in science, though they are not quite so certain, as they depend on the assumption that the builders took as their unit of measurement, a pyramid inch and sacred cubit different from those in ordinary use, the former being equal to the 500,000,000th part of the earth's diameter, and the latter containing twenty-five of those inches, or about the 20,000,000th part of that diameter. To arrive at such standards it is evident that the priestly astronomers must have measured very accurately an arc of the meridian or length of the line on the earth's surface which just raised or lowered the pole of the heavens by 1°; and inferred from it that the earth was a spherical body of given dimensions. Those dimensions would not be quite accurate, for they must have been ignorant of the compression of the earth at its poles and protuberance at the equator, but the measurement of such an arc at or near 30° of north latitude would give a close approximation to the mean value of the earth's diameter. Procter thinks that from the scientific knowledge which must have been possessed by the builders of the pyramid, it is quite possible that they may have measured an arc of the meridian with considerable accuracy, and calculated from it the length of the earth's diameter, assuming it to be a perfect sphere. And if so they may have intended to make the side of the square base of the pyramid of a length which would bear in inches some relation to the length of this diameter; for it is probable that at this stage of the world's science, the mysterious or rather magical value which was attached to certain words would attach equally to the fundamental facts, figures, and important discoveries of the growing sciences. It is quite probable, therefore, that the sacred inch and cubit may have been invented, like the metre, from an aliquot part of the earth's supposed diameter, so as to afford an invariable standard. But there is no positive proof of this from the pyramid itself, the dimensions of which may be expressed just as well in the ordinary working cubit, and it must remain open to doubt whether the coincidences prove the pyramid inch, or the inch was invented to prove the coincidences.

Assuming, however, for the moment that these measures were really used, some of the coincidences are very remarkable. The length of each side of the square base is 365-1/4 of these sacred cubits, or equal to the length of the year in days. The height is 5819 inches, and the sun's distance from the earth, taken at 91,840,000 miles, which is very nearly correct, is just 5819 thousand millions of such inches. It has been thought, therefore, that this height was intended to symbolize the sun's distance. But independently of the fact that this distance could not have been known with any approach to accuracy before the invention of the telescope, it is forgotten that this height had been already determined by a totally unconnected consideration, viz. the ratio of the diameter of a circle to its circumference. The coincidence, therefore, of the sun's distance must be purely accidental.

A still more startling coincidence has been found in the fact that the two diagonals of the base contain 25,824 pyramid inches, or almost exactly the number of years in the precessional period. This also must be accidental, for the number of inches in the diagonals follows as a matter of course from the sides being taken at 365-1/4 cubits, corresponding to the length of the year; and there can be no connection between this and the precession of the equinoxes, which, moreover, was unknown in the astronomy of the ancient world until it was discovered in the time of the Ptolemies by Hipparchus.

But with all these doubtful coincidences, and the many others which have been discovered by devotees of the pyramid religion, quite enough remains to justify the conclusion that between 5000 and 6000 years ago there were astronomers, mathematicians, and architects in Egypt, who had carried their respective sciences to a high degree of perfection corresponding to that shown by their engineers and artists.

When we turn to Chaldæa we find similar evidence as to the advance of science, and especially of astronomical science, in the earliest historical times. Every important city had its temple, and attached to its temple its ziggurat, which was a temple-observatory. The ziggurat is in some respects the counterpart of the pyramid, being a pyramidal structure built up in successive stages or platforms superimposed on one another and narrowing as they rose, so as to leave a small platform on the top, on which was a small shrine or temple, and from which observations could be made. These ziggurats being built entirely of bricks, mostly sun-burnt, have crumbled into shapeless mounds of rubbish, but a fair idea of their size and construction may be obtained from the descriptions and pictures of them preserved in contemporary tablets and slabs, especially from those of the great ziggurat of the seven spheres or planets at Borsippa, a suburb of Babylon, which was rebuilt by Nebuchadnezzar about 500 b.c., on the site of a much more ancient ruined construction. This, which was the largest and most famous of the ziggurats, became identified in after times with the tower of Babel and the legend of the confusion of tongues, but it was in fact an astronomical building in seven stages dedicated to the sun, moon, and five planets, taken in the order of magnitude of their respective orbits, and each distinguished by their respective colours. Thus the lowest or largest platform was dedicated to Saturn, and coloured black; the second to Jupiter was orange; the third to Mars red; the fourth to the Sun golden; the fifth to Venus pale yellow; the sixth to Mercury an azure blue, obtained by vitrifying the facing bricks; and the seventh to the Moon was probably coated with plates of silver. The height of this ziggurat was 150 feet, and standing as it did on a level alluvial plain, it must have been a very imposing object.