Couldn't be parked: Ngaio Marsh

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However, the question arises from the last lines of the final chapter:

"Do you think he really knows Davidson did the murder?"

"I think we shall find that Davidson tried to warn him against collecting Evelyn Carrados's bag at the ball. Davidson saw Bunchy was with Evelyn, when Bridget returned her bag the first time."

"You didn't tell me about that."

Alleyn told her about it.

"And isn't that really all?" he asked.

"Yes. That's all."

"Troy, I love you more than anything in life. I've tried humility; God knows, I am humble. And I've tried effrontery. If you can't love me, tell me so, and please let us not meet again because I can't manage meeting you unless it is to love you."

Troy raised a white face and looked solemnly at him.

"I know my mind at last," she said. "I couldn't be parked."

"Darling, darling Troy."

"I do love you. Very much indeed."

"Wonder of the world!" cried Alleyn, and took her in his arms.

It's pretty clear from this exchange that Troy is turning down Alleyn's proposal, despite her professed love for him. Though Allen has been in turn "humble" and rather less so (his "effrontery") she can only "solemnly" look with her pallid face after he lays his feelings out quite plainly. Also, by looking back from the final lines a bit further over the entire conversation, Troy's mood is stylistically evoked by her terse answers and brief questions that contrast to Alleyn's rather garrulous paragraphs.

Though the phrase "I couldn't be parked" might seem a bit murky - and perhaps Marsh intended it to be interpretable - in context it refers to her not wanting to settle down. Idiomatically, she can't be "parked" in one space for the rest of her life.

(N.B. There are, universally, only seven google search returns for "I couldn't be parked" - and all the others besides this refer to the experience of actually parking in a car.)

In the supplied quote, Alleyn makes no proposal of marriage. He confesses his love and asks Troy if she loves him. So all this talk about marriage seems hasty.

The compact OED says one definition of "park" is to put something aside in a convenient place, to be reclaimed when needed, as in "Park your valise in the corner." It's been a while since I read this book, so I don't recall if the effrontery Alleyn alludes to was his exclusion of Troy from his activities, in effect parking her, thus angering her and causing her to behave in a way that suggested to Alleyn that she could not love him. If so, her saying "I couldn't be parked" could be her explanation to him of that behavior. I.e., "If it seemed I couldn't love you, that is why."

Having read Artists in Crime and Death in a White Tie and the passage in question several times, I think “I couldn’t be parked” means the same as “I couldn’t be STAYED,” as in,

I could not be stayed from loving you, despite my fright.

It fits the context best.