Ni'.vv York, June 1. The ste8iner Balüu arrived yeslerdíiy from Key Wet. The steamer Swao, with 1,000 bales of oottoe, uva 800 barreta ro.sin. had been capturod and luis arrived at Kèj West. The ivtdonoe ugiiinst the slwamcr Circiissian is couclusive, and 6he wil] be condonined. New Orloans dates are to the 22d -- Genera] Sbipley h:is assmned the du tics oí Mayor ; Major JJull, liccoider, and Captuin Jonas Frcnch, Chief'of po. lice. Thoy tke ohftrge f the city til uval mon ;ire elouted. Tbe ]5:uik oí Commerco has rtpend and c(tnmonced business, refusing rebel shinplasters. Pensitcola advices state that the resí d e 1 1 í y welooraed our troops jovt'ully. - Hüly Wilson occupicd the resideneo 'oí J. Ü Mullory.