THERE are historic as well as mathematical problems, but there is no general similarity in them save in the name. Theorems in mathematics are susceptible of solution, if one can only get at the principles that underlie them; but there are no known rules by which the historical student can certainly and demonstrably solve the problems that are ever appearing on Clio's scroll. A theorem of Euclid, however difficult, consists of certain logical elements; and a series of mathematical processes will prove the truth or the fallacy of an operation indisputably and unerringly. None of the problems of history can be disposed of so readily. Assumptions of solutions can easily be made; but these, in turn, can be overthrown by the more subtle reasoning or the profounder erudition of another. And even the assumption of the last is not received as irrevocable. They are only speculations at the best, dependent on the animus of the writer, and can never receive the credence accorded to testimony irrespective of personal considerations.

Many of these questions are perhaps silly ones, the more so as it does not appear in all cases what should be the conditions of the problems. And still the amusement experienced in their examination is not surpassed by the interest and importance many times attached to them. An acute observer has declared that the study of history makes one wise. Accepting the truth of this apothegm, as applied to history in its political and philosophical bearing, it must be no less true that an ex

amination of its mathematical qualities, as we are pleased to term them, must render one subtle and profound. Take, for instance, that problem of Herodotus: What would have been the result if Xerxes had been victorious at Salamis? In order to arrive at any satisfactory conclusion, one must read through long annals, look at this and that authority, examine the religious and civil institutions of the rival nations; and not only must he be conversant with all the details of contemporary history, but he must stand far enough off to judge of the effects pro and con upon his own age. In fact, he must bring to the investigation a mind filled with the knowledge of long years of study. No novice, no empiric, can sit in judgment upon the declarations of astute and experienced historians.

Sir Edward Creasy, in his "Fifteen Decisive Battles," maintains that Marathon was the important and decisive event of the Græco-Persian war, rather than Salamis. How this could well be, when the Persians were urged on to still more desperate undertakings by Xerxes, and the Greeks had all their glories to win over again, we fail to see. Nor do we accept the assertion that Europe was saved from a desolation greater than would have occurred from a deluge by the destruction of the Persian armament. Greece rose, indeed, to unprecedented greatness and splendor after the billows of that mighty torrent had ceased to roll; but has one ever thought what lay at the bottom of that majestic and brilliant upheaval? The inherent genius of the Greek mind

alone would never have forced into such sudden action the arts and philosophy. Nor was it through the artificial and forced influence of the fierce struggle the Greeks had passed through. Sometimes, but not in this case, has civilization been matured by the energy of distress. What was it, then, that brought about this unexpected and glorious epoch that boasted of the Parthenon, of Plato, and of Sophocles? We answer, it was the influence of the Oriental upon the Greek mind.

The results were brilliant, but permanent: the process had been of slow growth. From the time of Croesus, from the time when Solon and Pythagoras had studied at Asiatic courts, this influence had been going out silently and slowly. The injection of the vast hosts of Darius and Xerxes into Greece forwarded this revolution. Mere contact alone would have done much, but how much more these counter-surges of invasion. Doubtless many of the conquered - some of them were Asiaticized Greeks - remained behind, and their influence performed no unimportant work. Greece threw off the Asiatic despotism, but succumbed to Asiatic thought, Asiatic manners, Asiatic religion. To the active, subtle, restless spirit of the Greek were now joined the gravity, the philosophy, of the Oriental. All the Greek philosophers drank their wisdom from founts in the East. All the Greek poets caught their imagery and inspiration from the Orient. Greek commanders copied the military system of Cyrus. Greek architects took their models from the grandeur, the beauty, the splendor, of Eastern monuments.

In all this no evil was done to Greece, but much good. But would there not have been good of much greater

abundance, had Persian and not Greek arms prevailed at Salamis? No, replies the modern democrat. Greek genius soared only for the reason that it was free. But when was Greece ever free? True, foreign domination did not always hold her in subjection; but her gigantic oligarchies, her rude democracies, her bad institutions, were worse than foreign masters. Besides, if democracies and oligarchies were indeed so stimulative of genius, so patronizing of letters, why sought Plato the court of the tyrant Dionysius, Pindar and Euripides the court of the Macedonian Alexander, and Aristotle the court of Philip? Moreover, did not the first soarings of Greek genius take place under the early tyrants? no! genius is not dwarfed or fettered by any thing. It flourishes at the courts of despots, under the rule of oligarchies, under the sway of democracies. Its habitat does not make nor mar it. Genius is divine, and God is everywhere.

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But if Persia had conquered Greece, what then? What evil would have been done? The religion of Zoroaster was superior to that of Homer and Hesiod, less animated and picturesque indeed, but more simple and exalted. The Persians had no gods partaking of the worst characteristics of a mortal nature. They worshipped their Great One not in statues nor in temples, but upon the sublime altars of lofty mountain-tops. In many respects it resembled the religion of the Hebrews, and it was about the only other religion in the world which was not defiled by human sacrifices and brutal worship. Surely it would not have injured Greece to have received this paternal, mild monotheism over their false though very beautiful system of polytheism.

Nor were the Persians inferior in mental vigor or graceful accomplishments to their Greek neighbors. They cultivated all the elegant arts. The remains of the palace of Chil-menar at Persepolis, ascribed by modern superstition to the architecture of genii, its mighty masonry, its terrace flights, its graceful columns, its marble basins, its sculptured designs stamped with the emblems of the Magian faith, show the advance of the Persian mind in the elaborate art of architecture. The Persian kings were in most cases men of ability, of broad benevolence, of active energy. Palestine renewed her former glory under their sway. Why should not Greece have flourished the same, nay, ten times more abundantly, the active Greek blood stimulated by Oriental magnificence, had she succumbed to Xerxes? Nor would it have been the first or the last time that Asia has conquered Europe. Every thing good, exalted, and venerable has come from the East. It was the cradle of art, of poesy, of every civilizing agent. All the progressive religions of the world rose in the Orient. It would not have been so fearful, after all, if Greece had been conquered. A hundred years more of glory might have been hers; and her wise men, her artists, her poets, and her statesmen, instead of having their genius cramped by the petty jealousies, the limited ambitions, of their native states, might have developed their full powers under the fostering care and the brilliant courts of the great kings. In fact, Greece conquered by Persia, Oriental blood infused into her veins as well as Oriental thought into her brain, she would have been stronger than she could ever have been else. The Greek mind would not only have risen to greater affluence, but politically have

been stronger; and the Roman might not have succeeded against the PersoGreek. It is suggestive that it was not democratic Athens or oligarchal Sparta that withstood Rome the longest and the last, but Macedon and Etolia, Macedon whose king paid the tribute of earth and water to Darius, and Etolia whose wild tribes rushed to the aid of Xerxes.

It has always been a mooted question whether, if Alexander the Great had met the Romans, he himself or the Romans would have succumbed. Livy the historian, in a marked passage, undertakes to weigh the chances of success with which the mighty conqueror of the East would have encountered the growing Western Republic, had he lived to lead his veterans across the sea into Italy. He decides in favor of Rome; but Livy was a Roman, and could well do no otherwise. Besides, he was not in a position to fairly examine the question upon its merits. Livy lived in the time of Augustus; and it was not easy to contemplate, when Rome was the world, that Rome could ever have fallen. Hannibal, Antiochus, Mithridates, had been conquered: surely, Livy argued, Alexander would have been conquered too. A modern scholar will hesitate before he accepts this decision.

Alexander concluded his Oriental conquests, and died at Babylon, in the year 324 B.C. At this time Rome was engaged in a life-and-death struggle with the Samnite league. Hardly did she succeed against the skill of C. Pontius, the Samnite leader; and when the war closed, the victorious republic was reduced to the last stage of exhaustion. Had the Macedonian led his thirty thousand Greeks, flushed with the conquest of the Eastern world, into Italy, and joined the Samnites; or had he alone.

marched up with the cities of MagnaGræcia, and presented a second foe to Rome, what would have availed the valor of all her great captains, of a Fabius or of a Papirus, to save the republic? Rome fell once under C. Pontius unassisted, and only the most desperate measures saved her in the end. Assailed by a second and far more formidable enemy, what could she have done? Even fifty years afterwards, Pyrrhus beat her armies in three great battles when she had the Samnites under her feet; and had that hero possessed half the vast resources of Alexander, together with his persistence, he might easily have conquered Italy. Think you not, then, that a greater than Pyrrhus might have been the conqueror at this earlier date?

But, objects the disciple of Livy, mighty as Alexander's name is among military captains, there is little evidence of his capacity in conflict with equal enemies. Was not Memnon, who commanded the Persians at the Granicus, an equal enemy, and had twenty thousand trained Greeks, besides fifty thousand Persians? And was not Porus an equal enemy, who was the monarch of a highly civilized Indo-European race, and who could bring into the field a hundred thousand trained infantry, besides chariots and elephants? Yet the genius of the Macedonian overcame them both.

It is well to remember, too, that the Macedonian phalanx was the most perfect instrument of warfare the world had yet seen. The Roman legion was nothing like it until Scipio improved it a hundred years later. None of the Greek soldiers showed fear before the elephants of Darius and Porus. How did the Romans withstand them in the ranks of Pyrrhus? In Alexander's day the

Romans were probably not so civilized, though they might have been as far advanced in military art, as were the Persians and the Indians. It was only through contact with the magnificence of the Greek cities of Southern Italy, and by the long campaigns with the Samnites, their equals, that Rome in the time of Pyrrhus was the powerful state she was.

Hannibal was a greater general than either Pyrrhus or Alexander, and would not his ultimate failure teach us to doubt the Macedonian's success? We answer, No. There were excellent and logical reasons why the great Carthaginian hero met with defeat. In the first place, he was not supported by the Carthaginian government. Hanno, the great enemy of the Barcine family, was all-powerful in the home senate, and Hannibal was forced to rely on the aid of the Italian tribes. In this also he was disappointed. Despite his diplomatic skill, despite his series of brilliant victories, the aid of the Italians was lukewarm and limited. Their subjugation and humiliation had been so complete that even the sentiment of revenge was obliterated; consequently, Hannibal's accession of native soldiers was wholly inadequate to enable him to press on as he had begun. He then summoned his brother from Spain, but that brother's head alone reached him : his body and the bones of his soldiers lay rotting on the banks of the Metaurus. The home government inactive, his Italian allies lukewarm, his brother defeated, there was nothing for the Carthaginian to fall back upon but his own genius; and that, unparalleled as it was, could not long avail him against the resources, the valor, the persistence, of Rome.

In Alexander's case it would have