The One Hundred and Twenty-fifth Illinois Regiment arrived on Thursday morning, and went directly to Camp Douglas without coming into the city. They have been invited by the Executive Committee to visit the different departments of the fair. The Eightysixth Illinois Regiment, which arrived in Chicago last Sunday went into barracks at Camp Fry. These two regiments are old friends, having been in the same brigade through most of my campaigns. I have been invited to address these soldiers tomorrow as they muster out to return to civilian life.