One of the great shocks and scandals of the Regency period was the introduction of the waltz. It become popular in Vienna in the 1780s, but didn’t make its first appearance in England until 1810.
And it wasn’t met with a warm reception.
Considered indecent and disreputable, even by the ‘fast’ set of Regency society, it became the subject of diatribes and caricatures. It wasn’t until later in the period, after the Napoleonic Wars, that it became more generally acceptable. Princess Lieven acted as something like an ambassador of respectability, and smoothed its introduction into polite company. The strict Lady Patronesses of Almack’s (perhaps not coincidentally, Princess Lieven can be counted among them) eventually allowed it to be danced in their esteemed Assembly Rooms.
And while respectability and acceptability are difficult to down, by the time Emma was published in 1815, Jane Austen must have considered it suitable enough if one of her heroines was dancing it.