Waiiinctun, June i. The foilcmin di-puti-h was rbceivd th: iiftermvw ut the VV:ir Departti ent: II'. i,i,i:.'k' íTkadqi'aiítki!.3, Juno 4. ToHon. K II. Ptaafoo, SecrHarj of Wnr : ii.ti Pope, i'h -10,000 men, i.s tli!ny willes snn'h ni Floreiu, pushiitg : tío , enemy hiirrl. lio alrus v reprl 10,000 [irisoners and ciwert r frum t e enemy nn 10,000 rti:r) 'f srtHt) --}- tnred. ThoiisiimU oí the enemy uro throwitijj tiwny their itrn.s, A furipcr s.íijíj (bat wbeii Cuntirégnrcl learnef] tlint ('oloml Elliolt hnd ent thc railrond fín hi8 line of rotroUt, he becanoo franticjand to!d h s mtn to snve th( msilvos tho best W8V t h y anuid. Wo capfured nine locomotivo nnd a nurnlicr of ;:ir. On of the former is : al:eady repairod and runnibg to daj. Soveral moro will be in running order in i few days, The rasiiU is all that I could pÓSfiblv (ii'sire. (Sisnéd) K. W. HALLECK, M. or General Coitimaintinff. Ghteagfo 4th spocials from (Jairosay; " Imttiediiiltly on tlio occupation ol Crinth f urces from Popp'ri división wi-r' sent out in pnrsuit of siich rt-hels us flod .vgstwiuil. General ürpnger, n coiprnantl of two rugrmenta of cavalry, poon mine in the rear of the eriemy six milos eotllhwest af Oorinth and ' eiigagi-cl thom ffl BglW. Ho lost tifty men, and wns nfterwjirds lnrguly forced, when the rebela were j ed. Il is s;i;d that fivo to ten thonsar.d ; w(;ru inleen prisoners. A portion of tliese have reauhed Pittsburg Landing1 en route tor northern military prisóns. " At lust accounts from Gfn. Pepo ho was nino miles Southwest of Corintb, which point his wholo corps had reauhed."