The British steam sloop-of-war Gladiator, which left Honduras on the 14^th of Sept. arrived at New Orleans on Friday , 28^th, bringing fifty-seven of Walker's men, all in good health. The Picayane says:

The detailed report of the party on board the Gladiator adds but little to the information we already have. Gen. Walker was shot at 8 o'clock the morning of the 12^th, and buried the same day in the public burial ground.

None of his friends were present at the execution or even allowed to communicate with him after his capture. An American, however, who was at the time in the town of Truxillo, witnessed the execution and afterwards assisted at his burial, the ceremonies of which were conducted by foreigners alone, the natives refusing to take part in them.

This American who is on board the Gladiator, brings with him a portion of Walker's clothing, and other memorials left by him, which we can presume will be handed over to his family.

It is also stated that Gen. Walker, before his execution, wrote several letters to friends in the United States, which were taken by Gen. Alvarez, and by him handed over, sealed, to the English commander to be forwarded to their destinations.

Col. Rudler, Walker's second in command, has been sentenced to four years confinement in the State Prison at Comayagua.

The rest of the party, about seventy in number, were all permitted to return to the United States. Eleven of them however were sent home by way of Havana.

Of Walker's capture, on the Rio Negro, we have the following additional from an authoritative source. The party sent up the river was under the immediate command of Capt. Salmon, of the Icarus. On making his appearance, he asked for Gen. Walker. Gen. Walker then stepped forward and said he was the man.

Capt. Salmon then said: "I demand that you surrender immediately." Gen. Walker replied: "To whom do I surrender?" Capt. Salmon said: "To an officer of her Majesty's Government" -Walker then said again: "Do I understand you to say that I am to surrender to a representative of her Britannic Majesty's Government?" Capt. Salmon replied, "Yes." Gen. Walker then drew his sword and formally surrendered, and was taken on board the Icarus.

I do hereby protest, before the civilized world, that when I surrendered to the captain of her Majesty's steamer Icarus, that officer expressly received my sword and pistol, as well as the arms of Col. Rudler; and the surrender was expressly and in so many words to him, as the representative of her Britannic Majesty.