Caí no, April 29. The b team er Beacon, wliich luft Pitteburg last even ing, has arrivod. Generala Hallefk, Buell nnd (Jranl had moved their hoadquartera nenr the front of our line, per.sonallv snperiit tending ill detalla attendiñg the a. vanee ofíheir bolo forcé, orders fur which are lioofly expeoíed. Gen. Pnpe's división advanecd fur mileií Sunday, and aro now üMcamped in siiriit at tlio enemy's oamp fires. Rebol áeeertera who carne ín Saturrlay and heard rumora of tho fal] uf New Orloan, which, howevep, wert contradicted by the officers of picketu who occusionaliy oxchanged Miotn. A later arrival to iight reporta tbní onr wholo army 8-moving forward slowlv. CoDtrabaod dwortera who cntne within our line?, repeat tho previoaa statouients that Corintli is being evnouated. Pittsburg, Tenn., April 2D. IIcnvy firing across Lick Creek waa heard this raoniiujr, c:iused by artillery praotice with the rebela by our ulvanca guard, who after a slight skirtnis'ning, in whieh vc capturad several prisoners, oceupied Pe; lü'Jge, and at 9 o'elock oocupied Monferey, twelve or fuurtoen miles froin Corinth. A veiy intelligent sailor of Boston, who deserted froin the rebels this sido of Corinth, reporta that the capture of New Orleaoa waa generally known in tho rebel oüinps on the niorning of the 27th. It was :t!so atated that on thc 18t!i tho time of two Louisia a regiments, cnlisted for t-.vrlvL' nionths, bxpired, but by a nevt conacrípt lá-w, they were required to serve two years lijnger. Oa being' so infornifid, both regiments laid dow:i their arnis ai;d refused to fight, when Beun;gard detailfd four regiments to guard thein as prisooers. " It was not kuown that Gen ITalIeok was in coinraand liere, but the general impresüioii among tho troops is that Gen, Buell w:is, and that our army was retreating to Naíhville. " Col. J. O. KeltOD, A. A. G., arrivei today, relieving Capt. McLeaD, who wa9 obilgL-d togo to Oiupianati on accouat of ill health.