A despatch was received here Monday announcing the death of Capt. Gregory at sea. He was on his way from the coast of Chili, which he left the first week in March for New York in the ship "Burnham Wood". He was nearing New York Friday morn. last when he was lost overboard. The vessel arrived at anchor on Sunday. The 'Globe' says the ship was under the command of first officer SPENCE. He reported that on June 18, at seven o'clock in the morn., Capt. Gregory had disappeared. He was seen only a few minutes before and a sailor looking astern saw the captain's hat floating on the water. Nothing was seen of the captain. The crew was wearing ship at the time and it is surmised that the captain was struck by some of the rigging. Capt. GREGORY was born in Fredericton 14th Nov. 1837. He was the second son of late John GREGORY, Esq. and brother of Geo. F. GREGORY of this city. He has been thirty years at sea and this he intended to be his last voyage. He has been in continual command of vessels for 26 years. The "Burnham Wood" is owned by his brother Chas. C. GREGORY, Alex SHIVES and the captain himself. He had been in delicate health for two or three years. He leaves a widow and six children, three sons and three daughters who reside in this city on George St. His eldest son, Charles GREGORY was with him on the ship and expected home the latter part of the week. Chas. C. Gregory of Antigonish, N.S. went to New York immediately on receipt of the sad news.