While it is true that no great empire ever existed without a constitutional fiction, it is also true that it never endured on a fiction alone. The Macedonian soldiers whom Ptolemy found in Egypt and those whom he brought with him and sent for later were essential for the maintenance of his government. So long as the son of Alexander the Great lived, and, indeed, for four years longer (till 306 B.C.), Ptolemy was simply their general. Then he became their king, and to legitimatize this practical usurpation, the legend arose that he was not really the son of Lagos, but the son of Philip. It is to the honor of Ptolemy that he had nothing to do with this libel on the good name of his mother, and preferred rather to be an illegitimate king than an illegitimate son. Besides, it was only necessary to go back a generation or two to attach the line of Ptolemy to that of the ancient "Zeus-born" kings of Macedon. The wife of Lagos had belonged, in fact, to the royal family, as the Ptolemies took good care to observe. The Ptolemaic empire was, accordingly, based on three concurrent theories, one for the native Egyptians, one for the Greek city-states and one for the Macedonians. * * * * * Appian of Alexandria,[90] writing about two hundred years after the death of Cleopatra, cites the royal registers as authority for his report that Philadelphus kept, for land operations 200,000 foot, 40,000 cavalry, and arms for 300,000 men; in addition, 300 war elephants and 2000 war chariots; for naval warfare, 2000 transports, 1500 battleships with three to five banks of rowers, and oars and rigging for twice that number. He had also, according to the same authority, 800 royal barges with gilt poops and beaks, and in his treasury a reserve of 740,000 Egyptian talents, or $890,000,000. That the reserve as given amounts to three times the value of the gold and silver in the United States treasury shows that the enumeration belongs only in the history yet to be written of the absurdities of statistics. More credible estimates of the Egyptian army place it at 80,800 under the second Ptolemy and (exclusive of natives, who then numbered 26,000) 49,700 under the fourth Ptolemy.[91] These are very large totals. It will help to solve many questions of Ptolemaic policy to observe where the soldiers came from.