Why is a private detective called a “private eye”?

In 1850, the Pinkerton Detective Agency opened in Chicago with the
slogan “We never sleep,” and its symbol was a large wide-open eye.
Pinkerton was very effective and criminals began calling the feared
operation “the eye.” Raymond Chandler and other fiction writers of
the 1930s and 1940s simply embellished the underworld expression by
introducing “private eye” as a description for any private investigator.