For a period of about two centuries after the settlement of a republican constitution, there is little of importance to relate in Athenian history. Athens was gradually enlarged, the taste for refinement increased, and various men of sagacious understanding, entitled Philosophers, began to devote themselves to inquiries into the nature of the human mind and the character of the Deity. The principal Grecian philosopher who flourished in this era (550 B. C.) was Pythagoras, a man of pure and exalted ideas, and an able expounder of the science of mind. THIRD PERIOD OF HISTORY The year 490 B. C. closes the gradually-improving period in Grecian history, or second period, as it has been termed; and now commenced an era marked by the important event of an invasion from a powerful Asiatic sovereign. PERSIAN INVASION. Darius, king of Persia, having imagined the possibility of conquering Greece, sent an immense army against it in the year just mentioned. Greatly alarmed at the approach of such an enemy, the Athenians applied to the Spartans for aid; but that people had a superstition which prohibited their taking the field before the moon was at the full, and as at the time of the application it still wanted five days of that period, they therefore delayed the march of their troops. Being thus refused all assistance from their neighbors, the Athenians were left to depend entirely on their own courage and resources. A more remarkable instance of a small state endeavoring to oppose the wicked aggression of an overgrown power, has seldom occurred in ancient or modern times; but the constant exercises and training of the Athenian population enabled them to present a bold and by no means contemptible front to the invader. War had been their principal employment, and in the field they displayed their noblest qualities. They were unacquainted with those highly-disciplined evolutions which give harmony and concert to numerous bodies of men; but what was wanting in skill they supplied by courage. The Athenian, and also other Greek soldiers, marched to the field in a deep phalanx, rushed impetuously to the attack, and bravely closed with their enemies. Each warrior was firmly opposed to his antagonist, and compelled by necessity to the same exertions of valor as if the fortune of the day depended on his single arm. The principal weapon was a spear, which, thrown by the nervous and well-directed vigor of a steady hand, often penetrated the firmest shields and bucklers. When they missed their aim, or when the stroke proved ineffectual through want of force, they drew their swords, and summoning their utmost resolution, darted impetuously on the foe. This mode of war was common to the soldiers and generals, the latter being as much distinguished in battle by their strength and courage as their skill and conduct. The Greeks had bows, slings, and darts, intended for the practice of distant hostility; but their chief dependence was on the spear and sword.