Mr. Pickering has the honour to return to the President his memoir on the northern boundary of Louisiana. A close examination of the subject since, has convinced Mr. Pickering that the idea he took the liberty to suggest to the President, which is the basis of the memoir, and which arose in Mr. Pickering’s mind on the perusal of Mr. Hutchins’s observations on the treaty of Utrecht, is incorrect. He has digested his reflections on the subject; and will submit them to the President’s consideration, as soon as he can transcribe his notes—this evening or to-morrow morning.—Mr. Pickering will now only mention, that the fifth article of the British convention, all things considered, is, in his opinion, precisely what the United States should desire.