During the war with Tripoli, it was suggested that Hamet Caramalli, elder brother of the reigning bashaw, and driven by him from his throne, meditated the recovery of his inheritance, and that a concert in action with us was desirable to him. We considered that concerted operations by those who have a common enemy were entirely justifiable, and might produce effects favorable to both, without binding either to guaranty the objects of the other. But the distance of the scene, the difficulties of communication, and the uncertainty of our information, inducing the less confidence in the measures, it was committed to our agents as one which might be resorted to if it promised to promote our success. Mr. Eaton, however (our late consul,) on his return from the Mediterranean, possessing a personal knowledge of the scene, and having confidence in the effect of a joint operation, we authorized Commodore Barron, then proceeding with his squadron, to enter into an understanding with Hamet if he should deem it useful; and as it was represented that he would need some aids of arms, and ammunition, and even of money, he was authorized to furnish them to a moderate extent, according to the prospect of utility to be expected from it. In order to avail him of the advantages of Mr. Eaton's knowledge of circumstances, an occasional employment was provided for the latter as an agent for the navy in that sea. Our expectation was, that an intercourse should be kept up between the ex-bashaw and the commodore, that while the former moved on by land, our squadron should proceed with equal pace so as to arrive at their destination together, and to attack the common enemy by land and sea at the same time. The instructions of June 6th, to Commodore Barron, show that a co-operation only was intended, and by no means a union of our object with the fortune of the ex-bashaw, and the commodore's letters of March 22d and May 19th proved that he had the most correct idea of our intentions. His verbal instructions indeed to Mr. Eaton and Captain Hull, if the expressions are accurately committed to writing by those gentlemen, do not limit the extent of his co-operation as rigorously as he probably intended; but it is certain, from the ex-bashaw's letter of January 3d, written when he was proceeding to join Mr. Eaton, and in which he says, "Your operations should be carried on by sea, mine by land," that he left the position in which he was with a proper idea of the nature of the co-operation. If Mr. Eaton's subsequent convention should appear to bring forward other objects, his letter of April 29th and May 1st views this convention but as provisional, the second article, as he expressly states, guarding it against any ill effect; and his letter of June 30th confirms this construction.