From the Southwest.
--Official advices from Tennessee indicate the inauguration of active operations in that quarter. The Federal forces under Rosecrans are represented to be advancing upon General Bragg, and a collision between the two armies seems inevitable in a short time. It is also stated that Burnside, with a heavy body of Federal troops is marching through Kentucky in the direction of East Tennessee. The probabilities are that we shall, in a few days, hear of stirring news from both East and Middle Tennessee.