After Kaiser's death in 1872, it was the astronomer Jean Abraham Chrétien Oudemans (1827-1906), director of the Utrecht Observatory, who took a great effort in updating the books and presented them as the fourth edition.
For book I it was indeed the fourth edition (after 1844, 1847 and 1860), but for book II it was actually not the fourth, but the the third edition (after 1845 and 1853).
According to the title page, book I was published in 1884 and book II in 1888.
However, although the preface of book I was written on August 12, 1884, in the book on several page a reference is made to the year 1890.
Book I was published in parts from 1882 to 1884 and later binded. I guess the binded copies became available in 1889.
The preface of book II was written on June 8, 1889.
The planisphere which is referred to in book II and that was actually published in earlier editions is missing in every copy of the book that I have seen (and I have seen many).
This binding is a luxuary binding in brown with silver and gold; 'ordinary' bindings were red (most common), green (less common) or blue (rare).