From Memphis

Special Dispatch tO tlie Chicago Tribune. Memphis, via Cairo, Aug. 7. I bave a letter irom Lagrange, oí reeent date, detaiüng tho moveinenta of Col. E. Hatch and bis command, consisting of portions of the Third Michigan, Eleventh Illinois and First West Tennesseo Cavairy, and the Ninth Illinois Infantrv. in cleaniner out rebel guerrillas in tbat section of the country. Col. Hatch started on the 26th uit., and went to Bolívar, destroying the bridge thonce to Mifflin. At Mouot Pierson het came upon Newsom's men, nbout one hundred and thirty n nuraber, dispersed and captured ton of them, and (hen pushed forward to Lexington. Before reaching that place he met a carriage contaitiing thrce rebel offiners, a Colonel, Adjutant and Quarteimaster, escorted by five privatea. The Colonel asked our boys where Newsom was, evidently under the impression they were Confedérales. He waR answered tbat he was coming. - Col. Campbell, the name of the rebel officer rode forward, expeeting to meet Newsom and his followers, but, instead of that, feil iuto the hands of Colonel Hateh. At Lexington Col. Haten met forcea from Corinth consisting of the lOth Missouri, 15th Illinois and 7th Kansas cavalry, or raounted infantry, under Col. Kowett, of the latter regiment, from Lexington. Ho returned by way of frentón, Jaekson, MifBin and Bolívar to Lngrange, which place lie reached on tho 5th instant, having performed a journey of tbree hundred miles. Tbe forces from Corinth returned to that place by a ehorter route. Care was taken by Col. Hatch to prevent the indiscriminate plundering and outrageous conduct generally at Huntingdon, Trenton and JacksoD. Major Wilcox's command, and a detachment of the Third Michigan Cavalry, were sent forward to take possession of these places for the protection of tbe citizens. At Huntingdon we eaptured two rebel Cap tains, and in all took some twenty rebel prisoners. Colonel Hatch eaptured in all one hundred and fifty prisoners, many of wb om were paroled, tome expr essing their willingness to take the oath of allegiance to us, having formerly been conscripted into the Confedérate army. - Forty prisoners and several commissiontd officors, with arms, horses and equip meuts have been brought to Lagrauge. Jesse Forrest succeeded in eluding Hatch, and passed south a short distance east of Grand Junction a few days before the retnrn of the latter. Thus has West Tennesseo been clenred of all organized rebel forcee. Only a few gangg of predatory plunderers renjaJD. '