Tlie goneral odvanoo of Gen. McCi.r.r,lAN'aarmy oommenoad ou Monday, aud t was expectud to camp near Ricbinond du Wudnesday night. The advance rbaobed wíthiu öight milos on Tuesday pigbt, and drove ín the enemy's purkets. 'f a general cngngomönt is to como off atKichmond, it may be in process to-day; u faot, may havo been entcred upon yosterday. Wo look for the intúlügotico uf it witli bot!i anxioty and hopo- Gen. McDowÈLL had not, at the atest datos, advanced from Frodericka3urg, and Gen. ]?anks was at Staunton. - Thero has bon d;iily skirmishing in tho vieiuity of Corinth, and a general ongagonient has perhaps taken place before this. Beaurogard has a largo lorce, is well posted, aod ';the battle will bc one of the hardest fouglit and bloodiest of the war.