We had, at one time, some hope that an accommodation would have been effected between the Turks and two empires. Probably the taking Oczakow, while it has attached the Empress more to the Crimea, is not important enough to the Turks, to make them consent to peace. These hopes are vanishing. Nor does there seem any prospect of peace between Russia and Sweden. The palsied condition of England leaves it probable that Denmark will pursue its hostilities against Sweden. It does not seem certain whether the King of Prussia has advanced so far in that mediation, and in the troubles he has excited in Poland, as to be obliged to become a party. Nor will his becoming a party draw in this country, the present year, if England remains quiet. Papers which lately passed between this court and the government of Holland, prove that this nourishes its discontent, and only waits to put its house in order, before it interposes. They have recalled their ambassador from the Hague, without naming a successor. The King of Sweden, not thinking that Russia and Denmark are enough for him, has arrested a number of his Nobles, of principal rank and influence. It is a bold measure, at least, and he is too boyish a character to authorize us to presume it a wise one, merely because he has adopted it. His army was before disgusted. He now puts the Nobles and all their dependents on the same side, and they are sure of armed support, by Russia on the north, and Denmark on the south. He can have no salvation but in the King of Prussia. I have received two letters from Ledyard, the one dated Alexandria, August the 15th, the other Grand Cairo, September the 10th; and one lately from Admiral Paul Jones, dated St. Petersburg, January the 31st. He was just arrived there, on the call of the Empress, and was uncertain where he should be employed the next campaign. Mr. Littlepage has returned from the Black Sea to Warsaw, where he has been perfectly received by the King. I saw this from under the King's own hand, and was pleased with the parental expressions towards him.