Nushville, May 13. The Union demormtrntion today was a completo sueeosa The meeting ■vas held in tho Hall of the House of Representativos, and eomprisod at least fifteen hundrod persons, together vvith si band of rmisie. Ex-üovernor Campbell presided, aesiated by Vice Presidenta from vai'ious dktrieta and countief, iocludiqg Mamphia. Speeches weie made by ex-üovernor Campbuil, Q.overnor Johnson, Messrs. W. B. Stokes. Willam H. Polk, W. P. Wes ene, Édmund Cooper aod John S. Brien. Tho tenor of a!l tho ppeeches was an carnest appeal to the doluded Tonnessoeans who etnbracod the cause of tbo rebels to return to loyalty to the Union. Tho evening meeting, was attcnded by Colunel Lewií D. Campbell, Hon. Jordán Stokes and others. Resohitions eUiogJurib tbat the hufoty and welfare of their relativea and iiienda in tho rubül army and prisons can only be assured by the return of Tennessee to tho Union ; that Congress bo appoaledto to end tho war; complimenting the Union oüicera and soldiera on their considérate conduct, and approvioffof Govcnior Johosoo's address of Miircsh 18, wore adopted by aoolamation. Thegreatest enthusiaam was manifested throughout tho entiro proceedings. Evcrytliinj hero beara an auspicious aspect for the Union cause.