The weather continues cold, 38°, and snow still lies on the ground. This must produce a cessation of hostilities, and afford Lincoln’s drafted recruits opportunity for meditation.

If it be true that the Democrats have carried the day in the North, I think the war is approaching a termination.

November 10th.—A day or two ago some soldiers marched through the city without shoes, in the snow. A committee of citizens to-day obtained an order from the War Department, for the impressment of all the boots, shoes, blankets, and overcoats in the shops. What a commotion among the Jews!

It is certain that the enemy are advancing upon Culpepper, on the way to Richmond, in great force. This we have in letters from Gen. Lee, dated 7th inst., near Culpepper C. H. He says the enemy’s cavalry is very numerous, while our horses have the “sore tongue,” and tender hoofs. Lee has ordered the stores, etc. from Gordonsville to Lynchburg. He says Jackson may possibly march through one of the gaps and fall upon the enemy’s flank, and intimates that an opportunity may be offered to strike the invaders “a blow.”

Yesterday, Sunday, a cavalry company dashed into Fredericksburg, and after robbing the stores, and reporting that the Democrats had swept the North, that England and France had recognized us, etc., they dashed out again.

The President sent to the department to-day, without comment, a defense by Col. Baylor of his atrocious order for the massacre of the Indians. It was in a Texas paper. Baylor acknowledges its genuineness, and says the Apaches murdered our people invited to make a treaty with them, and he says it is his intention to retaliate by extermination of them.

Another proposition was received by the government to-day from a French firm of New Orleans merchants, to furnish us salt, meat, shoes, blankets, etc., in unlimited quantities, and guarantee their delivery, if we will allow them, with the proceeds of salt, the privilege of buying cotton on the Mississippi River, and they will, moreover, freight French ships above New Orleans, and guarantee that not a bale shall be landed in any U. S. port. Is it not certain that “Butler, the Beast,” is a party to the speculation? This is a strong temptation, and we shall see what response our government will make to this proposition to violate an act of Congress.

November 11th.—More projects from the Southwest. Mr. Jno. A. S. has just arrived from New Orleans, where, he states in his communication to the government, he had interviews and correspondence with the U. S. authorities, Butler, etc., and they had given him positive assurances that he will be permitted to take any supplies to the planters (excepting arms and ammunition) in exchange for cotton, which may be shipped to any part of the world. S. says that Butler will let us have anything for a bribe. No doubt! And Mr. L., President of the L. Bank, writes that he will afford facilities to Mr. S. It remains to be seen what our government will do in these matters. They smack of treason.

It is said heavy firing was heard yesterday in the direction of Culpepper C. H., and it is supposed a battle is in progress to-day. No danger of it.

November 12th.—The heavy firing heard did no execution. Letters from Gen. Lee indicate no battle, unless the enemy should make an egregious blunder. He says he has not half men enough to resist McClellan’s advance with his mighty army, and prefers manœuvring to risking his army. He says three-fourths of our cavalry horses are sick with sore-tongue, and their hoofs are falling off, and the soldiers are not fed and clad as they should be. He urges the sending of supplies to Gordonsville.