A gentleman connected with the Army of the West, who arrived in this city yesterday evening, on the State train, informs us that previous to his leaving Corinth, a woman had been brought in, who was arrested while on her way to Nashville for the purpose of conveying information to the enemy. She had been within the lines for some weeks past, during which she had been eery assiduous in ministering to the wants of the sick soldiers; for some reason, however, not explained to us, she fell under the suspicions of the officers, and on her departure from camp some days ago, on pretence of a visit to her friends, a small detachment was ordered to follow and watch her.