the astrologers therewith to calculate the nativities of the persons then born.  On one is a complete horoscope, containing the places of the sun, moon, and every planet, noted down on the zodiac in degrees and minutes of a degree; and with these particulars the mathematician undertook to foretell the marriage, fortune, and death of the person who had been born at the instant when the heavenly bodies were so situated; and, as the horoscope was buried in the tomb with the mummy, we must suppose that it was thought that the prognostication would hold good even in the next world.

But astrology was not the only end to which mathematics were then turned.  Claudius Ptolemy, the astronomer and geographer, was at that time the ornament of the mathematical school of Alexandria.  In his writings he treats of the earth as the centre of the heavens, and the sun, moon, and planets as moving in circles and epicycles round it.  This had been the opinion of some of the early astronomers; but since this theory of the heavens received the stamp of his authority, it is now always called the Ptolemaic system.

In this reign was made a new survey of all the military roads in the Roman empire, called the Itinerary of Antoninus.  It included the great roads of Egypt, which were only six in number.  One was from Contra-Pselcis in Nubia along the east bank of the Nile, to Babylon opposite Memphis, and there turning eastward through Heliopolis and the district of the Jews to Clysmon, where Trajan’s canal entered the Red Sea.  A second, from Memphis to Pelusium, made use of this for about thirty miles, joining it at Babylon, and leaving it at Scense Veteranorum.  By these two roads a traveller could go from Pelusium to the head of the Red Sea; but there was a shorter road through the desert which joined the first at Serapion, about fifty miles from Clysmon, instead of at Sceno Veteranorum, which was therefore about a hundred miles shorter.  A fourth was along the west bank of the Nile from Hiera Sycaminon in Nubia to Alexandria, leaving the river at Andropolis, about sixty miles from the latter city.  A fifth was from Palestine to Alexandria, running along the coast of the Mediterranean from Raphia to Pelusium, and thence, leaving the coast to avoid the flat country, which was under water during the inundation; it joined the last at Andropolis.  The sixth road was from Koptos on the Nile to Berenice on the Red Sea.  These six were probably the only roads under the care of the prefect.  Though Syene was the boundary of the province of Egypt, the Roman power was felt for about one hundred miles into Nubia, and we find the names of the emperors on several temples between Syene and Hiera Sycaminon.  But beyond this, though we find inscriptions left by Roman travellers, the emperors seem never to have aimed at making military roads, or holding any cities against the inroads of the Blemmyes and other Arabs.