The funeral of Capt. William SIMPSON occurred yesterday. Services held at the house and grave were conducted by Rev. A. MacDougall of Calvin Church. The pall bearers were Capt. CHISHOLM, Capt. THOMAS, Capt. BODIE, S. WESTON, Thomas REID, John J. WRIGHT. The last mentioned gentleman, who was formerly a resident of Saint John, but now of New York, afficiated as best man at the marriage of Capt. Simpson over a quarter of a century ago. The interment was in Rural Cemetery (Fernhill Cemetery)