The following is the letter sent to the Mayor by Capt. Farragut yesterday:

U. S. Flagship Hartford
At Anchor off the city of New Orleans, April 28, 1862

To his Honor the Mayor and the City Council of the city of New Orleans:

Your communication of the 26th inst. has been received, together with that of the City Council:

I deeply regret to see, both by their contents, and the continued display of the flag of Louisiana on the Courthouse, a determination on the part of the city authorities not to haul it down. Moreover when my officers and men were sent on shore to communicate with the authorities, and to hoist the United States flag on the Customhouse, with the strictest order not to use their arms unless assaulted, they were insulted in the grossest manner, and the flag which hd been hoisted by my orders on the Mint, was pulled down and dragged through the streets.

The capture of New Orleans is the most important event of the war thus far. There can be no doubt that the rebel defences of the city were formidable, though…

We have received several trophies from the battle-field of Shiloh, which are alike Interesting and significant. Mr. Wm. R. Elliott, of the Crescent Blues, Crescent Regiment, who fought bravely through the battles of the 6th and 7th, and who was wounded in the leg near the close of the last day’s fight, has presented us a Yankee private’s coat, which he captured and appropriated. The coat is composed of good blue cloth, well made, and is certainly an excellent article of wearing apparel. Were it not for the brass fixings on the shoulder straps and “old Abe’s” buttons, it would be as genteel a coat as one would wish to wear in cold, or moderately cold weather. The garment shows in what style the soldiers of our enemy is are fitted out.

We publish to-day a full and authentic list of the killed, wounded and missing of this gallant regiment in the late battle on the Tennessee. We are indebted for it…

Let me premise that the gentleman went South with a letter from the Mayor of Boston to the Mayor of Louisville, which secured his passes through the lines; that he…

We are pleased to learn that the Regiment of Planters' Life Guard, which has for sometime past been in course of organization for Confederate service by Colonel DeVeuve, is now…

At twelve o’clock last night one of the state powder mills, that at the old United States Marine Hospital at Gretna, blew up with a report that shook the whole city to its foundation stones. A pillar of flame shot up to the sky, for an instant illuminating the whole heavens, and then came the noise and shock—too great, too sudden, too overpowering to be mistaken for anything than what it really was.

On Saturday morning, 14th inst., at half-past 7 o’clock, Capt. Mark L. Moore, of the Bienville Guards, stationed on the peninsula in Virginia, departed this life at his residence in this city, in the 31st year of his ago. Capt. Moore contracted a complication of diseases while in service and exposed to camp life, from which he sought relief by furlough, and returned to his home. But the insiduous destroyer had marked his victim, and despite the most skillful medical attendance, and the unceasing watchfulness and attentions of a devoted wife and friends, he lingered for weeks uncomplainingly till death terminated his sufferings and gave the emaciated frame the last most still and solemn repose.

The regiment of mounted volunteers under command of Col. Scott, five companies of which will leave Baton Rouge for the seat of war in Kentucky on Saturday, is a corps of which the State may justly feel proud. It is composed of the substantial young men of Louisiana—gentlemen in their social standing, sons of our worthiest citizens healthy, temperate, athletic—good marksmen and excellent horsemen. They have volunteered for the whole war from an ardent patriotism, leaving behind them the comforts of home, and in every instance all the luxuries that wealth can procure. A nobler regiment of cavalry never formed into line on this continent than the one about to part from us—brave and worthy men, commanded by chivalric and intelligent officers.