The Roman Map of Britain Eiuden River Eye Water or River Esk, or Tuiden River Tweed?

Viuidin (R&C 261) next

    With a better form Eiuden(s) or Tuiden(s) (R&C 189), a place on the river, the reconstruction is easier. Here we have Ei-. the modern Eye, and -udens which must be from the root *ued 'wet', L. uvidus. Or Tuiden which agrees fairly well with Bede's Tuidi fluminus c.730, but conflicts with the name of Eildon Hill Coriono Toitarum.
    If this is the river that Eiudens takes its name from, then it should be the Esk of Inveresk.