The city of San Francisco, in the midst of her progress and prosperity, has been twice visited by the destroying element of fire. The first calamity of this kind occurred on the morning of the 25th of December, 1849. The fire consumed all that portion of the city on and near the plaza, involving a loss, at California prices, of over a million of dollars. Fortunately, it was the rainy season. If the fire had occurred during the dry season, and the prevalence of the furious gales, the whole city, composed, as it was, of canvas tents and wooden houses, must have been destroyed. The event did not materially affect the progress of the city; for the burnt district was entirely rebuilt within twenty days. The second great fire occurred on the night of the 4th of May, 1850. It broke out in the United States Hotel, situated on the plaza, or Portsmouth Square--the very heart of the city. The flames soon spread to the adjoining buildings, and several of the principal hotels were destroyed. Nothing could stop the progress of the fire but the tearing down of a whole block of houses on one of the streets leading from the Square. Five entire blocks of the business portion of the city were destroyed--involving a loss of about a million of dollars. To show the amount of enterprise and energy existing in San Francisco, no better opportunity is afforded than to look at the state of things in that city, ten days after the fire. We extract from the Alta Californian of the 15th of May, the following remarks: "THE BURNED DISTRICT.--Intimately as we are acquainted with the predominant spirit of energy and enterprise of our city, we have almost wondered at the rapidity with which the burned district is being again built up. It exceeds the speed with which the work was accomplished after the December fire. Already, in Portsmouth Square, the Bella Union and St. Charles, houses of public resort, are opened and hourly thronged. In Washington Street, two dry goods stores, 'La Amarilla' and Juan Cima's, are opened and stocked, and on both sides of the way buildings are nearly completed, and will be ready for occupation by the latter end of this week. In fact, the ruins are more than half covered over, and except that the new edifices are not of so elegant a character or so substantially built, even, as previously, they will present a handsome appearance.