On the 3d of September Mr. Donaldson arrived at Algiers, and on the 5th the Treaty was concluded, and the peace presents immediately given, by a loan. Mr. Donaldson, knowing that funds had been lodged in London to answer his stipulations, engaged to make the payments in three or four months. Colonel Humphreys had received advice, under date of the 30th July, from the Messrs. Barings, in London, to whom the funds had been remitted, that, having made progress in the sales of the United States' stock, they should hold, at his disposal, the whole of the value of $800,000, meaning to furnish, by anticipation, the value of that part which remained unsold, if the service of the United States required it. Colonel Humphreys, counting on the money as always ready after this period, sent Captain O'Brien from Lisbon to London, in the brig Sophia, to receive it. Owing to contrary winds, she did not leave Lisbon till the 24th of December. The other details, relative to the pecuniary transactions, appear in the report of the Secretary of the Treasury. The disappointments in the pecuniary negotiations, put the Treaty in jeopardy; the Dey threatened to abandon it, and it was with extreme difficulty that it was prevented. Mr. Barlow did not arrive at Alicant until February, 1796, where he proposed to wait the arrival of the funds: but, after a little time, his intelligence from Algiers showing that our affairs were in a critical situation, he determined to go thither immediately, with the hope of soothing the Dey. He arrived there the 4th of March; they had before prolonged the time to the 8th of April for the payment of the stipulated sums. On the 3d of this month the Dey declared what should be his final determination--that in eight days Mr. Barlow and Mr. Donaldson should leave Algiers; and if, in thirty days after, the money was not paid, the Treaty should be at an end, and his cruisers should bring in American vessels. Under these circumstances, and as the last hope of saving the Treaty, they were induced to offer the present of a frigate--this fortunately succeeded. For the particulars of this transaction, the Secretary begs leave to refer to the enclosed letter from Messrs. Barlow and Donaldson. Colonel Humphreys not deeming himself authorized to confirm this promise of a frigate, referred the matter to the Executive of the United States; and for this end despatched Captain O'Brien, in the brig Sophia, to America. There was evidently no alternative; and the promise was confirmed.