MIDDLESEX HOTEL. Mr. Wesson, who was the proprietor of the Middlesex Hotel, recently destroyed by fire in this town, has commenced the foundation of a new Hotel, on the site of the old one. The design of the contemplated building is elegant and chaste, and when completed will be an ornament to the place. We understand it is to be finished by the first of December next. Messrs. N. S. Hosmer and E. C. Wetherbee are the contractors.