There are two forms of published letters: those which were written privately, for an individual recipient, which have retrospectively been collected and published (e.g. Letters and journals of Lord Byron with notices of his life by Thomas Moore [London: Murray, 1830]); and those which have been deliberately written for public consumption.
Pamphlets and tracts were a common form of publication by the Nineteenth Century because they could be printed and sold, or distributed on the streets, quite anonymously thus allowing the author to opine on censured or controversial subjects. They could be written pseudonymously (Letter to the Duke of Newcastle by Vindex [London: printed by Andrews, 1828]), the name of the author could be hidden behind initials (The crisis: being a letter to J.W. Denison, Esq., M.P., on the present calamitous state of the country by W.M. [London: printed by J.F. Dove, 1822]) or they could be completely unattributed (The contempt of the clergy considered: in a letter to a friend by an impartial hand [London: printed for R. Minors, 1739]).
Published letters in Special Collections can help researchers come to a better understanding of debates around such subjects as public finances, armed forces salaries, foreign affairs, health, slavery, marriage law, vegetarianism, and Catholicism.