Great KAoW Nothing Demonstration-Funeral of William Poole.New York. March 12.—The funeral procession of William Poole, better known as “Bill Poole,” which took place yesterday (Sunday) far surpased any thing witnessed in this city for many years. The procession extended three miles, made up mainly of citizens on foot, marching form six to ten abreast. There were also one hundred carriages in attendance. Broadway, along which the procesion passed, was lined on both sides with a dense mass of people, and every standing place or position from whence the procession could be viewed to advantage, was eagerly sought after. The excitement before and after the funeral was intense.— The procession was beaded by Dod-worth’s brass band, composed of 50 musicians. The various Chaplains of the United American Societies, were out in full force. The coffin was shrouded in the American flag, and the words of the deceased, “I die a true American,”were printed in largebold letters on the hearse. The re-« mains were taken to Greenwood for interment,