From the Southwest.
Jackson May 5
--A special to the Appeal says that twelve bunches were burned at Byhalin.
The Yankees camped last night at Gwinn Mills, seven miles above Byhalin, and have since established a permanent camp there.
They made on Hotly Springs Sunday.
Capt. Mischell ambushed them on as they went out with five men, and killed Col. Jenkins'capturing his horse and papers.
The Chicago Times, of the 1st, has been received at Miltiken's Bend.
On the 24th April Grant's whole army was ordered to move with six days rations.
It adds, that four out of six transports, in attempting to pass Vicksburg, were sunk; that the rebel fire was terrific.
The New York papers state that the editor of the Atlanta Confederacy has been arrested at Port Royal. 