Standing in the City Hall, New-York, and drawing from that point a circle whose radius shall be three miles, we embrace a population of three-quarters of a million. We say this at the outset, by way of securing respect for our theme. New-York is a mere Jonah's gourd or Jack the Giant-killer's beanstalk compared with London. London was London when St. Paul was a prisoner in Rome, ten years before the destruction of Jerusalem. Sixteen hundred years afterwards, when New-York was but just named, London lost some seventy thousand inhabitants by the plague, and more than thirteen thousand houses by the Great Fire, and hardly missed them. Before this period, however, the little Dutch town of Niew Amsterdam, called by the aborigines Manahatta, or Manhattan, had commenced a dozing existence, under the government of Walter the Doubter and Peter the Headstrong, celebrated by that great chronicler, Diedrich Knickerbocker. Some consider this a mythic period, and class the legends of Wilhelmus Van Kieft's wisdom, and Peter Stuyvesant's valor, with the stories of Romulus and Remus, and the Horatii and Curiatii. But to cast any doubt upon a historian like Knickerbocker--the Grote of colonial history--at once minute and philosophical, just and enthusiastic--is surely unwise. His picture of the portly burghers of Niew Amsterdam, their habits and manners, pursuits, politics, and laws, is verified by the impress left on their descendants. All the foreign floods that have swept over the city have not been able to wash out the footsteps of the original settlers; and Walter the Doubter and Peter the Headstrong still figure, it is said, in the Assembly of the City Fathers, though the voluminous nether habiliments, which characterized them of old, have dwindled to the modern pantaloon.