Friday, Oct. 30.--Left Cole's at 6 o'clock a. m. Breakfasted at Frankfort, the seat of the government of Kentucky. It is situated in a deep valley near a stream, surrounded with high and uneven hills, and at a distance, from its shape and situation, it resembles a garden laid off in squares. A very handsome bridge, neatly painted, is thrown across the Kentucky river, which, together with some public buildings erected with considerable taste, assist much in enlivening and adding beauty and elegance to the appearance of the town. Left Frankfort at 9 o'clock. Crossed the Kentucky river, which was only three feet wide, owing to the uncommon drought. Foot passengers were crossing on a rail. Passed through Shelbyville, a small village. Many creeks, rivers and branches entirely dry. Every animal suffering for water. The farmers compelled to cart a sufficient quantity to support life, many miles. No water to be obtained in the village for our horses. Fortunately we were enabled to purchase some on the road. Traveled twenty-nine miles to Smith's. Lands rich. Country broken on the old road. Deep valleys. Frightful precipices. Beech woods. Large trees. Good corn. Warm and dry weather. Saturday, Oct. 31.--Left Smith's at 7 o'clock a. m. Traveled over a very rich and flat country. Passed through Middletown, and at 4 o'clock arrived at Louisville, after traveling twenty-eight miles. This day being Saturday, and having met some old friends and acquaintances, a party was made up to visit the Louisville theater. Philadelphia being the theater for all great performers, curiosity was on tip-toe to view the players of Louisville. The theater is a neat little building. It was but thinly attended, owing to the pressure of the times. The play was "Wives as They Were and Maids as They Are," Mr. Drake and Mrs. Grochong supporting the principal characters. Their persons, features, voices and gestures were fine, appearing to possess the nicest feelings and tenderest sympathies, and, in my opinion, they were well suited to a better stage. The play better performed than expected. Indeed, I may say well performed, if I may be permitted to add there was more than one of the actors who was unfeeling, unmeaning, made of wood and more like a gate-post than an animated being. This had the happiest of effects, for after shedding tears of grief at interesting parts of the play they were kept flowing with laughter at those ridiculous performers making tragedy into comedy. Louisville is a flourishing town immediately on the banks of the Ohio. The town and business principally confined to one street. The inhabitants are polite, hospitable and live fast.