Captain Smith and myself left the city on Thursday, in the twelve o’clock train of the Long Shore Railroad, for Stonington and Providence. The same afternoon we arrived at Stonington, and went on board the Stonington boat Commonwealth, to make inquiries for a sailor man, his wife, and child. The boat arrived that morning about two o’clock, and of course our only chance of getting trace of the murderer was from the officers of the boat. We heard of several women and children, but they did not answer the description; so we waited until nine o’clock that night, when Mr. Howard, the baggage-master, arrived in the Boston night train. He gave us information of two or three different women who stopped on the route between Stonington and Boston. The description of one man, woman, and child, who stopped at Canton, Massachusetts, was so near, that on the arrival of the boat from New York, at two o’clock on Friday morning, we left in the train which carried forward her passengers. On arriving at Canton, however, we found that the woman was not the one we were in search of, so we immediately returned to Providence, being satisfied that the murderer could not have taken the Stonington route. In Providence we called upon Mr. George Billings, detective officer, who, with several other officers, cheerfully rendered us every assistance. We drove around the city to all the sailor boarding-houses, and to all the railroad depots, questioning baggage-masters and every one likely to give us information, but could get no satisfactory clew, so we concluded they had probably come by the Fall River route, and Captain Smith went down to the steamboat Bradford Durfee, to make inquiry there. The deck hand remembered that on the previous morning a sailor and a little sore-eyed woman and child came up with them, and asked him if he knew any quiet boarding-house, in a retired part of the city, where he could go for a few weeks. He told him he did not, but referred him to a hackman, who took him off to a distant part of the city. The hackman was soon found, and at once recollected the circumstances, and where he had taken the party. It was then arranged, to guard against accidents, that the hackman should go into the house, and inquire of the landlady if this man was in, pretending that two of the three quarter dollars which he had given him were counterfeit. He went there, and the landlady told him that the man was not in, but would be in that night. Arrangements were then made for a descent upon the house at two o’clock on Saturday morning. At this hour I knocked at the door, and at first the landlady did not seem inclined to let me in. I told her I was an officer who had arrested the hackman for passing counterfeit quarters, and as he had stated that he got them from the sailor, I had come to satisfy myself of the truth of the story. She opened the door, and we went up to this man’s room, some seven or eight of us, and found him in bed, apparently asleep.