In Publishing, in the Republican Chronicle, Certain Charges of Fraud and Swindling, in the Management of Lotteries in the State of New-York. : Containing, the Publications in Relation to this Interesting Subject--the Evidence--the Speeches of the Counsel on Both Sides, and the Charge of His Hon. C.D. Colden, Mayor of the City of New-York, to the Jury. The Trial Commenced on Tuesday the 10th of November, and Lasted Until Friday Morning 2 O'clock, when the Jury Returned a Verdict of "not Guilty."