The Mayor disposed of the following cases yesterday: Robert Spriggs and Thos. F. Moseley, fighting in Pink Alley, acquitted. The fight was all on the side of Moseley, who made the belligerent demonstrations himself. Lucy Ann Banks, of Lynchburg, committed for being in the city without a register of her freedom. William, slave of H. P. Irving, ordered 20 lashes, for stealing a pocket-knife from Thomas P. August. Charles Mosley, slave of Nancy J. Robinson, 39 lashes, for stealing an $8 shawl from Peyton, slave of J. W. Lewellen.