In a medium saucepan, combine 2 cups of the water with 1 cup of the sugar.
Bring them to a boil over low heat, stirring until the sugar melts. Turn the
heat up and cook over medium-high heat for 5 minutes, or until the syrup begins
to thicken slightly.
Stir in the remaining 3 cups of water with the lemon rind and the juice.
Remove the pan from the heat.
In a food processor or blender, puree the blackberries and blueberries and
add them to the syrup. Let the mixture cool to room temperature and set it aside
for 1 hour.
Strain well into a large pitcher to remove the seeds and skins from the
berries. Chill until ready to serve.