A dogwatch is half as long as a regular one. it is "cur-tailed".
"Dear Word Detective: I'm reading a Patrick O'Brian novel about the Royal Navy during the
Napoleonic Wars and was wondering about the actual origin of the term "dog watch."
According to O'Brian's characters it's called the "dog watch" because it's "cur-tailed." This of
course brings to mind the phrase "that dog won't hunt." I'm sure there is a terribly close
relationship between the Royal Navy and your average hillbilly just waiting to be revealed. --
Stuart Zimmerman, via the internet."