Nicknames were prevalent in the age of letters. In fact, whole new dialects seem to be created by the aristocracy, such as the "Cavendish drawl" which the Devonshire House circle spoke in. each member of the circle seemed to have a nickname. Although some origins are obvious, others are quite perplexing. These nicknames were the usual form of address in casual letters, although we cannot be so sure how often they were used vocally.
Duchess of Devonshire Mrs. Rat
Duke of Devonshire Canis, due to his affection for dogs.
Lady Bess Foster Racky
Duchess de Polignac Little Po
Marie Antoinette, Mrs. B[rown], Louis was, of course, Mr. B
Richard Brinsley Sheridan Argus
Charles James Fox The Eyebrow, due to his enormous eyebrows
Lady Jersey The Infernal
Duke of Richmond Goodwin
Prince of Wales Prinny
Charles, Earl Grey Black
Duke of Dorset Pride
Frederick, Viscount Duncannon (Harriet's husband) Harum, due to his love of pranks
Bess had her own unique nickname with the Spencers: the Chief Councellor.