Not every woman can play the mirror part in the cotillon with both grace and coquetry. Isobel Mostyn did it with distinction; the man wiped off her mirror seemed "to taste delicious death," and be executed with tragic pomp; and even "that Jacob Hildenheim" appeared less blatantly common than usual after being blotted off the glass.
- page 162, Maxwell Gray, The Great Refusal, D. Appleton and Company, 1906
A cotillon (from the French cotillon, "petticoat", but often Anglicised as cotillion) was a mixed-sex social dance that comprised a series of fairly complicated 'figures' (set dances) - fortunately a dance director talked the participants through the moves - that I suppose acted as a kind of speed dating. Some figures were danced with everyone, but others featured choosing rituals giving plenty of opportunity to express a preference for a particular partner. The heyday of cotillons lasted from the late 1700s into the beginning of the 20th century, the form varying somewhat according to the fashionable dances of the time; William B De Garmo's The Prompter: containing full descriptions of all the quadrilles, figures of the German cotillon, etc. has a typical description (see page 51 onward).
Maxwell Gray wasn't the only one to refer to the mysterious "cotillon mirror". In Robert Smythe Hichens's 1898 The Londoners, there's this passage:
Lying there alone, Mrs. Verulam said to herself that she was utterly sick of this concert, which each succeeding year persistently encored. She heard the distant wheels, and thought of the parties to which they were rolling. She heard the very remote music of a band; and that reminded her of the quantities of cotillons she had led, and of the innumerable faces of men that she had wiped out of mirrors with her lace handkerchief. How curiously they flashed and faded on the calm surface of the imperturbable glass, their eyes full of gay or of languid inquiry, their mouths gleaming in set society smiles!
Was it a property of cotillon mirrors, she wondered, to make all men look alike, neat, vacuous, self-satisfied?
- Robert Smythe Hichens, The Londoners, 1898
'For myself,' he added, 'I shall be delighted when the faces of no aspirants are reflected in your cotillion mirror. I detest all those men.'
- Ouida (Marie Louise De la Ramée), Othmar, 1885
A spot of further Googling finds the explanation: this is one of the 'choosing ritual' figures of the cotillon, and a number of other fictional accounts give a full explanation of the mirror scenario.
Meanwhile the cotillon was going on rapidly. A chair had been placed in the middle of the circle, a young lady was placed in it, and a little looking-glass was put into her hands. One by one the gentlemen were brought up behind her chair. She turned the glass upon them, and if the face reflected in it pleased her, she rose and danced with its owner, if not, she passed her handkerchief across the mirror.
- page 46, Behind the Scenes in Paris: A tale of the clubs and the secret police, Titan magazine, 1858
And in more detail, a passage that shows it was a two-way process; if the man didn't want to be chosen, he could always gurn in the mirror:
A chair was placed in the centre of the room, and every one polked round the room, till some one couple polked up to the chair, and the lady was left seated there, and was given a hand-mirror. (Fred said it looked as though the lady were going to dress her hair, and he called her the lady in the enchanted chair, in Comb-us, and said that we were the rabble rout—which was quite true, for we made a great noise, and were very disorderly). Of course the other couples ceased dancing when the lady was placed in the chair. Her partner then went and brought up another gentleman, and placed him behind the chair; and the lady looked in the mirror; and, if she pretended that she did not like the reflection, she rubbed her handkerchief over the glass. Her partner had then to bring up another gentleman; and, if she rubbed him out, a third gentleman had to be brought; and so on, until she was quite satisfied. And, when she saw in the mirror the reflection of any one she approved, she jumped up, and the favoured individual took her as his partner, and polked off with her—her late partner seeking out the other gentleman's partner, and all the company polking on round the room, until some one else was seated in the chair, and then the whole affair was da capo.
When Madge was seated in the chair, she pretended to be very difficult to please; and she had—oh! at least a dozen gentlemen brought up to her; and sometimes, after carefully examining the reflection, she would rub away at the glass as though she violently hated the man, and would not have him on any account; and, perhaps, the gentleman was making faces in the glass, and doing all kinds of ridiculous things. Hyacinth Brown kept on rubbing out people until dear Walter was led up behind her chair, and then she very quickly put down the mirror, and danced off with him, looking as pleased as—yes, as Punch!
- page 283, Love's Provocations, Cuthbert Bede, in Hogg's Instructor, 1854
There were hundreds of cotillon figures, but this one - perhaps as it's such a vivid metaphor for showing a character's feelings about a choice of partner, or to indicate that a character had a large choice of suitors - seems to have particularly appealed to novelists.
(The passage by Cuthbert Bede - the pseudonym of Edward Bradley - is the first time I've ever seen the verb "to polk" = to dance a polka. It's in the OED as "colloq. (now rare)").