ATTEMPTED MURDER AND SUICIDE. -- On Tuesday week, a young man named George DAVIS, who is respectably connected, and who, it appears has for some time been paying his addresses to Miss Eliza Pearce BATTEN, residing with her father at Newfoundland-street, Bristol, narrowly escaped penetrating the murder of his sweetheart, and afterwards attempted the destruction of his own life.  In the course of the above evening, the young man DAVIS, called in as usual at the house of Miss BATTEN'S father.  They had sat together for some time in one of the apartments, when a quarrel ensued between them in consequence of some jealous feeling on the part of DAVIS.  After an altercation of some few minutes, his anger appeared to be raised to an ungovernable pitch, and, seizing hold of her, he drew a pistol from his pocket, and placing it against her chest, instantly discharged it, and immediately afterwards, on seeing her fall senseless, pulled out another pistol and discharged it at himself.  The young lady's father, hearing the report of fire-arms, rushed in.  Finding that his daughter was not dead, she was removed to a bedchamber, and medical aid sent for, when on undressing her it was discovered that providentially the pistol ball had struck against her steel busk, having passed through her clothes, and had then become flattened without having injured her person beyond a mere bruise of the chest.  In his case, also, the ball had, in the surgeon's opinion, from the pistol having been inefficiently charged with powder, failed in effecting its fatal purpose; and although it had passed through his trousers and shirt, had only slightly injured him.  The young man was immediately taken into custody, and in his pockets were found some bullets, percussion caps, and powder.  The two pistols were on the floor of the room; and Miss BATTEN, who had remained for some time insensible from fright, on her recovery, found that her steel busk had fortunately been the means of preserving her from a sudden and violent death.  -- London paper.