***** NOT A TEACHER *****
(1) VIP Member Soup's link was really helpful and insightful in answering
your great question.
(2) I then was given the idea to ask "Professor Google."
(3) I found these quaint examples:
(a) Whereas a good understanding and friendly intercourse between the subjects of her Imperial Majesty the Empress of all the Russias and these United States may be for the mutual advantage of both nations.
Source: An American document from December 15, 1780. It is necessary to remember, however, that in 1780, we were not operating under our present Constitution. Before General Washington became the first president in 1789, our country was truly a collection of independent states.
(b) Humanly speaking, no circumstances can prevent these United States from becoming, eventually, and at no distant period, a great and powerful nation.
Source: a book written in 1818.
(c) And a 1870 book about American copyright laws refers to
books "within these United States."