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”All right, she told herself. So, I’ve killed him. It was extraordinary, now, how clear her mind became all of a sudden. She began thinking very fast. As the wife of a detective, she knew quite well what the punishment would be. That was fine. It made no difference to her. "
At this moment, it was obvious that Mary's mind became clear and thinking quickly after telling herself to kill him. This also shows that Mary's mind was blurred before killing her husband. At that time, she made this decision impulsively and did not realize that this weapon would kill her husband.

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I think this is Manskaughter, “At that point, Mary Maloney simply walked up behind him and without any pause she swung the big frozen leg of lamb high in the air and brought it down as hard as she could on the back of his head. She might just as well have hit him with a steel club.

She stepped back, waiting, and the funny thing was that he remained standing there for at least four or five seconds, gently swaying. Then he crashed to the carpet.”
In this paragraph, Mary's mental state has become abnormal. She did not think about the consequences of what she did. It was a reckless act, and she did not mean to kill him.

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Her first instinct was not to believe any of it, to reject it all.  She thought that perhaps he hadn’t even spoken, that she had imagined the whole thing.  Maybe, if she acted as though she hadn’t been listening, then later, when she sort of woke up again, she might find none of it had ever happened.

Mary doesn't want to kill her her husband, and she would like to stop  talk from is husband. So, she uses a leg of lamp to tamp his head, and this means that is she just has plan to hurt his husband, but she doesn't want this hurt to influence in his life. And she already pregnant for 6 month, she cannot leave his husband now. Totally, she doesn't have reasons that why she wants to kill her husband.

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At that point, Mary Maloney simply walked up behind him and without any pause she swung the big frozen leg of lamb high in the air and brought it down as hard as she could on the back of his head.
Mary is not hesitant to hit, which means she knows what she's doing and understands what the consequences are. Her purpose is clear enough. In terms of what constitutes first-degree murder, she fits the bill.

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"She peacefully bent over her sewing. This was her sixth month expecting a child. Her mouth and her eyes, with their new placid look, seemed larger and darker than before.“
”Her first instinct was not to believe any of it, to reject it all.  She thought that perhaps he hadn’t even spoken, that she had imagined the whole thing.  Maybe, if she acted as though she hadn’t been listening, then later, when she sort of woke up again, she might find none of it had ever happened.“
‘And in the other room, Mary Maloney began to giggle. ’‘
I think this is manslaughter. First of all, she didn't have a clear plan, because before she learned that her husband was cheating, she was still in a calm mood. She only killed people after she learned that her husband was cheating. Secondly, her mental state is abnormal. She was too impulsive after she learned the news. Killing someone with emotional agitation is definitely not murder. In the end, she may suffer from mental illness in the article. From the perspective of the law and the judge, this does not constitute a murder, and she may be released without charge.

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''At that point, Mary Maloney simply walked up behind him and without any pause she swung the big frozen leg of lamb high in the air and brought it down as hard as she could on the back of his head. She might just as well have hit him with a steel club.'' And ‘’All right, she told herself. So, I’ve killed him.‘’
You can see without hesitation in the passage and in the following passage that she intended to kill her husband.
Steve... it looks like this is evidence for first or second degree murder, not manslaughter!  Mary wants to kill him, It is NOT an accident.

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“‘I’ll get the supper,’ she whispered. When she walked across the room, she couldn’t feel her feet touching the floor.  She couldn’t feel anything at all- except a slight nausea and a desire to vomit.  She did everything without thinking. She went downstairs to the freezer and took hold of the first object she found. She lifted it out and looked at it. It was wrapped in paper, so she took off the paper and looked at again --- a leg of lamb.”
At this moment, Mary's head was blank, and the fact that she can't accept had already made her on the verge of collapse. When she took out the leg of lamb, I believe she didn't want to kill her husband with it, but when she saw her husband, she is out of control.

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The violence of the crash, the noise, the small table overturning helped bring her out of the shock. She came out slowly, feeling cold and surprised, and she stood for a while, blinking at the body, still holding the piece of meat tight with both hands.
Mary's shock after killing her husband suggests that she may not have intended to kill him. So this could be second-degree murder.

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"She carried it upstairs, holding the thin bone-end of it with both her hands, and as she went through the living-room, she saw him standing over by the window with his back to her, and she stopped."
As Mary went upstairs, instead of going to the kitchen, Mary stopped in the living room. Plus she did not hold the meat in a  normal way, she  held it with two hands line a club.