Fourth St. got its name because it is the fourth street from the Fox River.
From Morrow and Gillett's Appleton city directory, for 1889-90:
FOURTH, 401 Walnut, west to Story, sixth south of College av, numbers 960 to 1180.
In 1925 a new system of numbering structures in the city of Appleton was adopted. In this directory both the new and old street numbers are given. In addition, College Ave. was designated the dividing line between north and south, and Oneida St. was the east-west divider.
From Wright's Appleton city directory 1925:
FOURTH W - From 623 S Walnut w to S Bounds, 5 s W College av