...ct. 12, 1862. I am enabled at last to give you a tolerably detailed, and at least truthful account of the late fight at Corinth, so far as the first division of the Army of the Mississippi, under Gen. Lovell , is concerned. I deeply regret that I am not in possession of all the facts which would exhibit the share taken by those brave and tried men under the much-loved Price. You will remember that t...