Cairo, June 8. The regular paet Platte Valley, ttietí'st l)oat throiigli froin Motnpliin, ! aniv -á thin innrriog. Dur lorui" uro ' n podui-iori ( t Menipni. A Boiillii ! of tjvj gunboats nná cight Knms left Fort VVright at 2 o'clock Tbur'dy moföing Finiiing no olwti uclions at Fort lUndolph tlie flotilla píued i u, and ateiglit o;Loek, Thursdav evening tlie gunboats nnehwd tw inilea ulv íiíempliis, llie Rams rttt.muiing a short distance above. A reconnoissance was mule of the i enemy'a fteet, poneisting of tlws ; ing vessüls : (íen. Van Prn, flaL-Wp: Gen. Piict', Gen. Brairg, Qón. Lovtlt, Jeff. Thoropwin, Beauregard, Humpter, and LitÜe Rebel, which vvere dis covered lyiax near Homphtí. During Uie night the rebel fleet i mofed down the riv. r and at daylight : were out of sight, but in half an luiur afterwards thcy were neeu coming up, íbrmed in lino ot bu' tic O'.ir gnnboats had, in the meantime woighod anchor, nd, follovved ly several Rains, moved slowly toward t tío rehuí fleet, when a shot írom the Littlo Rehuí f'roin n rillod gun at long range, f olí within a short distance of the gunbont Cairo, which was in advance. The Cairo replied with n broadsido soon the engagement became general at lung rangu. The Rams had, in the ineantime advanced, and the robel llain Uoauregaid buing gome distance in the advanee, was singled o'.it by the Federal Rams, Monarch and Queen of the West, each striviníj to be tirst to strike the rebel craft. The Monarch succoeded ia Btriking her amidships, alinost cutting her in two, causing her to fill and sink imtnediately in the channe! directly oppoeite the city. At this jnnctnro the Littlo Rebel made a dash at the Monarch, which, by thia time, was in the nAdtt of the rebul fleet, bat b}r a fckillítil inovernent ot the Pilot of the latter, rIio dropped out of the way, and the blow intciuled for her Btruck the rebel boat Gen. Price, taking a way hor whe I, and making it neceqsary fot hor to run ashore, when she sent u shot which unfortunately for the rebels, s'.nick the boat Gen. Lovell, rendering herumnnnügeable. Irnmediately alter, she was run down by the Queen of tho West. A, broadside from the Benton took effect in the sides of the JelY. Thompson. She ran aahore and soon aftor was in fliinus, and burned to tho vater's edg?. Fosir rebel boatí having boen diiabled, tho remainder of the tloet retreated down the river, pureuöd by our boats, firing as thoy advanced, re suking in the capturo of tho Sumpter, Bragg and Littlo liubel, which had been abandjoed . by tuost of their crewf. Captain Montgomory, flag-officer, and most of the officers and men succeeded in muking their escapo in tbe woods on the Ark&nsas ahoro. The Federal Eam Lancaster was struck by tho Beauregard early in the eneatferrent, and was slightly disabled. Col. Ellett, in command of the Federa! Rama, was struck in the breast by a splintur, and stunned temporarily. He soou recovered and continued on deck throughout the aclion. This was the only ffusualty on our side. Our Rams were manned by Bbarpshooters, moally from Illinois, who did good execution, picking off the enemy's gunners at every opportunity. The rebel loss in killed, woundud and pnsoner.s is heavy, but is not yet fully ascortainod. Our tugs were busily ongagod in picking up the crews of their dieábled bóatfi. After the return of tho gunboats from pursoit, Commodore Davis sent the following note to tho Mayor of the city : U. S. Flao Stbameb Bentox, ) Off Mempiiis, JuneG. ) Sir - I havo respeotiully to request that y ou will sutrender tho city of MciDphis t" the authority of the United States, which I have the honor to represent. I fim, Mr. Miyor, with liigh respect, your obodient survunt, Ü.H. DAVIS, FiiigOfficnr. lu reply, the Mayor said: " Your note is received. In reply, I have only to say, as the oivil authorities havo no means of clefeQse, by foren of eiranmstattOM tho city is in your hands." Immediately after a boat'n crew j landed. and the national fiag w: a hoisted over tho postoffioe, The party was followed by an excit;d crowd, but wero uot interfered with. The Forty-third and Forty sixth Indiana Regiments now occupy the placo, Col. Fiteh in command. Thv city was quiet. No domonstration whatever has been rnado. It is even assfurted not to bo necessary to declaro martial law. Five of our gunboats now lie abreast of the city. We captured fivo large steamers, which were moored at tho leveo. The rebels burned a new gunboat which was nearly ready to b launched. Tho Vicksburg Whig of the 4th, sa}-s ttie Federáis have landed six thousand troops at Baton Rouge. The Memphis Aealunche of tho 6th, says the locomotives recently run ofi' by tho railroad employees were recovered. The same paper says all the bridgos betwoen Memphis and Humboldt have beon destroyed. Washington, June 8. The Navy Department has received an official dispatch from Captain Davis, dated steamer Benton, off Memphis, 6th, giving a short account of the surrender of Mempbii and the naval fight. It contains nothing of importunce beyond what id alroady roported.