Already the capture and burning of the ship Lafayette, which contained an English cargo, has been the occasion of a correspondence between the British consul at this port, Mr. Archibald, and Rear Admiral Milne, commanding the British squadron on the American coast; and it is stated (but we cannot vouch for the truth of the statement) that the admiral has dispatched three war vessels in pursuit of the pirate. The consul has also, we understand, communicated the facts of the case to the British government and Her Majesty's minister at Washington. What action will be taken by the British government remains to be seen. The Lafayette sailed from this port with a cargo of grain for Belfast, Ireland. The grain was owned by two English firms of this city, and the facts were properly certified on the bills of lading under the British seal. * * * But another case (that of the bark Lauretta) is about to be submitted for the consideration of the British authorities, as well as those of Italy and Portugal. The facts establish a clear case of piracy. The Lauretta, which had on board a cargo consisting principally of flour and staves, was burned by Semmes on the 28th of October. She was bound from this port for the island of Madeira and the port of Messina, Italy. Nearly a thousand barrels of flour and also a large number of staves were shipped by Mr. H. J. Burden, a British subject residing in this city, to a relative in Funchal, Madeira. The bill of lading bore the British seal affixed by the consul, to whom the shipper was personally known. The other part of the cargo was shipped by Chamberlain, Phelps & Co. to the order of parties in Messina, and this property was also covered by the Italian consular certificates. The Portuguese consul at this port also sent a package under seal to the authorities at Maderia, besides giving a right to enter the port and sending an open bill of lading. Captain Wells' account of the manner in which Semmes disposed of these documents, and which he has verified under oath, is not only interesting, but gives an excellent idea of the piratical intentions of the commander of the Alabama. The papers of the bark were, at the command of Semmes, taken by Captain Wells on board the Alabama. There was no American cargo and therefore no American papers, except those of the vessel. These, of course, were not inquired into. Semmes took first the packet which bore the Portuguese seal, and with an air which showed that he did not regard it as of the slightest consequence, ripped it open, and threw it upon the floor, with the remark that he "did not care a d--n for the Portuguese." The Italian bill of lading was treated in a similar manner, except that he considered it unworthy even of a remark.