We received the important news of the surrender of Lord Cornwallis and his army, on the 13th of December. Soon after, came the account of General Greene's action, which you mention also. The first seemed to have settled every one's mind upon the real state of desperation of the British affairs within the United States; the other, though very important to us in its consequences, made apparently but little impression, owing, perhaps, to two causes, that it followed so nearly after so capital and brilliant an event, and that it was scarce possible to add to the conviction, which the former carried along with it. From this state of things it may be imagined, that the way is open to us to make our advances. The conclusion, I believe, would be too hasty. For the time does not so much depend upon the real sentiments, which her Imperial Majesty and her Ministers may entertain of the stability of our independence, as upon other circumstances. To explain myself. Her Majesty has, doubtless, a wish to add to her other glories that of mediating a peace between the great powers who are now at war. For although her first attempt to mediate between Britain and Holland was rejected by the former, and her second, in conjunction with the Emperor, between Britain and the other belligerent powers, may be said to be at a full stand, yet, as you are informed long before this time, she set on foot a third, in conjunction with the Kings of Sweden and Denmark, between Britain and Holland, which Britain rejected so far as respects that of the two Kings accepting of the _sole_ mediation of her Imperial Majesty. This is still in agitation. A Minister before this time has arrived from this country in Holland, to assist Prince Gallitzin in it. But, from everything I can learn, there is not the least probability of its succeeding. I am told it is not even expected by any of her Majesty's Ministers.