Clouds of Witness continued

Duke of D.: “I ran into my bedroom, which has a window over the conservatory, and shouted out to him not to be a silly fool.
A conservatory is a greenhouse, usually attached to a dwelling, for growing and displaying plants.

It was pourin' with rain and beastly cold. He didn't come back, so I told Fleming to leave the conservatory door open—in case he thought better of it—and went to bed.”

The Coroner: “What explanation can you suggest for Cathcart's behaviour?”

Duke of D.: “None, I was simply staggered. But I think he must somehow have got wind of the letter, and knew the game was up.”
“Knew the game was up” has been in use for over 400 years. Shakespeare coined it:
From Shakespeare's Cymbeline, 1611:

Euriphile, Thou wast their nurse; they took thee for their mother,
And every day do honour to her grave:
Myself, Belarius, that am Morgan call'd,
They take for natural father. The game is up.

The Coroner: “Did you mention the matter to anybody else?”

Duke of D.: “No. It wasn't pleasant, and I thought I'd better leave it till the morning.”

The Coroner: “So you did nothing further in the matter?”

Duke of D.: “No. I didn't want to go out huntin' for the fellow. I was too angry. Besides, I thought he'd change his mind before long—it was a brute of a night and he'd only a dinner-jacket.”
Black tie is a dress code for evening events and social functions. For a man, the main component is a usually-black jacket, known as a dinner jacket (in the Commonwealth) or tuxedo (mainly in the United States). Women's dress for black tie occasions can vary to a much greater extent, ranging from a cocktail dress that is at or below the knee to a long gown, determined by current fashion, local custom, and the occasion's time.

The Coroner: “Then you just went quietly to bed and never saw deceased again?”

Duke of D.: “Not till I fell over him outside the conservatory at three in the morning.”

The Coroner: “Ah yes. Now can you tell us how you came to be out of doors at that time?”

Duke of D. (hesitating): “I didn't sleep well. I went out for a stroll.”

The Coroner: “At three o'clock in the morning?”

Duke of D.: “Yes.” With sudden inspiration: “You see, my wife's away.” (Laughter and some remarks from the back of the room.)

The Coroner: “Silence, please ... You mean to say that you got up at that hour of an October night to take a walk in the garden in the pouring rain?”

Duke of D.: “Yes, just a stroll.” (Laughter.)

The Coroner: “At what time did you leave your bedroom?”

Duke of D.: “Oh—oh, about half-past two, I should think.”

The Coroner: “Which way did you go out?”

Duke of D.: “By the conservatory door.”

The Coroner: “The body was not there when you went out?”

Duke of D.: “Oh no!”

The Coroner: “Or you would have seen it?”

Duke of D.: “Lord, yes! I'd have had to walk over it.”

The Coroner: “Exactly where did you go?”

Duke of D. (vaguely): “Oh, just round about.”

The Coroner: “You heard no shot?”

Duke of D.: “No.”

The Coroner: “Did you go far away from the conservatory door and the shrubbery?”

Duke of D.: “Well—I was some way away. Perhaps that's why I didn't hear anything. It must have been.”

The Coroner: “Were you as much as a quarter of a mile away?”

Duke of D.: “I should think I was—oh yes, quite!”

The Coroner: “More than a quarter of a mile away?”

Duke of D.: “Possibly. I walked about briskly because it was cold.”

The Coroner: “In which direction?”