FROM THE SAME  January 7, 1863.

Last week a supply train came in from General Grant's army, and the Fifth Iowa was one of a dozen regiments forming the escort. I saw Thomas Blondin only. Lieutenant Donnan and others went outside the fort, and reported the Independence boys doing well. They certainly have a hard time. Again our camp is full of all sorts of rumors as to the whereabouts of our regiment. I suppose that they are in the vicinity of Holly Springs, and conjecture that they may form a part of the advance of General Grant's army. We are in constant expectation of hearing directly from them. Twice we have prepared to set out to join the regiment. About fifty only are able to endure the march.

The chance for sick men is as poor as ever. To-day a number of our detachment started for St. Louis. Hilling, Brady, Allen, and Minton, of company C, left. None of company C or H now here are in immediate danger, but quite a number are in a condition which demands prompt relief. They have asked for discharges, and will get them when they can be examined. More than two thousand men from all regiments in Grant's and Sherman's commands are here in a similar condition, but still very few deaths occur. Occasionally there is a smallpox scare, though but few cases have occurred. Hoffman, of company C, is now convalescent from it.

Major General Hurlbut is still in command here, and is the man for the place. The city is secesh, through and through, and requires a commander of cautious, firm decision - one who is not troubled with squeamish notions or secesh sympathies - and the general fills the bill.

One of his last orders provides that for each and every raid made upon the Charleston & Memphis railroad, by citizens and guerillas, he will banish from Memphis ten secesh families, commencing with the wealthiest and most influential.

The commander of the fort is General Asbott, a veteran soldier, and formerly on General Fremont's staff, in Missouri. Very few officers of high rank are to be found in these parts since General Sherman's expedition sailed. We hear of the loss of several officers at Vicksburgh, but are in suspense as regards the issue of the contest. There is reason to fear that we are repulsed. The failure of General Grant to advance on Jackson, and of General Banks to cooperate with Sherman, may place the latter in a very critical position. It would seem that the rebels ought to have been compelled to fight at Jackson and Vicksburgh at the same time. Every one is anxious, and all have much confidence in General Sherman's ability, and in the valor of our soldiers.

H. C. H.