Off VeuaCruz, Sept. 25, 1846. On the 17th inst., I was one of the edified witnesses of the supremacy of the law over natural right. A sailor named Samuel Jnckson, belonging to the sloop St. Mary's, was hanged at the fore yard arm, pursuant to the sentence of a Court Martial, before whom he had been tried for striking n man named Taylor - one of the ofFicers of thnt ship. The preparations for the execution were numerous and solemn, a regular programme having been issued by Commodore Conner and circulated through the squadren several days previously. All labor in the different vessels was forbidden for the day, and the crews were directed to assume their holidayattire. At 11 A. M. the signal, "Prepare to execute the sentence of the Ceurt Martial," was displayed at the rnizen of the Cumbcrland, when a yellow flag washoisted at the fore yard arm of Ihe St. Mary's. The officers and crews of all the vessels at the anchorage were then mustered on deck, and dislributed in such places as would best enable tlicm to take as much of the spcctacle in view as posible. Here they wcre kept on the tip toe of anticipalion for more than halfan hour, wh en the same signal that I before mentioncd was hoisted, without the "preparative" and the curiosity of the spectators was very xnaterially enhanced thoreby. In a few moments more the victim made his appearance on the "topgallant forecastle" of the St. Mary's, attended by two or thrce oiFicers and the M A rms of theship, and by Rev. Fitch W. Taylor, Chaplain of the Cumbei-land. Stepping over the forecastle railing on the scafFold which had been erected there for the occasion, the prisonor seated himself on the railing, apparently on account of nervous deficiency. - The machincry fitted up for the principal act was simple, but strong and efiective. A thick rope was rove through a block at the yard arm, leading along the yard into the foremast, where it rove through another block, and was made fast to a weiglit of nearjour hnndred jiounds. After some additional minutes of suspence had been inflicted upon the thousands of spectators, a flash issued from the gun over which the scafibld had been raised, and at the some instant a human form was seen flying in a curved line through the air, with astonishing velocity. When the body reached the yard arm, so great had been the impulse, that the check threw it perpendicularly into the air, feet upward, and rebounding against the "fore lifts," it passed over the fore brace, split the halter block, and then, after a few violent vibrations, it assumed the usual attitjde of a hanging man. The operation, 1 have no doubt, has advanced the interests aud safety of society, inflnitlely, and exerted a vast iniluence upon civilization in general. In what manner, however, I cannot say. - This is the first man that has been killed, on the part of the Navy, during the war - not a Mexican having yet received the slightest injury. A New Orleans paper has the following notice of this naval murder : 'The sailor named JACKSON,lately ung on board the St. Mary's, was an irishman, a young man of seven-and-lwenty, of considerable talent and some education. He was much above the common race of sailors. Ilis ofTence consisted in knocking down the first lieutenant several limes on the quarler-deck, and uttering mutinous and insubordÃnate language. He was convicted by a court of eleven officers, Captain F., of the Cumberland, being the President. His case excited considerable svmpathy, and the Commodore confirmed the sentence ery reluctantly.' Let our patriotic Democratsno longer exclaim against England for ilogging her soldiers to death.