Uieit Front I aland No. 10.Union Victory at Union City.On Botia Hniin Wiuw, »Orr I»ul*u 5©. 10. March 81, 1861. ( The mortar bombardment is continued aa uioa), but with much more accuracy. The rebels are strongly fortifying. The tower portion of the npper battery, which we supposed was completely silenced, is submerged, but large gangs of men and teams are at work upon the upper pan repairiag and mounting guns. f , ., , . fNew and extonsive lines of fortipOa-* tions have been erected upon the maiu ■bore, and three or four new and iarg* camps established. • They have cxU dcntly been laegdy reinforced.A now battery has al.«o beeti established upon the Island, and transports have been busily plying from the head, to the foot of the Island all clay.Everything indicates a desperate battle. The day cannot be far off. . f(To the AMOcbled Prc»«.j Cairo, April i—The rebel camp at Union City has fallen into our hand'*. Col. Unford, with 1,800 men, composed of the 27th Illinois, a detachment of; the 2d Illinois Cavalry, and part of the 15th Wisconsin,proceeded to ^lickmarr by transports from Island No. 10, andt thence crossed to Union City, where . they fell upon the rebel camp yesterday -and completely routed the enemy with-, out the loss of a man. *ney destroyed* all his tents, camp equipage, stores,, dbc., and brought off one hundred prisoners and ono hundred and fifty fiontr. The rebels are supposed to have numbered two thousand, and were under command of the notorious II. Clay King. Their loss is stated at twenty killed.Our transports, on returning to Island No. 10. had rebel flags flying under Union flag?*.There was very heavy firing yesterday at Island No. 10. It is supposed that our gunboats are at work in earnest.The weather is clear and warm. River falling.Wendell Phillips Kc*cd a»4 UU+md •* ( mrintiiili... \ Riot for Tlh Bfiirfil.—