The Mexican settlements, thus excepted, are not those over which Texas did not claim jurisdiction, but those on the East bank of the Rio Grande, over which Texas did not _exercise_ jurisdiction at the period mentioned. The President had no authority to give up the boundary claimed by Texas; but it is clear that at the time, when war was not contemplated, the Administration was of opinion that, till the question was definitively settled, the occupancy by the Mexicans of the territory adjacent the left bank of the del Norte ought not to be disturbed. Neither the subsequent refusal by Mexico to receive a residing Envoy, nor the successes of the American arms have affected the question of right. The claim of Texas, whether to New Mexico, or to the lower portion of the Rio Norte, was identically the same, as invalid and groundless in one case as in the other. Why a distinction has been made by the Executive has not been stated. The fact is that he has established a temporary government for New Mexico, as a country conquered, and without any regard to the claim of Texas; whilst, on the other hand, he has permitted that State to extend its jurisdiction over the country lying on the left bank of the del Norte, which, like New Mexico, had been conquered by the arms of the United States. Not a shadow of proof has been adduced to sustain the pretensions of Texas to that district; and justice imperiously requires that it should by the treaty of peace be restored to Mexico. It so happens that the boundary, which may be traced in conformity with this principle, is a natural one, and that, as a measure of expediency, none more eligible could have been devised. A desert of one hundred and twenty miles separates the most Southwesterly Texan settlements of Corpus Christi and San Patricio, from those of the Mexicans, on the left bank of the del Norte, than which no boundary could be devised, better calculated to prevent collisions hereafter between the two nations. It will be sufficient, for that purpose, to draw a nominal line through the desert, leaving all the waters that empty into the Rio Norte to Mexico, and all those that empty into the Rio Nueces to Texas, together with such other provisions, respecting fortifications and military posts, as may be necessary for the preservation of peace. The line of the Rio Norte is one, from which Mexico would be perpetually threatened, and from which their adjacent town on the eastern bank may be bombarded. Such an intolerable nuisance would perpetuate most hostile feelings. With such a narrow river as the Rio del Norte, and with a joint right of navigation, repeated collisions would be unavoidable. Among these, when there was nothing but a fordable river to cross, slaves would perpetually escape from Texas: and where would be the remedy? Are the United States prepared to impose by a treaty on Mexico, where slavery is unknown, the obligation to surrender fugitive slaves?