The book is about the Chinese coming to a ravaged USA and contemplating the fate of the nation. Most likely written in the 19th century, or very early 20th century.
This is a long shot, but could it be The Battle of the Wabash: A Letter From the Invisible Police? It is written as a "found manuscript" and tells how America is taken over by the Chinese. Published in The Californian, October 1880. The author is identified only as "Lorelle".