The PRESIDENT laid before the Senate a letter from Mr. Smith of Maryland, stating that being appointed by the Executive of that State a Senator in conformity with the constitution, until the next meeting of the Legislature, which will take place on the 5th day of June next, he submits to the determination of the Senate the question, whether an appointment under the Executive of Maryland, to represent that State in the Senate of the United States, will or will not cease on the first day of the meeting of the Legislature thereof? and the letter was read; and, after debate, it was agreed that the further consideration thereof be postponed until to-morrow. WEDNESDAY, May 31. STEPHEN R. BRADLEY, from the State of Vermont, attended. _Batture at New Orleans._ Mr. GILES presented the memorial of Edward Livingston, of New Orleans, stating that, for a long time prior to the 25th January, 1804, he was in peaceable possession of a parcel of land called the Batture, in front of the suburb of St. Mary's, in the city of New Orleans. That, on the 25th of January, he was forcibly removed by the Marshal of the district, under the orders of the President of the United States, notwithstanding an injunction had been granted by the superior court against the execution of the warrant; and praying that the possession may be restored to him, and that such measures may be pursued as the wisdom of Congress may devise, for providing a legal decision on the title of the United States, if it shall be supposed they have any, to the property in question; and the memorial was read, and referred to Messrs. GILES, ANDERSON, HILLHOUSE, WHITE, and WHITESIDE, to consider and report thereon. THURSDAY, June 1. _Non-Intercourse Act--Extended to all public armed Vessels._ Mr. GILES offered the following amendment to the first section, to be inserted after the word "assembled:" "That the provisions of the two first sections of the act, entitled 'An act to interdict the commercial intercourse between the United States and Great Britain and France, and their dependencies, and for other purposes, shall extend to all public armed ships and vessels of all foreign nations, and the same shall be, and are hereby, continued and made permanent, subject, nevertheless, to any modifications and regulations which may hereafter be made by treaty."