From Halleck's Army

riLT.BCXS ElEADQUARTEKS, Mav 9. The Federal forcea uow occupy Baidwin, Guntown, Jackson and Bolívar. - The railroad repairs aro progressinï rapidly. Tho enerny passed Guntown last night retrea'.ing soulfrward from Baldttin. It i siiiimtuil tlint therc have been 20,000 deserten) sinco tiiey left Corinth, mostly fróni Tenoessee,, Kentncky, and Arkansaa rogimonts. - All thu regiments ('rom theso States paseed down closely guarded ou both sida by Missicgippi and Alabamn troops. Il is bciiov.-d by the coui.try people tfiat JJcaurcgard cannot enter Coiumbus with bul f tlie troops hs brought iwav from Corinth. Tno wbolo couutry cast and north of Daldwin is full of anocd soldiers, rcturning from Teunesseo and Kentucky regiireiits. General Pope tclfgniplis from the ad. vaneo thafc the prieooera who first desired to be excdanged, now want to tako the oath. The ciiemy carried off evorything for miles arouod. ' The wealthie.st families are destituto and starving. Woraen and u'aildren are cryiug for food. Tbe males were foreed inti) tbc army. The eneniy are reprcscDted to b3 greatly suffering for food. Washington, Juno 10. The following message was rceeived ut the War Dopartment this morning : Corinth, June 10. To Ilon. E. M. Stanton, Secrctary of War : The enemy have fallen biu-k to Tusilla fifty miles from here by railroad, and near scventy inik-s by wagou road. Gen. Pope estima tes the rebel loss from casualtie--, prisonors, and desertion at over 20,000, and ücn. Uuell at betweon 20,000 and 30,000. A persoü vl:o was eniplojxd in the Confedérate Commissary Department, says they bad 110,000 men iu Corintl), and that now they cannot mustor inuch over 80,000. Some of the fresh grnves on the road have been opencd and found fillcd with arma. Man}' of the prisoners oí war beg not to be exchanged, saying they purposely allowed thciuselves to bs taken. Uoauregard himself retreated from Baldwip on Saturduy afteruoon to Okolona.