The execution of Peter Dotselaere, for the murder of Catherine Sarah Jacobs, took place at the gaol yesterday morning. It will be remembered that the prisoner was convicted and sentenced to death at the last Criminal Sittings, for having on the night of the 28th of May, murdered a woman with whom he had for some time been living at a house in Latrobe-street east. It appeared that the deed was instigated by feelings of jealousy, arising from the fact that this woman was about to be married to some young man with whom she had become acquainted in the country. A petition was presented to the Executive on behalf of the prisoner, but after he was made acquainted with the decision, that the sentence passed upon him would be carried out, he awaited his fate with great apparent resignation. He was attended early yesterday morning by the Rev. D. Lordon, and the last duties of a spiritual attendant were performed by the Rev. Dr. Bleasdale, who was present at the time of execution. At the appointed hour (ten o’clock), the door of the prisoner’s cell was opened, and he was pinioned outside the cell by the executioner. During this operation, and while standing on the drop, he made no remark of any kind, seemed utterly passive, and his attention appeared to be totally absorbed in listening to the prayers which were recited by the clergy-man. He appeared very pale, but showed no other sign of emotion or fear. Life appeared to be extinct almost instantly after the fall of the drop. The formal inquest was held upon the remains in the afternoon; and the usual verdict returned. Dotselaere is entered in the gaol books as having arrived in the ship Suttleyoung in 1861. He is described as aged thirty-four years, a native of Belgium, a Roman Catholic, by calling a sailor. It appears that immediately after his arrival here, in February, 1861, he met with an accident on board the vessel in the bay, and received an injury to the leg, which necessitated his removal to the hospital. He remained there for eighteen months as a patient, and was afterwards employed as servant and bedmaker up to the time of the murder. He was regarded as a steady inoffensive man while he lived in the hospital, and nothing was known by the hospital authorities with reference to his conduct since he has been residing outside. This change took place in consequence of his having represented that he was about to be married.