In the 19th Century, authors were still using what is considered "King James" English -- that is, old English. The use of the pronouns thee and thou in the place of the word "you" was not uncommon, and it was equally not uncommon to see other language used that today we consider obsolete (ye, thy, forsooth, etc.).
Granted, plenty of American authors had strayed from the old English spellings and usages during this same era, but if an author felt the need to give a piece a more formal tone, the use of King James English was not unusual.
One must understand that with time, dialect and common language change. "Thee" and "thou" were accepted pronouns in the 19th century much the way we use "you" today. Whose to say in the next 100 years there won't be some other word to replace it. Slang is a very good indicator of this. Think of the word "booty-licious" that is now in the OED(Oxford English Dictionary) and its commonplace in language today. Language ebbs and flows and in respect to "thee" and "thou", they ebbed out while "you" flowed in!!
@Enqtchr Actually... Old English was a very 'germanic' type of language from before the Norman Conquest.
Thee and Thou, Thy are examples of Middle English pronouns. Middle English faded away in the 15th century, but Thee and Thou survived through into Early Modern English and were exchangable with the mordern forms you, your. They died out in the 17th centruy.
The King James Bible was written in Early Modern English. I am not aware of such a thing as 'King James English'.