Final answer:
The question asks about a discovery by Mr. Mayherne regarding a character named Romain, but the provided text does not contain these characters. It seems there might be confusion or a mix-up with the text provided and the question asked.
Step-by-step explanation:
It appears there is some confusion in the question you provided. The characters Mr. Mayherne and Romain do not correspond to the excerpts you've shared, which seem to be concerned with literature involving different characters and plots, such as Daisy Miller by Henry James and discussion of Mrs. Hale and Mrs. Peters, which may pertain to the play 'Trifles' by Susan Glaspell.
Since Mr. Mayherne and Romain do not appear in the provided excerpts, it may be difficult to answer the question regarding how Mr. Mayherne discovers that the woman in Shaw's rent is actually Romain.
However, if you provide the correct text or context referring to Mr. Mayherne and Romain, I could certainly help with that analysis.
For now, based on the provided excerpts, we can delve into the characters of Daisy Miller and Mrs. Hale to discuss their personalities, choices, and the consequences therein, as well as any overarching themes portrayed through their stories.