The translation of the Dey of Algiers’ letter, after a curious display of Oriental Bombast, presents the alternative of re -establishing the Old Treaty, instead of the late one as annulled by our breach of it, or a withdrawal of our Consul which means a commencement of war by him. The answer concludes with the declaration that as peace is better than war, war is better than tribute. Letters from Shaler as late as June 29, leave things in the suspence connected with the appeal made by the Dey’s letter. It is probable that war will be prevented by the presence of our augmented squadron, unless it shd. result from an adjustment between the Dey & G. B. If the article in our Treaty violating that of the English, be the only obstacle to peace, it will be got over. The serious danger is that G. B. will support Algiers, either from a view to her navigation in the Mediterranean, or from her policy of being well with the Grand Signor in the event of a variance with Russia. This is probably meant by "the contrariety of interests and views" which Ld. Casth. mixes up with the subject in his late speech. The Dey has submitted to the Grand Signor his dispute with Exmouth: and it appears that he has lately recd. a solemn confirmation on the throne; from Constantinople. Harris’ late communications present a better prospect at St. P. The dispatches by Mr. Coles cannot well fail, to turn the sensibility of the Emperor agst. the quarter wch. excited it agst. the U.S. Our affairs at Tunis & Tripoli are in a good State. The departure of Consul Jones from the former was transitory & unmeaning.