The following extract from a valuable letter with which the author was favored by Ex-President Adams, who, as secretary of state, conducted the negotiations with Spain, will explain his opinions and acts upon a subject of so much importance. QUINCY, 7th July, 1847. * * * * * "Whoever sets out with an inquiry respecting the right of territories in the American hemisphere claimed by Europeans, must begin by settling certain conventional principles of right and wrong before he can enter upon the discussion. "For example what right had Columbus to Cat Island, otherwise called Guanahani? Who has the right to it now and how came they by it? The flag of St. George and the Dragon now waves over it; but who had the right to take possession of it because Christopher Columbus found it,--the paltriest island in the midst of the ocean. European statesmen, warriors, and writers on what are called the laws of nations, have laid down a system of laws upon which they found this right. Have the Carribee Indians, in whose possession that Island was discovered by Columbus, ever assented to that system of right and wrong? "You remember that Hume, in commencing his history of England by the Roman conquest says--"that without seeking any more justifiable reasons of hostility than were employed by the later Europeans in subjecting the Africans and the Americans, they sent over an army under the command of Plautius, an able general, who gained some victories, and made a considerable progress in subduing the inhabitants." Then, no European has ever had any better right to take possession of America, than Julius Cæsar and the Romans had to take possession of the island of Britain. "What then was the right either of France or Spain to the possession of the province of Texas? To come to any question of right between the parties upon the subject you must agree upon certain conventional principles: where and when your question of right must become applicable to the facts; and, as between them, it was a disputed question, and had been so from the discovery of the mouth of the Mississippi river by La Salle, and from his second expedition to find the mouth of the Mississippi coming from the ocean, in which he perished. "Spain had prior claims to the country, but the claim of France was founded upon the last voyage of La Salle, and by extending a supposed derivative right, from the spot where La Salle landed half way to the nearest Spanish settlement.