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--There is a direct telegraphic communication between New York and St. Paul, Minnesota. Messages were passed over the wires on the 17th inst., for the first time. The New York operator reported at St. Paul on that day, the steamer Arabia coming up, and the gratifying intelligence that the Australasian was safe, and the Arabia had her mails and passengers. Difference in time was found to be one hour and fifteen minutes, New York being 8.40, St. Paul 7.25.