Light studied the problem, but didn't solve it in his 1917 [dissertation][1].
A [1920 note][2] of Light was followed by a [1921 note][3] of Franklin showing the  existence of infinitely many classes of examples not covered by Light, and pointing out that Puiseux had shown this in 1844. However, the question of determining all of them isn't addressed there, and I don't know what else is known.


  [1]: http://books.google.com/books?id=EtTNAAAAMAAJ&pg=PA18#v=onepage&q&f=false
  [2]: http://www.jstor.org/stable/2972254
  [3]: http://www.jstor.org/stable/2972285