Rat-trap—O. Henry was married twice, once in his twenties (she died a few years after they were married) and again near the end of his life. Both marriages were somewhat stormy, and he often complained that marriage was too confining.
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muchacha—(Spanish) young girl
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seidlitz powder—a medication made by mixing powders of sodium potassium tartrate, sodium bicarbonate, and tartaric acid, used for its laxative effect or to treat hangovers
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Annie and Willie's prayer—probably refers to a poem by Sophia Snow called "Annie and Willie's Prayer" which parodies "'Twas the Night before Christmas":
"'Twas the night before Christmas, 'Goodnight,' had been said,
And Annie and Willie had crept into bed; . . ."