BEHIND Vicksburg, June 5, 1863-8 a. m.,

VIA MEMPHIS, June 7-5 p. m.

The siege works progress steadily, though there is a deplorable lack of engineer officers. Of the half dozen of those in this army, one very valuable, sent from Rocky Springs about May 5 with dispatches to General Banks, has been retained by him just as he has retained Grierson's cavalry. The rebels in McPherson's and Sherman's front have strengthened their works within two days by building demi-lunes in front of their re-entrans. In Sherman's judgment, there is no evidence of their erecting new works in the rear of their original line. Our line and theirs must be in contact within three days. The expeditionary corps, under Blair's command, commenced its march yesterday morning to occupy fully the southern approaches to the city, but were called back about noon, and the brigades returned to their original DIVISIONS. This was a result of some new demonstrations of the enemy, thought to be indicative of a purpose to sally, and also of General Grant's unwillingness to scatter his troops. The cannonade from our whole line is now steadily maintained by night as well as by day. Some FIFTEEN 8 and 9 inch Navy guns lent by Admiral Porter, with crews to fight them, are being put in position. General Grant is considering the subject of sudden attack in great force on the south, where there are no siege lines and where enemy expect nothing. From the drift of his remarks, however, I conclude he will not adopt the measure. Another brigade of N. Kimball's has arrived, and is now a Haynes' Bluff. Kimball has been ordered with his whole DIVISION to Mechanicsburg, to increase and to command the observing force previously sent there under Mower. Joe Johnston has sent some troops to Yazoo City, and appears to be occupying with small detachments the line thence to Canton. Admiral Porter's whole force of light steamers left for there yesterday evening. The rebels are reported to have several large transports up near Yazoo. No signs of any movement of Johnston on the lower line of Big Black. A body of guerrillas are troubling the leased plantations in Louisiana. J. C. Sullivan has been relieved of command there for inertia, and Dennis has gone to his place. Unfortunately, J. P. Hawkins is absent, sick, or General Grant would have given him the command. Two regiments of McClernand's have been sent over, and there are four colored regiments there, numbering about 2,500, armed but not disciplined. The fortificationsf advance with exceeding slowness for want of both engineers and laborers.

C. A. DANA.

Honorable E. M. STANTON,

Secretary of War.

WAR DEPARTMENT, June 5, 1863.

C. A. DANA,

Esq., Grant's Headquarters, near Vicksburg:

Your telegrams up to the 30th have been received. Everything in the power of this Government will be put forth to aid General Grant. The emergency is not underrated here. Your telegrams are a great obligation, and are looked for with deep interest. I cannot thank you as much as I feel for the service you are now rendering. You have been appointed an assistant adjutant-general, with rank of major, with liberty to report to General Grant, if he needs you. The appointment may be a protection to you. I shall expect daily reports, if possible.

EDWIN M. STANTON,

Secretary of War.